individual course description...kadıoğlu e. kamali m.-genel matematik,robert a.adams-calculus,...

INDIVIDUAL COURSE DESCRIPTION

Course Unit Title ABSTRACT MATHEMATİCS I

Course Unit Code MAT 103

Type of Course Unit COMPULSORY

Level of Course Unit FİRST CYCLE

Number of ECTS Credits Allocated 5

Theoretical (hour/week) 3

Practice (hour/week) -

Laboratory (hour/week) -

Year of Study 1

Semester when the course unit is

delivered 1

Name of Lecturer

Mode of Delivery FACE TO FACE

Language of Instruction TURKISH

Prerequisities and co-requisities NONE

Recommended Optional

Programme Components NONE

Work Placement NONE

Objectives of the Course Give the language of mathematics and basic concepts.

Learning Outcomes

1.Understanding the logic of preposition

2.Comprehension the methods of proof

3.Recognise the sets

4.Investigation the functions

5.Learning the relation concept

Course Contents Prepositions ,quantitatives , prof methods ,sets , relations ,equation and order relation ,functions

, process,introduction to algebraic structures

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS

Theoretical Courses Teaching & Learning Methods

1 Logic of propositions Telling and explenation

2 Quantitatives Telling and explenation

3 Proof methods Telling and explenation

4 Sets Telling and explenation

5 Midterm exam

6 Relation Telling and explenation

7 Identical relation Telling-explenation and question-answer

8 Equation and order relation Telling and explenation

9 Functions Telling and explenation

10 Midterm exam

11 Sets algebra Telling and explenation

12 Process Telling and explenation

13 Introduction to algebraic structures Telling and explenation

14 Difference of two sets Telling-explenation and question-answer

15 Final exam

Recommended or

Required Reading

1.Soyut Matematik, S.Akkaş, H.H.Hacısalihoğlu Z.Özel, A.Sabuncuoğlu, Gazi Üniversitesi Yayınları,

1984

2.Bridge to Abstract Mathematic, Ronald P. Morash, New York, Random Hauuse, Birkhauser, 1987

3.Discrete and Combinatorial Mathematics, Ralph P.Grimaldi, Addison-Wesley,New York 2000

Assesements

Term (or year) Learning

Activities Quantity Weigh %

Assignment 1 10

Project

Presentation/ Preparing

Seminar

Mid-terms 2 90

Total 100

Contribution of Term (Year) Learning Activities to Success

Grade 50

Contribution of Final Exam to Success Grade 50

TOTAL 100

Planned Learning Activities, Teaching Methods, Evaluation Methods and Student Workload

Activities Quantity Duration

(hour) Total Work Load (hour)

Course Duration (Including the exam week:

16xtotal course hours) 15 2 30

Hours for of-the-classroom study (Pre-study,

practice, literature survey, reading) 15 4 60

Assignments 1 12 12

Project

Presentation/ Preparing Seminar

Field study(Internships/Clinical

Study/Laboratory/Trip and Observation)

Mid-terms 2 8 16

Final examination 1 10 10

Total Work Load 34 36 128

Total Work Load / 30 (h) - - 4.26

ECTS Credit of the Course - - 5

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME OUTCOMES

Learning

Outcomes

Programme Outcomes

PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10

LO1 5 5 4 4 5 4 4

LO2 5 5 4 4 5 4 4

LO3 5 5 4 4 5 4 4

LO4 5 5 4 4 5 4 4

LO5 5 5 4 4 5 4 4

Contribution Level: 1 Very Low 2 Low 3 Medium 4 High 5 Very High


Course Unit Title ANALYSİS I








Year of Study 1


delivered 1

Name of Lecturer


Language of Instruction TURKİSH




Work Placement NONE

Objectives of the Course To teach the concept of function and to detailed examine the concept of limit,continuity and

derivative for the single variable function

Learning Outcomes

1.Recognition the number systems

2.To comprehension properties of absolute value and full value

3.To solve the inequality

4.To explain the concept of function

5.To identify the specific functions

6.To comprehension the limit and contunuity

7.To answer the question “what is the derivative

8.To solve the undefined cases by aid of derivative

Course Contents

Numbers,absolute value,full value,inequalities.The concept of functions,some specific

functions.Some practical drawings.Trigonometric functions.İnverse trigonometric

functions.Exponential and logarithmic functions.Hyperbolic functions.The concept of

derivative.General rules of differential.Derivative of trigonometric and inverse trigonometric

function.Drawings of curve.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1

Numbers(Naturel

numbers,İntegers,Rational and irrational

numbers,Real and Complex numbers)

Telling and explanation

2 Absolute value and full value Telling and explanation

3 İnequalities and the concept of functions Telling and explanation

4 Some specific functions Telling-explanation and Question-Answer

5 Midterm exam

6 Some easy graph drawings Telling and explanation

7 Trigonometric and inverse trigonometric

functions Telling and explanation

8 Exponential,logarithmic and hyperbolic

functions Telling and explanation

9 The concept of derivative and general rules

of differential Telling and explanation

10 Middterm exam

11

The geometric interpretation of derivative

and the derivative of exponential and

logarithmic functions

Telling-explanation and Question-Answer

12 Derivatives of trigonometric and inverse

trigonometric functions Telling and explanation

13 Drawings of curve Telling and explanation

14 Undefined cases Telling and explanation

15 Final exam

Recommended or

Required Reading

Kadıoğlu E. Kamali M.-Genel Matematik,Robert A.Adams-Calculus, Balcı M.- Matematik Analiz

Assesements



Assignment 2 20

Project -


Seminar -

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 5 11 55

Project




Mid-terms 2 20 40






Learning

Outcomes

Programme Outcomes


LO1 5 5 5 5 4 3

LO2 5 5 5 5 4 3

LO3 4 4 4 4 4 3

LO4 5 5 5 4 4 3

LO5 4 4 4 4 4 3

LO6 4 5 5 4 4 3

LO7 5 5 5 4 4 3

LO8 5 5 5 4 4 3



Course Unit Title ANALYTICAL GEOMETRY I






Practice (hour/week) NONE

Laboratory (hour/week) NONE

Year of Study 2


delivered 3

Name of Lecturer RESEARCH ASSİSTANTS OF MATHEMATİC DEPARTMENT






Work Placement NONE

Objectives of the Course To give the fundamental concept of Analytical geometry and to provide the using of this

cource´s subjects first of all in geometry and the other cources.

Learning Outcomes

1)He/She is able to interpret passing from synthetic geometry to analytical geometry

2)He/She is able to define different coordinate systems

3)He/She is able to use the detailed knowledge related to vectors

4)He/She is able to calculate passing formulations from one to other coordinate systems which

are Euclidean, cylindrical , spherical and toroidal coordinate systems,

5)He/She is able to analyse the translations and rotations on plane geometry

6)He/She is able to do the applications of vector algebra on line and plane on space

7)He/She is able to calculate reflections with respect to a plane and a line

8)He/She is able to use conics

Course Contents

Vectors, vector spaces,the inner products of vectors, inner product spaces, vectorial product and

the scalar triple product, coordinate frames and coordinate systems, affine coordinates,

cylindrical and spherical coordinate systems, translations and rotations on the plane, the

applications of vector algebra, the line and plane on space, conics

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Vectors, affine coordinate systems on the

plane, vector spaces [1] Pages 1-16

2 Inner product and inner product spaces, the

Hess form of the line [1] Pages 22-32

3 Inner product space, orthonormal vector

systems [1] Pages 33-56

4 Vectorial product, the scalar triple product,

Lagrange identity [1] Pages 57-65

5 First exam

6 Affine space, affine frame, changing of the

affine coordinate systems [1] Pages 69-81

7

Euclidean space, Euclidean frame,

cylindrical , spherical and toroidal

coordinate systems

[1] Pages 81-98

8 Translations and rotations on the plane

geometry [1] Pages 98-108

9 The applications of vector algebra, line and

plane on space [1] Pages 132-139

10 Second exam

11 Line-plane relations, angle bisector planes,

the condition of two and three planes [1] Pages 139-146

12 The pencil of lines, the common point of

line and plane, intersection of two lines [1] Pages 146-151

13 Reflection with respect to a plane and a

line [1] Pages 151-161

14 Conics, sections of a conic and a line [1] Pages 161-165

15 Final exam

16

Recommended or

Required Reading

[1]Prof. Dr. H. Hilmi HACISALİHOĞLU,"2 ve 3 Boyutlu uzaylarda Analitik Geometri", altıncı baskı,

Ankara, 2003.

[2]Prof. Dr. Rüstem Kaya," Analitik Geometri", beşinci baskı, Eskişehir, 2003.

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50

Contribution of Final Exam to Success Grade %50

TOTAL 100








Assignments 1 5 5

Project - - -

Presentation/ Preparing Seminar - - -


Study/Laboratory/Trip and Observation) - - -

Mid-terms 2 7,5 15


Total Work Load - - 95

Total Work Load / 30 (h) - - 3,16



Learning

Outcomes

Programme Outcomes


LO1 3 3

LO2 3 3

LO3 3 3

LO4 3 3

LO5 3 3

LO6 3 3

LO7 3 3

LO8 3 3



Course Unit Title INTRODUCTİON TO COMPUTER






Practice (hour/week) 2


Year of Study 1


delivered 1

Name of Lecturer






Work Placement NONE

Objectives of the Course Teaching use of computer at a university level and teaching IT operation and programmings

will become necessary at profession lives with the high level applications .

Learning Outcomes

1.Understanding the basic concepts

2.Comprehension the units of computer

3.Learning the software and hardware

4.Comprehension the properties of processors

5.Using the Word with the high level

Course Contents

Information technology,Basic concepts

Organization of computer,Computers,Units of entry-exit

Softwsre of computer,Concept of software,Computer programming

Processor systems,Types of processor,Basic fuctions of processor systems,Use of processor

system

Word processors-General properties and using the Word processors

Process tables-Properties and using the Process tables

Word-Properties and using the Word

Wee

kly

Det

ail

ed

Cou

rse

Co

nte

nts

Week

TOPICS


1 Basic concepts Telling-explanation and application

2 Organization of computer Telling-explanation and application

3 Units of computer Telling-explanation and application

4 Software and hardware Telling-explanation and application

5 Midterm exam

6 Processor systems Telling-explanation and application

7 Using the processor systems Telling-explanation and application

8 Word processors Telling-explanation and application

9 Process tables and using the Process tables Telling-explanation and application

10 Midterm exam

11 Introduction the Word Telling-explanation and application

12 Basic information of Word Telling-explanation and application

13 Document preparation in the Word Telling-explanation and application

14 Advanced Word informations Telling-explanation and application

15 Final exam

Recommended or Lecture notes

Required Reading

Assesements



Assignment 2 20

Project


Seminar

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 2 10 20

Project




Mid-terms 2 12 24



Total Work Load / 30 (h) - - 6



Learning

Outcomes

Programme Outcomes


LO1 5 4 4 5 4 3 4 4

LO2 5 4 4 5 4 3 4 4

LO3 5 4 4 5 4 3 4 4

LO4 5 4 4 5 4 3 4 4

LO5 5 4 4 5 4 3 4 4



Course Unit Title PHYSISCS I

Course Unit Code F 101







Year of Study 1


delivered 1

Name of Lecturer






Work Placement NONE

Objectives of the Course To have students gained the background for static and dynamics.

Learning Outcomes

1) Explains measurement and the fundamental unit systems

2) Analyzes the static, kinematic and dynamic processes.

3) Applies these processes to mathematics in general.

4) Makes solutions to the problems related to static, kinematic and dynamic processes.

5) Proposes new models for the static, kinematic and dynamic systems

6) Aplies the fundamental laws of physics to mechanics systems

Course Contents

Physics and measurement, Motion in one dimention, Vectors, Motion in two dimension, Rules

of Motion, Circular Motion, Work and Kinetic Energy, Potantiel Energy and Conservation of

Mechanical Energy, Linear Momentum and Collisions, Rotation of a Rigid Body around an

axis. Rolling Objects and Angular Momentum, Static Equilibrium and a Rigid Body, Gravity

Oscillation and Waves.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Unit Systems [1] Pages 1-16

2 Vectors [1] Pages 22-32

3 One Dimensional Motion [1] Pages 33-56

4 Two Dimensional Motion [1] Pages 57-65

5 First exam

6 Newton?s Laws of Motion [1] Pages 69-81

7 Applications of Newton?s Laws of Motion [1] Pages 81-98

8 The Newton?s Law of Universal

Gravitation [1] Pages 98-108

9 Work and Energy [1] Pages 132-139

10 Second exam

11 Conversation of Energy [1] Pages 139-146

12 Momentum and Motion of Systems [1] Pages 146-151

13 Statical Equilibrium of Rigid Bodies [1] Pages 151-161

14 Angular Momentum and Rotation [1] Pages 161-165

15 Final exam

16

Recommended or

Required Reading

[1] Y.Güney, İ.Okur, Fizik-I (Mekanik), Değişim Yayınları, 2009, Sakarya [2]Prof. Dr. Rüstem Kaya,"

Analitik Geometri", beşinci baskı, Eskişehir, 2003.

[2] Keller, F. J., ?Fizik 1?, çev. Ed. Akyüz R.Ö. ve arkadaşları, Literatür Yayınevi, 2002, İstanbul

[3] Serway, ?Fen ve Mühendislik İçin Fizik? Palme Yayıncıcılık, Çev.Edit. Kemal Çolakoğlu, 2002,

Ankara

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 1 15 15

Project - - -




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1 3 5 3

LO2 3 4 3

LO3 3 3 3

LO4 3 3

LO5 3 3

LO6 3 3

LO7 3 3

LO8 3 4 3



Course Unit Title TURKISH LANGUAGE AND LİTERATE I

Course Unit Code TD 101







Year of Study 1


delivered 1

Name of Lecturer






Work Placement NONE

Objectives of the Course Express the structural properties and wealth of Turkish language.

Learning Outcomes

1.Perception the concept of language

2.Comprehension the structure of Turkish

3.Detected learning Turkish grammar

4.Understanding the word and sentence structure

5. Speaking firely and effectine

Course Contents

Language, languages and Turkish language

Grammar,word and sentence

Types of word

Types and elements of expression,Main idea and auxiliary ideas

Subject and subject types,explanation ,discussion,description,narration

Diction

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Language Telling and explenation

2 Languages and Turkish language Telling and explenation

3 Grammar Telling and explenation

4 Word structure Telling and explenation

5 Midterm exam

6 Sentence structure Telling and explenation

7 Word types Telling and explenation

8 Expression elements Telling and explenation

9 Main idea and auxiliary ideas Telling and explenation

10 Midterm exam

11 Subject and subject types Telling and explenation

12 Explenation and discussion Telling and explenation

13 Description and narration Telling and explenation

14 Diction Telling and explenation

15 Final exam

Recommended or

Required Reading

Lecture notes

Assesements



Assignment

Project


Seminar

Mid-terms 1 100

Total 100


Grade 50


TOTAL 100








Assignments

Project




Mid-terms 2 4 8






Learning

Outcomes

Programme Outcomes


LO1 4 5 5

LO2 4 5 5

LO3 4 5 5

LO4 4 5 5

LO5 4 5 5



Course Unit Title ABSTRACT MATHEMATİCS II








Year of Study 1


delivered 2

Name of Lecturer






Work Placement NONE

Objectives of the Course Make up for number systems by the sets theory

Learning Outcomes

1.Understanding the equivalent and equal set concepts

2.Comprehension the natural numbers

3.Apply the method of induction

4. Comprehension the integers

5. Comprehension the rational , real and complex numbers

Course Contents

Equivalent sets

Definition of the natural numbers

Operation and ordering in the natural numbers

Induction method

Integer sets

Operation and ordering in the integers

Rational and real numbers

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Mathematical structures Telling and explanation

2 Group,ring and field Telling and explanation

3 Vector spaces ,Equivalent sets Telling and explanation

4 Creation of the natural numbers Telling and explanation

5 Midterm exam

6 Operation and ordering in the natural

numbers Telling-explanation and Question-answer

7 Induction method Telling and explanation

8 Integer sets Telling and explanation

9 Operation and ordering in the integers Telling-explanation and Question-answer

10 Midterm exam

11 Rational numbers Telling and explanation

12 Real numbers Telling and explanation

13 Complex numbers Telling and explanation

14 Sum and product symbol Telling and explanation

15 Final exam

Recommended or

Required Reading

Lecture notes,

Soyut Matematik, S.Akkaş, H.H.Hacısalihoğlu Z.Özel, A.Sabuncuoğlu, Gazi Üniversitesi Yayınları,

1984

Bridge to Abstract Mathematic, Ronald P. Morash, New York, Random Hauuse, Birkhauser, 1987

Discrete and Combinatorial Mathematics, Ralph P.Grimaldi, Addison-Wesley,New York 2000

Assesements



Assignment 1 10

Project


Seminar

Mid-terms 2 90

Total 100


Grade 50


TOTAL 100








Assignments 1 12 12

Project




Mid-terms 2 8 16






Learning

Outcomes

Programme Outcomes


LO1 5 5 4 4 5 4 4

LO2 5 5 4 4 5 4 4

LO3 5 5 4 4 5 4 4

LO4 5 5 4 4 5 4 4

LO5 5 5 4 4 5 4 4



Course Unit Title ANALYSİS II








Year of Study 1


delivered 2

Name of Lecturer






Work Placement NONE

Objectives of the Course Teaching the undefinite integral , definite integral , integral applications ,sequencess and series

fort he single variable functions

Learning Outcomes

1.Perception the differential concept

2.Comprehernsion the undefinite integral

3. Comprehernsion the definite integral

4.Making the field computation

5. Making the volum computation

6.Comprehension the sequences and series

Course Contents

Differential

Undefinite integral

Definite integral,The main theorem of the integral computation

Derivative of the integrals,The mean value theorem

Applications of the integrals(Field computation)

Computation the volume with the section method , Computation the volume with the disc

method , Computation the volume with the shell method

Generalized integrals (1. and 2. Type generalized integrals )

Sequences and series

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Differential Telling and explanation

2 Basic undefinite integrals Telling and explanation

3 The variable Exchange and partial

integration Telling and explanation

4 The integral of the rational functions Telling and explanation

5 Midterm exam

6 The integral of the trigonometric functions Telling and explanation

7 Definition of the definite integral Telling and explanation

8 Basic definite integrals Telling and explanation

9 Geometric interpretations Telling and explanation

10 Midterm exam

11 Field computation Telling and explanation

12 Volume computation Telling and explanation

13 Sequences Telling and explanation

14 Series Telling and explanation

15 Final exam

Recommended or

Required Reading

Ders notları,Genel Matematik-Ekrem Kadıoğlu,Calculus-Robert A.Adams

Assesements



Assignment 5 20

Project


Seminar

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 5 12 60

Project




Mid-terms 2 20 40






Learning

Outcomes

Programme Outcomes


LO1 5 5 5 5 4 3

LO2 5 5 5 5 4 3

LO3 4 4 4 4 4 3

LO4 5 5 5 4 4 3

LO5 4 4 4 4 4 3

LO6 4 5 5 4 4 3

LO7 5 5 5 4 4 3

LO8 5 5 5 4 4 3



Course Unit Title ANALYTICAL GEOMETRY II








Year of Study 2


delivered 4







Work Placement NONE

Objectives of the Course To give the fundamental concept of Analytical geometry and to provide the using of this

cource´s subjects first of all in geometry and the other cources.

Learning Outcomes

1)He/She is able to distinguishe the plane and space analytic geometry

2) He/She is able to use detailed knowledge related to conics

3) He/She is able to classify the conics

4) He/She is able to restate curves of line, circle and ellipse etc. with coordinates of point

5) He/She is able to calculate tangents of parabola, ellipse and hyperbola and circle

6) He/She is able to interpret the curves in space, circular helix and helix on the cone

7) He/She is able to classify revolving curves, ellipsoid, hyperboloid and ruled surfaces

8) He/She is able to debate the quadratic forms and quadratic surfaces

Course Contents

General second order surfaces on the plane,parallel translating the axis, rotating the axis,

elements of conics,second order surfaces, curves and surfaces in three dimensional space,helix,

cycloid, epicycloid,hypocycloid ,cardioid, ellipsoid, hyperboloid, ruled surfaces.General second

order surfaces on the plane, parallel translating the axis, rotating the axis, elements of conics,

second order surfaces, curves and surfaces in three dimensional space, helix, cycloid,

epicycloid, hypocycloid, cardioid, ellipsoid, hyperboloid, ruled surfaces.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Line coordinates, the equations with the

linear coordinates. [1] Pages 184-191

2 Point-Line duality, linear dependence,

duality in space. [1] Pages 191-202

3 Parabola, ellipse, hyperbola, circle, tangent

at conics [1] Pages 203-216

4 Tangent at ellipse and hyperbola, linear

equations of ellipse and hyperbola. [1] Pages 216-222

5 First exam

6

Conics with the same foci, confocal

parabolas, cycloid, vertex and diagonal at

conics

[1] Pages 222-230

7 General quadratic equations, pencil of

conics, center, diagonal, asymtot [1] Pages 231-265

8 Elements of conics, focus and directrix at

conics. [1] Pages 267-288

9 Curves in space,circular helix, helix on the

cone [1] Pages 289-303

10 Second exam

11 Cycloid curves, cardioid [1] Pages 305-315

12 Folium of Descartes, Cassini oval,

Lemniscate, sphere and cylinder surface [1] Pages 316-327

13 Cone, Rregression surface, torus [1] Pages 331-350

14 Quadratic forms and Quadratic surfaces [1] Pages 355-358

15 Final exam

16

Recommended or

Required Reading

[1] Prof. Dr. H. Hilmi Hacısalihoğlu, "2 ve 3 Boyutlu uzaylarda Analitik Geometri", Altıncı baskı,

Ankara, 2003.

[2] Prof. Dr. Rüstem Kaya, "Analitik Geometri", Beşinci baskı, Eskişehir, 2003.

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 1 %80

Total 100


Grade %50


TOTAL 100








Assignments 1 5 5

Project - - -




Mid-terms 2 7,5 15






Learning

Outcomes

Programme Outcomes


LO1 3 3

LO2 3 3

LO3 3 3

LO4 3 3

LO5 3 3

LO6 3 3

LO7 3 3

LO8 3 3



Course Unit Title INTRODUCTION TO COMPUTER II








Year of Study 1


delivered 2

Name of Lecturer






Work Placement NONE

Objectives of the Course Teaching use of computer at a university level and teaching IT operation and programmings

will become necessary at profession lives with the high level applications

Learning Outcomes

1.Prepare the presantation with the Powerpoint

2.Make various applications with the Excel

3. Make various applications with the Access

4.Recognition the Internet

5.Using the Internet effectively

Course Contents Prepare Powerpoint presantation , Excel applications , Access applications,Internet

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 What is the Powerpoint Telling-explanation and application

2 Recognition Powerpoint objects Telling-explanation and application

3 Recognition Powerpoint shortcuts Telling-explanation and application

4 Prepare starting Presantations With the

Powerpoint Telling-explanation and application

5 Midterm exam

6 Prepare effective presantation with the

Powerpoint Telling-explanation and application

7 What is the Excel Telling-explanation and application

8 Recognition Excel objects Telling-explanation and application

9 Prepare data with the Excel Telling-explanation and application

10 Midterm exam

11 Table generation paths with the Excel Telling-explanation and application

12 What is the Access Telling-explanation and application

13 Effective Access using Telling-explanation and application

14 Internet Telling-explanation and application

15 Final exam

Recommended or

Required Reading

Lecture notes

Assesements



Assignment 2 20

Project


Seminar

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 2 10 20

Project




Mid-terms 2 12 24






Learning

Outcomes

Programme Outcomes


LO1 5 4 4 5 4 3 4 4

LO2 5 4 4 5 4 3 4 4

LO3 5 4 4 5 4 3 4 4

LO4 5 4 4 5 4 3 4 4

LO5 5 4 4 5 4 3 4 4



Course Unit Title PHYSICS II

Course Unit Code F 102







Year of Study 1


delivered 1

Name of Lecturer






Work Placement NONE

Objectives of the Course To help students gain the fundamental knowledge of electricity and magnetism during their

education.

Learning Outcomes

1) Analyzes the electrical charge and being neutral

2) Analyzes the forces and electric fields produced by charged systems.

3) Determines the technological uses of the capacitors.

4) Makes analysis about the electrical current and conductivity..

5) Understands how magnetic forces and fields are produced.

6) Applies the electromagnetic induction, Faraday and Lenz law to electrical circuits.

7) Analyzes the alternating and direct current circuits.

Course Contents

Coulomb Force, Electric Field, Electric Flux, Gauss?s Law, Electrical Potential, Capacitors,

Current Formation and Resistor, Constant Current, Circuits of Direct Current, Kirchhoff?s

Laws, Magnetic Field, Biot-Savart?s Law, Induction, Faraday?s Law, Lenz?s Law, Inductance,

Energy in a Magnetic Field, Oscillations in an LC Circuit.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Coulomb?s Law and Electric Forces [1] Pages 1-16

2 Coulomb?s Law and Electric Forces [1] Pages 22-32

3 Electrical Potential [1] Pages 33-56

4 Capacity and Capacitors, Properties of

Dielectrics [1] Pages 57-65

5 First exam

6 Current and Resistor [1] Pages 69-81

7 Direct Current Cicuits [1] Pages 81-98

8 Electromagnetic Force [1] Pages 98-108

9 Magnetic Field Sources [1] Pages 132-139

10 Second exam

11 Faraday?s Law [1] Pages 139-146

12 Self Inductance and ? Mutual Inductance [1] Pages 146-151

13 Alternating Current (RL and RC) Circuits [1] Pages 151-161

14 Alternating Current (RLC) Circuits [1] Pages 161-165

15 Final exam

16

Recommended or

Required Reading

[1] Fen ve Mühendislik için Fizik II (Elektrik ve Manyetizma), R.A.Serway; Çeviri Editörü: Kemal

Çolakoğlu, (5. baskıdan çeviri), Palme Yay., 2002

[2] Fizik II (Elektrik), F.J.Keller, W.E.Gettys, M.J.Skove, Çeviri Editörü: R.Ömür Akyüz, Literatür Yay.,

2006

[3] Temel Fizik II (Fishbane, Gasiorowicz ve Thornton, 2. baskıdan çeviri; Çeviri Editörü: Cengiz Yalçın;

Arkadaş Yay., 2003

[4] Fizik İlkeleri 2 F.J. Bueche, D.A. Jerde, Çeviri Editörü: Kemal Çolakoğlu;(6. baskıdan çeviri), Palme

Yay., 2000

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 1 15 15

Project - - -




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1 3 5 3

LO2 3 4 3

LO3 3 3 3

LO4 3 3

LO5 3 3

LO6 3 3

LO7 3 3

LO8 3 4 3



Course Unit Title TURKISH LANGUAGE AND LİTERATE II

Course Unit Code TD 102







Year of Study 1


delivered 2

Name of Lecturer






Work Placement NONE

Objectives of the Course Express the subject of written expression in the dailylife. Comprehension the importance of

punctuation in the written expression.

Learning Outcomes

1.Using the written expression effectively

2. Using the verbal expression effectively

3.Using the punctuation marks

4.Comprehension the rules of orthography

5.Propose the solution for the language problems

Course Contents

Types of teaching manuscript

Types of the written expression and their properties

Verbal expression properties

Types of prepared speaking

Importance of the punctuation in the written expression

Punctuation Marks

Importance of the rules of orthography in the language

Usings of the rules of orthography

Suitable using with rules of the language in the special or formal attemts

Expression wrongs about words

Our language’s expression defects which are comes from affecting other language .

Solution of the this days language problems

Achievment in the verbal and written expression

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Types of teaching manuscript Telling and explanation

2 Types of the written expression and their

properties Telling and explanation

3 Verbal expression properties Telling and explanation

4 Importance of the punctuation in the

written expression Telling and explanation

5 Midterm exam

6 Punctuation Marks Telling and explanation

7 Importance of the rules of orthography in

the language Telling and explanation

8 Usings of the rules of orthography Telling and explanation

9 Suitable using with rules of the language in

the special or formal attemts Telling and explanation

10 Midterm exam

11 Expression wrongs about words Telling and explanation

12 Our language’s expression defects which

are comes from affecting other language Telling and explanation

13 Solution of the this days language

problems Telling and explanation

14 Achievment in the verbal and written

expression Telling and explanation

15 Final exam

Recommended or

Required Reading

Lecture notes

Assesements



Assignment

Project


Seminar

Mid-terms 2 100

Total 100


Grade 50


TOTAL 100








Assignments

Project




Mid-terms 2 4 8






Learning

Outcomes

Programme Outcomes


LO1 4 5 5

LO2 4 5 5

LO3 4 5 5

LO4 4 5 5

LO5 4 5 5



Course Unit Title ANALYSIS III








Year of Study 2


delivered 3




Prerequisities and co-requisities ANALYSIS I-II, LİNEAR ALGEBRA I-II



Work Placement NONE

Objectives of the Course

Many quantities can be regarded as depending on more than one variable, and thus to be

functions of more than one variable and functions of a single real variable that have vector

values. It is discussed that kind of functions in this course.

Learning Outcomes 1) He/She is able to recognize function of several variables.

2) He/She is able to recognize limit and continuity at the function of several variables.

3) He/She is able to recognize the total differential

4) He/She is able to calculate extremes values of a given function.

5) He/She is able to expand a given function to Taylor’s and Mac-Lauren’s series.

6) He/She is able to find out the partial derivative of implicit functions.

7) He/She is able to calculate the derivative in any given direction.

8) He/She is able to calculate the derivative of integrals dependent on a parameter.

Course Contents

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Functions of several variables [1] Pages 1-27

2 Limits and continuity [1] Pages 28-64

3 Partial derivatives, directional derivatives,

gradients [1] Pages 65-106;

4 Total increment and total differential [1] Pages 107-139

5 First exam

6 Approximation by total differentials [1] Pages 263-284

7 Taylor’s and Maclaurin’s formula [1] Pages 140-154

8 Extreme values for a function of several

variables [1] Pages 286-307

9 Applications of differential calculus to

solid geometry [1] Pages 311-320

10 Second exam

11 Rules for differentiating vector functions [1] Pages 320-329

12

Tangent and normal plane equation of a

curve, Tangent plane and normal equation

of a surface [1] Pages 330-338

13 Differentiating integrals dependent on a

parameter [1] Pages 387-436

14 The gamma function, Laplace

transformation [1] Pages 387-436

15 Final exam

16

Recommended or

Required Reading

[1] PISKUNOV, N., Differential and integral calculus, Vol. I, Translated from the Russian by George

YANKOVSK, Mir Publishers, MOSCOW, 1974.

[2] FLEMING, W.H., Functions of several variables, Addison-Wesley Publishing Company, INC.,

ATLANTA, 1965.

[3] WEBB, J.R.L., Functions of several variables, Ellis Harwood Limited, LONDON, 1991.

[4] ADAMS, R. A., Calculus: A complete course, Addison-Wesley Publishers Limited, CANADA, 1995.

Assesements



Assignment 5 %20

Project NONE NONE


Seminar NOEN NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 5 11 55

Project - - -




Mid-terms 2 20 40






Learning

Outcomes

Programme Outcomes


LO1 4 4 4 5 5 4

LO2 4 4 4 5 5 4

LO3 4 4 4 5 5 4

LO4 4 4 4 5 5 4

LO5 4 4 4 5 5 4

LO6 4 4 4 5 5 4

LO7 4 4 4 5 5 4

LO8 4 4 4 5 5 4



Course Unit Title DIFFERENTIAL EQUATIONS I



Level of Course Unit FIRST CYCLE

Number of ECTS Credits

Allocated 4




Year of Study 3


delivered 5

Name of Lecturer

Mode of Delivery (Face-To-Face,

Distance Learning) FACE-TO-FACE





Work Placement NONE

Objectives of the Course This lesson is planned for to solve equations involving derivative and to give applications.

Learning Outcomes

At the end of this course you will be able to:

1) Recognize differential equation

2) Classifie differential equations

3) Find equation which solution is known

4) Recognize and solve first order equation

5) Find a curve which cuts another curve

6) Recognize high order equation

7) Find a solution linear homogenous equation with constant coefficient

8) Find a solution linear nonhomogenous equation with constant coefficient

Course Contents

Definition of differential equation and basic information, Definition of differential equation and

basic information, Solving of differential equations, Geometrical explanation of the solutions of

differential equations, Initial and bounded value conditions, Initial and bounded value conditions

First order equations, First order equations, Picard iteration tecnique, Clairaut and lagrange

equations

Clairaut and lagrange equations, Second order equations with constant coefficient, D operator

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Definition of differential equation and

basic information Explaining Method, Questioning Method



3 Solving of differential equations Explaining Method, Questioning Method

4 Geometrical explanation of the solutions of

differential equations Explaining Method, Questioning Method

5 Mid-Term Exam

6 Initial and bounded value conditions Explaining Method, Questioning Method


8 First order equations Explaining Method, Questioning Method


10 Mid-Term Exam

11 Picard iteration tecnique Explaining Method, Questioning Method

12 Clairaut and lagrange equations Explaining Method, Questioning Method


14 Second order equations with constant

coefficient Explaining Method, Questioning Method

15 D operator Explaining Method, Questioning Method

16 Final Exam

Recommended or

Required Reading Lecture Notes

Assesements



Assignment 2 20

Mid-terms 2 80

Total 100

Contribution of Term (Year)

Learning Activities to Success

Grade

2 50

Contribution of Final Exam to

Success Grade 1 50

Total 100





16xtotal course hours)

15 3 45


practice, literature survey, reading)

15 3 45

Assignments 2 15 30

Project




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title FOREIGN LANGUAGE I








Year of Study 2


delivered 3

Name of Lecturer OKT. RECEP MUTLU SALMAN


Language of Instruction ENGLISH




Work Placement NONE


The aim of this course is;for undergratude student in B1 Level of English(European Language

Portfolio Global Scale), to have basic gramer, to understand oral production, to speak

interactively, to understand reading and to express themselves in written form for undergratude

students

Learning Outcomes

1) Having attended this course, He/She is able to have a sufficient level of English (European

Language Portfolio Global Scale, Level A2) for their field of study

2)He/She is able to understand short and clear messages,

3) He/She is able to understand short, daily passages,

4) He/She is able to communicate in simple, everyday situations,

5) He/She is able to talk about themselves and their environment in a simple language,

6) He/She is able to write short, simple notes and messages.

Course Contents

English grammar, vocabulary, reading comprehension, oral production and writing skills in

order to help students follow occupational English courses in next years and prepare them for

learning English further after university and in professional life

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1

Personal pronouns, Present Simple tense,

verb, to be, Verb to be, negative and

interrogative form

Lesson Book

2

Nouns : singular and plural, Possessive

adjectives, The indefinite article,

Prepositions

Lesson Book

3 Numbers, Questions with, what and how

old, Determiners Lesson Book

4 Countable uncountable nouns, Possessives Lesson Book

5 FIRST EXAM

6 Have got / has got, this , that, these, those Lesson Book

7 Simple Present Tense affirmative, Time

adverbials with S. Present Tense

8

Simple Present Tense negative,

interrogative, State verbs (love, hate),

Performative verbs

Lesson Book

9 Telling the time, Revision Lesson Book

10 SECOND EXAM

11 Gerunds Lesson Book

12 There is / there are, Prepositions (at, in,

under)

Lesson Book

13 Can and Can not, Ability, request,

permission

Lesson Book

14 Giving directions, Imperatives, Cardinal

numbers

Lesson Book

15 FINAL EXAM

16

Recommended or

Required Reading

Lesson Book

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 1 %80

Total 100


Grade %50


TOTAL 100








Assignments 1 5 5

Project - - -




Mid-terms 2 5 10






Learning

Outcomes

Programme Outcomes


LO1 4 4

LO2 4 4

LO3 4 4

LO4 4 4

LO5 4 4

LO6 4 4

LO7

LO8



Course Unit Title LİNEAR ALGEBRA I








Year of Study 2


delivered 3

Name of Lecturer RESEARCH ASSİSTANT OF MATHEMATİC DEPARTMENT






Work Placement NONE

Objectives of the Course The objective of this course is to give the fundamental knowledge of matrices and determinants,

introducing the equation systems and investigating the solutions of equation systems.

Learning Outcomes

1) He/She is able to understand the geometry of m dimensional real vector space and basic

concepts.

2)He/She is able to understand basic concepts

3) He/She is able to recognize the systems of linear equation and matrices.

4) He/She is able to solve a given linear equation system.

5) He/She is able to explain the properties of determinants.

6) He/She is able to apply matrices and determinants to a systems of linear equation.

7) He/She is able to understand the theory of the systems of linear equation

Course Contents Algebraic structures, Matrices, Determinants, Linear equation systems, Theory of linear

equation systems.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Algebraic structures

2 Algebraic structures

3 Matrices

4 Matrices

5 FİRST EXAM

6 Matrices

7 Determinants

8 Determinants

9 Determinants

10 SECOND EXAM

11 Linear equation systems

12 Linear equation systems

13 Theory of linear equation systems

14 Theory of linear equation systems

15 FİNAL EXAM

16

Recommended or

Required Reading

[1] Lenear Algebra and Geometry, D.M. Bloom, Cambridge Universty Press, London, 1979.

[2]Lineer Cebir, H.H.Hacısalihoğlu, Gazi Üniversitesi Yayınları, 1985

[3]Lineer Cebir, A.Sabuncuoğlu, Nobel Yayınları, Ankara, 2004

Assesements



Assignment 2 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 2 8 16

Project - - -




Mid-terms 2 5 10






Learning

Outcomes

Programme Outcomes


LO1 1 4 4 4 4

LO2 1 4 4 4 4

LO3 1 4 4 4 4

LO4 1 4 4 4 4

LO5 1 4 4 4 4

LO6 1 4 4 4 4

LO7 1 4 4 4 4

LO8



Course Unit Title PROBABILITY AND STATISTICAL I








Year of Study 2


delivered 3

Name of Lecturer RESEARCH ASSISTANT OHF MATHEMATİCAL DEPARTMENT



Prerequisities and co-requisities ANALYSIS I-II



Work Placement NONE

Objectives of the Course The aim of this course is to show notions, definations with respect to Probability and

Probability Theory and is to explain relations with events

Learning Outcomes

1) He/She is able to use the rules of probability

2) He/She is able to use random variables and their functions.

3) He/She is able to summarize expected value, Variance and moments.

4) He/She is able to restate distributions of random variables.

5) He/She is able to restate some important distributions.

6) He/She is able to define basic concepts of a process.

7) He/She is able to describe multivariable distributions and inference.

Course Contents

Combinatorial Analysis, Probability axioms, random variables and their functions, expected

value, momet and moment generating functions, distributions of change variables, investigating

of some discrete and constant distributions, multivariable distributions, covariance and

correlation

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Counting tecniques, permutation and

combination. [1] Pages 1-15

2 Repeated combination, combination

generating functions. [1] Pages 16-22

3

Introduction to probability, some rules of

probability, Independent events,

Conditional Probability, Bayes´ theorem.

[1] Pages 51-70

4

Random variables and distribution of a

random variable. Probability function and

distribution function.

[1] Pages 107-117

5 FIRST EXAM

6 Expected value, Variance and variational

coefficient. [1] Pages 118-122

7 Moments and moment generating funtions [1] Pages 126-135

8 Some discrete distributions [1] Pages 169-194

9 Introducing some important continuous

distributions [1] Pages 195-217

10 SECOND EXAM

11 Processes and Poisson process.

Multivariable distrubution. [1] Pages 223-227

12 Expected values and moments for

multivariable distrubutions. [1] Pages 239-247

13 Covariance and correlation. [1] Pages 248-261

14 Regression, Distributions for function of

random variables [1] Pages 262-270

15 FINAL EXAM

16

Recommended or

Required Reading

[1] Ö.Faruk GÖZÜKIZIL ve Metin Yaman, Olasılık Problemleri, Sakarya Kitabevi, 2005.

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 1 5 5

Project - - -




Mid-terms 2 7,5 15






Learning

Outcomes

Programme Outcomes


LO1 3 5 4 5

LO2 3 5 4 5

LO3 3 5 4 5

LO4 3 5 4 5

LO5 3 5 4 5

LO6 3 5 4 5

LO7 3 5 4 5

LO8



Course Unit Title INTRODUCTION TO TOPOLOGY I








Year of Study 2


delivered 3

Name of Lecturer RESEARCH ASSİATANT OF MATHEMATİC DEPARTMENT



Prerequisities and co-requisities ABSTRACT ALGEBRA I-II, ANALYSIS I-II



Work Placement NONE


The aim of this course is to give the fundamental concepts of general topology and the methods

of proof. Also, the other aim is to give information about metric and topological properties of

mathematical concepts in metric spaces that are important for the mathematics science.

Learning Outcomes

1) He/She is able to define the basic concepts of metric space,

2) He/She is able to decide whether arbitrary functions are metric or not,

3)He/She is able to proof basic theorems in metric spaces

4) He/She is able to define basic concepts of topology which are the bases of theoretical courses

5)He/She is able to decide whether giving structure is topology or not,on an arbitrary set

6)He/She is able to proof important theorems by using the properties of topological space

7)He/She is able to solve problems by using topology

8)He/She is able to develop the culture of mathematic by getting abstract thinking ability

Course Contents

Metric spaces, submetric spaces, isometries, Open and closed disks, spheres, diameters,

Topology of metric spaces, Sequences and continuity in metric spaces, Topological structure

and open sets in topological spaces closed sets and properties of the family of closed subsets in

topological spaces, neighborhoods of a point and fundamental systems of neighborhoods, Bases

and subbases of a topology, Continuity of functions in a topological space and

homeomorphisms, Sequences in the topological space and limit of a sequence, T2 spaces,

Subspaces, finite products of topological spaces.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Metric spaces, submetric spaces,

isometries [1] Pages 1-4

2 Open and closed disks, spheres, diameters [1] Pages 4-13

3 Topology of metric spaces [1] Pages 14-16

4 Sequences and continuity in metric spaces [1] Pages 17-33

5 FİRST EXAM

6

Topological structure and open sets in

topological spaces closed sets and

properties of the family of closed subsets

in topological spaces, neighborhoods of a

point and fundamental systems of

neighborhoods

[1] Pages 33-36

7 Bases and subbases of a topology [1] Pages 37-40

8 Systems of open neighborhoods [1] Pages 40-49

9 Equality of topologies and comparison of

topologies [1] Pages 50-51

10 SECOND EXAM

11 Contact and limit points of a set in the

topologic space [1] Pages 51-54

12 Interior point and interior of a set, closure

point and closure of a set [1] Pages 54-57

13

The frontier of a subset, dense, nowhere

dense, somewhere dense subsets of

topological spaces

[1] Pages 57-64

14 Continuity of functions in a topological

space and homeomorphisms [1] Pages 64-67

15 FINAL EXAM

16

Recommended or

Required Reading

[1] Gürkanlı A. Turan, Genel Topoloji, Samsun, 1993.

[2]Lipschutz, S., General Topology, Schaum Publishing Co., 1965

[3]Özdamar, E., Görgülü A., Alp, A., Genel topoloji, Uludağ Üni. Yayınları, 1999.

[4]Aslım, G., Genel topoloji, İzmir, Ege Üniversitesi, 1988

Assesements



Assignment 2 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 2 4 8

Project - - -




Mid-terms 2 10 20






Learning

Outcomes

Programme Outcomes


LO1 4 3 3 5

LO2 4 3 3 5

LO3 4 3 3 5

LO4 4 3 3 5

LO5 4 3 3 5

LO6 4 3 3 5

LO7 4 3 3 5

LO8 4 3 3 5



Course Unit Title CLASSICAL INEQUALITIES

Course Unit Code SMAT 203

Type of Course Unit OPTIONAL



Allocated 4




Year of Study 2


delivered 3

Name of Lecturer







Work Placement NONE

Objectives of the Course To introduce some classical inequalities arising in Mathematics and to apply these inequalities to

some problems

Learning Outcomes


1) He/She recognize classical inequalities.

3) He/She learn proof these inequalities.

4) He/She apply these inequalities to some problems.

5) He/She define Wirtinger type ineualities.

Course Contents Inequalities, Classical Inequalities, Maximum Problems, Applications

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Clasical inequalities Explaining Method, Questioning Method

2 Aritmatic-geometric mean inequality Explaining Method, Questioning Method

3 Cauchy-Shwarz inequality Explaining Method, Questioning Method

4 Holder?s and young?s inequalities Explaining Method, Questioning Method

5 Mid-Term Exam

6 Triangle inequality, minkowsky?s

inequality Explaining Method, Questioning Method

7 Maximum problems Explaining Method, Questioning Method

8 Dido problem, inverse problem, rich

american footballer Explaining Method, Questioning Method

9 Integral inequality Explaining Method, Questioning Method

10 Mid-Term Exam

11 Gronwal inequality Explaining Method, Questioning Method

12 Jensen inequality, logaritmic-convexity


13 Back Minkovsky?s inequality, hardy?s


14 Wirtinger type inequalities Explaining Method, Questioning Method

15 Sobolev inequalities Explaining Method, Questioning Method

16 Final Exam

Recommended or

Required Reading

Lecture Notes

[1] Korowkin, K.K., ?Inequalities?, T.M.D. yay. (çeviri) 1974.

[2] Beckenbach,E.F., Bellman, B., ?Introduction to Inequalities?, TMD yay. (çeviri) 1962.

Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



10 1 10

Assignments 1 10 10

Project - -

Presentation/ Preparing Seminar - -



- -

Mid-terms 2 7,5 15






Learning

Outcomes

Programme Outcomes


LO1 1 1 3 3 3

LO2 2 2 3 3 3

LO3 3 3 2 2 2

LO4 1 1 1 1 1

LO5 2 2 2 2 2

LO6 2 2 4 4 4

LO7 3 3 2 2 2

LO8 1 1 1 1 1



Course Unit Title MATHEMATICAL THINKING





Allocated 4




Year of Study 2


delivered 3

Name of Lecturer







Work Placement NONE

Objectives of the Course Construct a general culture about what matematic is.

Learning Outcomes


1) Have enough knowledge about mathematics’ historical development

2) Identify famous mathematicians and their working methods

3) Identify prof methods.

4) Identify achademic studying methods

5) have knowledge about education of mathematics and apply these.

Course Contents Historical development of mathematics, methods of mathematical thinking, instruments of

mathematics, theorems and methods of proving

W ee kly

De

tail

ed

Co

urs

e Co

nte

nts

Week TOPICS


1 Historical development of mathematics Explaining Method, Questioning Method

2 Historical development of mathematics Explaining Method, Questioning Method

3 methods of mathematical thinking Explaining Method, Questioning Method

4 methods of mathematical thinking Explaining Method, Questioning Method

5 Mid-Term Exam

6 Instruments of mathematics Explaining Method, Questioning Method

7 Instruments of mathematics Explaining Method, Questioning Method

8 Theorems and methods of proving Explaining Method, Questioning Method

9 Theorems and methods of proving Explaining Method, Questioning Method

10 Mid-Term Exam

11 Certainty in mathematics Explaining Method, Questioning Method

12 Certainty in mathematics Explaining Method, Questioning Method

13 Opinions about Fundamentals of

mathematics Explaining Method, Questioning Method

14 Opinions about Fundamentals of

mathematics Explaining Method, Questioning Method

15 Mathematics education Explaining Method, Questioning Method

16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 3 45

Assignments 1 10 10

Project - -




- -

Mid-terms 2 7,5 15






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title ANALYSIS IV








Year of Study 2


delivered 4




Prerequisities and co-requisities ANALYSIS I-II-III, LİNEAR ALGEBRA I-II



Work Placement NONE


It is extend the concept of definite integral to functions of several variables and functions of a

single real variable that have vector values. They are used to represent and calculate quantities

specified in terms of densities in regions of the plane or spaces of higher dimensions. Such

integrals are discussed in this course.

Learning Outcomes

1) He/She is able to strengthen culture of general mathematics.

2) He/She is able to make the construction of multiple integrals.

3) He/She is able to establishe a connection between with the double integral and the twofold

iterated integral.

4) He/She is able to evaluate double integral changing variables if necessary.

5) He/She is able to establishe a connection between the triple integral and the threefold iterated

integral.

6) He/She is able to evaluate triple integral changing variables if necessary.

7) He/She is able to understand the concepts of line integrals and surface integrals.

8) He/She is able to evaluate the line integrals and surface integrals.

Course Contents

Introduction to double integrals, Calculating double integrals, Change of variables in a double

integral, Applications of double integrals, Triple integrals, Applications of triple integrals,

Change of variables in a triple integral, Line integrals, Surface integrals, Applications of surface

integrals, The divergence theorem, Green’s Theorem and Stokes’s Theorem, Applications of the

divergence theorem, Green’s Theorem and Stokes Theorem.

Wee

kly

Det

ai

led

Cou

r

se

Con

t

ents

Week TOPICS


1 Introduction to double integrals [1] Pages 158-161

2 Calculating double integrals [1] Pages 161-166

3 Change of variables in a double integral [1] Pages 166-172

4 Applications of double integrals [1] Pages 172-187

5 FİRST EXAM

6 Triple integrals [1] Pages 197-200

7 Change of variables of triple integral [1] Pages 200-204

8 Applications of triple integral [1] Pages 204-209

9 Curvilinear integrals [1] Pages 216-225

10 SECOND EXAM

11 Curvilinear integrals, Green’s Theorem

and its applications [1] Pages 225-232

12 Surface integrals [1] Pages 232-236

13 The applications of surface integrals [1] Pages 232-236

14 Divergence Theorem and Stokes Theorem [1] Pages 236-244

15 FİNAL EXAM

16

Recommended or

Required Reading

[1] PISKUNOV, N., Differential and integral calculus, Vol. II, Translated from the Russian by George


[2] FLEMING, W.H., Functions of several variables, Addison-Wesley Publishing Company, INC.,

ATLANTA, 1965.

[3] WEBB, J.R.L., Functions of several variables, Ellis Harwood Limited, LONDON, 1991.

[4] ADAMS, R. A., Calculus: A complete course, Addison-Wesley Publishers Limited, CANADA, 1995.

[5] PISKUNOV, N., Differential and integral calculus, Vol. I, Translated from the Russian by George


Assesements



Assignment 5 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 5 11 55

Project - - -




Mid-terms 2 20 40






Learning

Outcomes

Programme Outcomes


LO1 4 4 4 5 5 4

LO2 4 4 4 5 5 4

LO3 4 4 4 5 5 4

LO4 4 4 4 5 5 4

LO5 4 4 4 5 5 4

LO6 4 4 4 5 5 4

LO7 4 4 4 5 5 4

LO8 4 4 4 5 5 4



Course Unit Title DIFFERENTIAL EQUATIONS II





Allocated 4




Year of Study 3


delivered 6

Name of Lecturer







Work Placement NONE

Objectives of the Course This lesson is planned for to solve equations involving derivative and to give applications.

Learning Outcomes


1) Recognize and solves equations with variable coefficient

2) Recognize and solves eigenvalue problems

3) Know the feature of Sturm Liouville problem

4) Solve some nonlinear equations

5) Solve equations using convergent series

6) Know Laplace transform

7) Solve equation use Laplace transform

Course Contents

Definition of differential equation and basic information, Definition of differential equation and

basic information, Solving of differential equations, Geometrical explanation of the solutions of

differential equations, Initial and bounded value conditions, Initial and bounded value conditions

First order equations, First order equations, Picard iteration tecnique, Clairaut and lagrange

equations

Clairaut and lagrange equations, Second order equations with constant coefficient, D operator

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS






3 Solving of differential equations Explaining Method, Questioning Method

4 Geometrical explanation of the solutions of

differential equations Explaining Method, Questioning Method

5 Mid-Term Exam





10 Mid-Term Exam

11 Picard iteration tecnique Explaining Method, Questioning Method



14 Second order equations with constant

coefficient Explaining Method, Questioning Method

15 D operator Explaining Method, Questioning Method

16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 3 45

Assignments 2 15 30

Project




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title FOREIGN LANGUAGE II

Course Unit Code FL 202







Year of Study 2


delivered 4

Name of Lecturer OKT. RECEP MUTLU SALMAN






Work Placement NONE


The aim of this course is;for undergratude student in B1 Level of English(European Language

Portfolio Global Scale), to have basic gramer, to understand oral production, to speak

interactively, to understand reading and to express themselves in written form for undergratude

students

Learning Outcomes

1) Having attended this course, He/She is able to have a sufficient level of English (European

Language Portfolio Global Scale, Level B1) for following their field of study and

communicating with their colleagues

2) He/She is able to speak regarding everyday life

3)He/She is able to travel abroad where English is spoken

4) He/She is able to explain thoughts ,plans and wishes of him/her

5) He/She is able to write short personal letters describing experiences and impressions.

6) He/She is able to understand conversation in school, job and similar places

7) He/She is able to understand texts regarding job and including favorites words

Course Contents

English grammar, vocabulary, reading comprehension, oral production and writing skills in

order to help students follow occupational English courses in next years and prepare them for

learning English further after university and in professional life.

Wee

kly

Det

ail

ed

Cou

rse

Con

ten

ts

Week

TOPICS


1

Present Continuous Affirmative, Present

Continuous negative and question form,

Time adverbials with Present Continuous

Lesson Book

2

Adjectives (before and after nouns),

Adjectives after pronouns, Verb +

adjective d. Modifying verb + adjective

Lesson Book

3 Stative and dynamic adjectives, ed and ing

adjectives

Lesson Book

4 Adverbs (fast, quickly), Adverbs of

manner, place and time

Lesson Book

5 FIRST EXAM

6 Simple Past tense affirmative, Time

adverbials with Simple Past tense

Lesson Book

7 Regular and irregular verbs, Time clauses

with the Simple Past Tense

Lesson Book

8 Comparatives and superlatives, Regular

adjectives

Lesson Book

9 Comparatives and superlatives, Irregular

adjectives

Lesson Book

10 SECOND EXAM

11 Present Perfect affirmative, Time

Adverbials

Lesson Book

12

Present Perfect in use (experience,

accomplishment), for, since; still, yet, ever,

never, since, just, already e. Present

Perfect Continuous

Lesson Book

13 Revision Lesson Book

14 Simple Future, will / be going to,Past

Continuous, Time Adverbials

Lesson Book

15 FINAL EXAM

16

Recommended or

Required Reading

Lesson Book

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 1 %80

Total 100


Grade %50


TOTAL 100








Assignments 1 5 5

Project - - -




Mid-terms 2 5 10






Learning

Outcomes

Programme Outcomes


LO1 5 5

LO2 5 5

LO3 5 5

LO4 5 5

LO5 5 5

LO6 5 5

LO7

LO8



Course Unit Title LİNEAR ALGEBRA II








Year of Study 2


delivered 4

Name of Lecturer RESEARCH ASSİSTANT OF MATHEMATİC DEPARTMENT






Work Placement NONE


The objective of this course is to find structures of several spaces and linear equation between

these spaces by using vector spaces. İnterpretting the problems producing an idea and attaining

an ability of solving for problems.

Learning Outcomes

1) He/She is able to learn construction of linear space.

2) He/She is able to learn the concept of linear independence and linear dependence.

3) He/She is able to learn concepts of basis and dimension.

4) He/She is able to comprehend the linear transformations.

5) He/She is able to relate linear spaces with the concept of linear transformations.

6) He/She is able to get the information about eigen values and eigen vectors

7) He/She is able to realize the construction of inner product .

Course Contents Vector spaces, Linear transformations, Eigen values, Eigen vectors, Diagonalization, Inner

product spaces, Dual spaces and Aygen spaces

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Eigen values

2 Eigen values

3 Eigen vectors

4 Eigen vectors

5 FİRST EXAM

6 Diagonalization

7 Diagonalization

8 Vector spaces

9 Vector spaces

10 SECOND EXAM

11 Linear transformations

12 Linear transformations

13 Inner product spaces

14 Inner product spaces

15 FINAL EXAM

16

Recommended or

Required Reading

[1] Lenear Algebra and Geometry, D.M. Bloom, Cambridge Universty Press, London, 1979.

[2]Lineer Cebir, H.H.Hacısalihoğlu, Gazi Üniversitesi Yayınları, 1985

[3]Lineer Cebir, A.Sabuncuoğlu, Nobel Yayınları, Ankara, 2004

Assesements



Assignment 2 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 2 8 16

Project - - -




Mid-terms 2 5 10






Learning

Outcomes

Programme Outcomes


LO1 1 4 4 4 4

LO2 1 4 4 4 4

LO3 1 4 4 4 4

LO4 1 4 4 4 4

LO5 1 4 4 4 4

LO6 1 4 4 4 4

LO7 1 4 4 4 4

LO8



Course Unit Title PROBABILITY AND STATISTICAL II








Year of Study 2


delivered 4

Name of Lecturer RESEARCH ASSISTANT OHF MATHEMATİCAL DEPARTMENT



Prerequisities and co-requisities ANALYSIS I-II, PROBABILTY AND STATICTICAL I



Work Placement NONE


The aim of this course is to introduce the concept of sampling and to present some distributions

theoretical results and point estimation and interval estimation that are engendered by sampling,

to introduce the subject of the tests of hypotheses which are important problems in statistics and

to give simple regression and correlation.

Learning Outcomes

1) He/She is able to consolidate basic probability culture.

2) He/She is able to classify datas

3) He/She is able to realize measures of centered tendency and variation.

4) He/She is able to realize the concept of point estimation

5) He/She is able to demonstrate interval estimation for any parameter.

6) He/She is able to explain first and second type of error.

7) He/She is able to design hypotheses tests for various parameters.

8) He/She is able to explain differences between independence and goodness of fitting.

Course Contents

Basic concepts and terminology, Classify and analysis of datas, Measures of centered tendency

and variation, Sampling and sampling distributions, Mean of sampling, variance of sampling

and their properties, Point and interval estimations of parameters, Statistical inference, Variety

of hypothesis and first and second type of error, Testing basic hypotheses, Parametric

hypotheses testing, Nonparametric hypotheses testing; test of independence, homogeneity and

goodness of fitting.

Wee

kly

Det

ail

ed

Cou

rse

Con

ten

ts

Week

TOPICS


1 Basic concepts and terminology [1] Pages 270-278

2 Organization and analysis of data [1] Pages 270-278

3 Measures of centered tendency and

variation [1] Pages 279-297

4 Sampling and sampling distributions [1] Pages 313-323

5 FIRST EXAM

6 Mean of sampling, variance of sampling

and their properties [1] Pages 313-323

7 Point and interval estimations of

parameters [1] Pages 324-358

8 Interval estimations of parameters [1] Pages 324-358

9 Testing basic hypotheses, first and second

type of error [1] Pages 363-368

10 SECOND EXAM

11 Hypotheses test for mass mean with

normal distribution [1] Pages 369-380

12 Comparing confidence interval with testing

hypotheses [1] Pages 380-384

13 Testing hypotheses for mass variance with

normal distribution and Binom parameter [1] Pages 385-398

14 Choosing sampling size for testing means [1] Pages 399-406

15 FINAL EXAM

16

Recommended or

Required Reading

[1] Akdeniz, F., Olasılık ve İstatistik, , Adana,Doğa Matbaacılık, 2000 (Ders Kitabı)

[2] Ersoy, N., Erbaş, SO, Olasılık ve İstatistiğe Giriş, 5. Baskı, Gazi Büro Kitabevi, Ankara, 2005.

[3] DeGroot, MH, Schervish, MJ, Probability and Statistics, 3rd Ed., P. Addison Wesley, 2004

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 1 5 5

Project - - -




Mid-terms 2 7,5 15






Learning

Outcomes

Programme Outcomes


LO1 3 5 4 5

LO2 3 5 4 5

LO3 3 5 4 5

LO4 3 5 4 5

LO5 3 5 4 5

LO6 3 5 4 5

LO7 3 5 4 5

LO8



Course Unit Title INTRODUCTION TO TOPOLOGY II








Year of Study 2


delivered 4




Prerequisities and co-requisities INTRODUCTION TO TOPOLOGY I



Work Placement NONE


The aim of this course is to give the fundamental concepts of topology and the methods of

proof. Besides, the other aims are to discuss the advanced topological concepts, to discover the

relations between topology and the other disciplines and to learn topics about compact spaces,

local compact spaces, connected spaces, separation axioms convergence, countability.

Learning Outcomes

1) He/She is able to define compactness in topologic space,

2) He/She is able to compare the compactness in classical analysis with compactness in

topologic space,

3) He/She is able to prove fundamental theorems in compact topologic space,

4) He/She is able to define countable compactness and sequentially compactness,

5) He/She is able to prove the theorems related to countable compactness and sequentially

compactness,

6) He/She is able to define the concepts of the connected spaces,

7) He/She is able to solve the problems by the aid of the concepts of the connected spaces

8) He/She is able to classify topologic spaces,

Course Contents Compact spaces, local compact spaces, sequentially compactness, countable compactness,

connected spaces, separation axioms, convergence, countability.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Compact topological spaces [1] Pages 89-107

2 Local compact spaces [1] Pages 107-109

3 Compactness [1] Pages 109-112

4 Countable compactness, sequentially

compactness [1] Pages 112-120

5 FIRST EXAM

6 Connected spaces [1] Pages 120-126

7 Connectedness on the reel line, some

applications of connected spaces [1] Pages 126-131

8 Local connected spaces [1] Pages 131-139

9 Separation Axioms,T0-spaces, T1-spaces [1] Pages 139-143

10 SECOND EXAM

11 Regular spaces and T3-spaces [1] Pages 143-145

12 Normal spaces and T4-spaces [1] Pages 145-152

13 Urysohn Lemma, Tietze Extension

Theorem [1] Pages 152-157

14 Convergence, nets, subnets, convergence

of nets [1] Pages 157-170

15 FINAL EXAM

16

Recommended or 1] Gürkanlı A. Turan, Genel Topoloji, Samsun, 1993. [1] Gürkanlı A. Turan, Genel Topoloji, Samsun, 1993.

Required Reading

[2] Lipschutz, S., General Topology, Schaum Publishing Co., 1965

[3] Özdamar, E., Görgülü A., Alp, A., Genel topoloji, Uludağ Üni. Yayınları, 1999.

[4] Aslım, G., Genel topoloji, İzmir, Ege Üniversitesi, 1988




Assesements



Assignment 2 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 2 4 8

Project - - -




Mid-terms 2 10 20






Learning

Outcomes

Programme Outcomes


LO1 4 3 3 5

LO2 4 3 3 5

LO3 4 3 3 5

LO4 4 3 3 5

LO5 4 3 3 5

LO6 4 3 3 5

LO7 4 3 3 5

LO8 4 3 3 5



Course Unit Title FIELD EXTENSIONS





Allocated 4




Year of Study 2


delivered 4

Name of Lecturer







Work Placement NONE

Objectives of the Course To teach algebraic integer numbers ring which is an extension of integer numbers ring

Learning Outcomes


1) Apply concepts about vectoral spaces.

2) Understand linear transformations

3) Identify field extensions and apply them.

4) Understand …….. fields

5) Understand algebraic integer numbers ring.

6) Comprehend quadratic number fields.

Course Contents

Vectoral spaces, Base of the vector space, Linear transformations, Field extensions

Algebraic and transandant numbers, Degree of extension, Algebraic extensions, Prime tests in

polynomials, Algebraic integer number fields, Algebraic integer number fields, Norm and

discrimnant, Bases, Quadratic number fields

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts Week

TOPICS


1 Vectoral spaces Explaining Method, Questioning Method

2 Base of the vector space Explaining Method, Questioning Method

3 Linear transformations Explaining Method, Questioning Method

4 Field extensions Explaining Method, Questioning Method

5 Mid-Term Exam

6 Algebraic and transandant numbers Explaining Method, Questioning Method

7 Degree of extension Explaining Method, Questioning Method

8 Algebraic extensions Explaining Method, Questioning Method

9 Prime tests in polynomials Explaining Method, Questioning Method

10 Mid-Term Exam

11 Algebraic integer number fields Explaining Method, Questioning Method

12 Algebraic integer number fields Explaining Method, Questioning Method

13 Norm and discrimnant Explaining Method, Questioning Method

14 Bases Explaining Method, Questioning Method

15 Quadratic number fields Explaining Method, Questioning Method

16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






1 10 10



Assignments

Project




Mid-terms

Final examination 2 7,5 15



ECTS Credit of the Course - - 4.33


Learning

Outcomes Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title OPTIMIZATION





Allocated 4




Year of Study 2


delivered 4

Name of Lecturer







Work Placement NONE

Objectives of the Course The aim of this lesson is to investigate the optimization theory.

Learning Outcomes


1) He/she describe the methods of optimization research.

2) He/she describe the linear programming problem.

3) He/she constitues the form of the linear programming problem

4) He/she investigates solutions of the linear programming problem

5) He/she check optimum of the solutions

6) He/she investigate optimum solutions

7) He/she investigate constitue of mathematic problem and solutions.

Course Contents

Mathematical operations research models

Construction of the LP model

Graphical LP solution

Graphical sensitivity analysis

Analytic solution

Determination of the feasible solution space

Analysis of selected LP models

The simplex method

The simplex algorithm

Special cases in simplex method application

Duality and sensitivity analysis

Economic interpretation of duality

Dual simplex method

Primal- dual computations

Wee

kly

Det

ail

ed

Co

urs

e

Con

ten

ts

Week

TOPICS


1 The methods of optimization research Explaining Method, Questioning Method

2 The methods of optimization research Explaining Method, Questioning Method

3 The method in model construction Explaining Method, Questioning Method

4 Graphical LP solution Explaining Method, Questioning Method

5 Mid-Term Exam

6 Maximization and minimization problems

and its solutions Explaining Method, Questioning Method

7 Graphical sensitivity analysis Explaining Method, Questioning Method

8 Analytic solution, investigate of the

feasible solution space Explaining Method, Questioning Method

9 Analysis of selected LP models Explaining Method, Questioning Method

10 Mid-Term Exam

11 The simplex method, the simplex

algorithm Explaining Method, Questioning Method

12 Special cases in simplex method

application Explaining Method, Questioning Method

13 Duality and sensitivity analysis Explaining Method, Questioning Method

14 Dual simplex method Explaining Method, Questioning Method

15 Primal- dual computations Explaining Method, Questioning Method

16 Final Exam

Recommended or

Required Reading

Lecture Notes

[1] İmdat Kara, ?Doğrusal Programlama?Bilim Teknik yayınev.1991

[2] Hamdy. A. Taha.?Yöneylem Araştırması?Arkansas Üni.,2000,(evirenler: Ş.Alp. Baray- Şakir Esnaf.)

Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






1 10 10



Assignments 2 20 40

Project




Mid-terms 2 15 30


Total Work Load 90




Learning

Outcomes

Programme Outcomes


LO1 3 3 3 3 4 4

LO2 4 4 4 4 4 4

LO3 3 3 3 3 4 3

LO4 2 2 2 2 2 2

LO5 3 3 3 3 4 3

LO6 5 5 5 5 5 5

LO7 4 4 4 4 4 4

LO8 2 2 1 2 2 2



Course Unit Title ABSTRACT ALGEBRA I





Allocated 7




Year of Study 3


delivered 6

Name of Lecturer







Work Placement NONE

Objectives of the Course Helping to learning of the information about number theory

Learning Outcomes


1) Identify divisibility, prime numbers and congruenses

2) Solve congruenses.

3) Identify Fermat, Euler and Wilson theorems.

4) explain subgroup, cyclic subgroups and normal subgroups

5) Explain group homeomorphism and isomorphism

6) Identify symmetric group.

Course Contents Algebraic structures, rings

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Divisibility and prime numbers Explaining Method, Questioning Method

2 Congruenses Explaining Method, Questioning Method

3 Congruenses Explaining Method, Questioning Method

4 Euler-Fi function Explaining Method, Questioning Method

5 Mid-Term Exam

6 Fermat Euler and Wilson theorems Explaining Method, Questioning Method

7 Fermat Euler and Wilson theorems Explaining Method, Questioning Method

8 Lineer congruenses Explaining Method, Questioning Method

9 High order congruenses Explaining Method, Questioning Method

10 Mid-Term Exam

11 Quadratik reversibility Explaining Method, Questioning Method

12 Quadratik reversibility Explaining Method, Questioning Method

13 Legendre symbol Explaining Method, Questioning Method

14 Jacobi symbol Explaining Method, Questioning Method

15 Jacobi symbol Explaining Method, Questioning Method

16 Final Exam

Recommended or

Required Reading

Lecture Notes

An Introduction To The Theory Of Numbers, Ivan Nıven-Herbert S. Zuckerman, New York. London,

1960

Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 3 45

Assignments 2 15 30

Project




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title PARTIAL DIFFERENTIAL EQUATIONS I



Level of Course Unit BACHELOR (FİRST CYCLE)





Year of Study 4


delivered 7

Name of Lecturer

Mode of Delivery FORMAL EDUCATİON


Prerequisities and co-requisities Differential equation course is recommended.


Programme Components -

Work Placement -


To solve the partial differential problems arising in science.

Learning Outcomes

1.At the and of this course you will be able to recognize and clasify PDEs

2 At the and of this course you will be able to solve first order linear and nonlinear PDEs.

3 At the and of this course you will be able to clasify 2nd order PDEs.

4 At the and of this course you will be able to solve second order linear equations.

5) At the and of this course you will be able to obtain solution by reducting canonical form

6 At the and of this course you will be able to identifie and interpret wave, Laplace and heat

equations.

Course Contents PDEs, first order equations, linear equatios, nonlinear equations, high order equations, linear

second order equations, nonlinear second order equatios, canonical form

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Introducing the PDEs TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

2 First order equations TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES


QUESTION TECHNIQUES

4 Linear equatios TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

5 Mid-term exam


QUESTION TECHNIQUES

7 Nonlinear equations TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES


QUESTION TECHNIQUES

9 High order equations TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

10 Mid-term exam

11 Second order equations TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

12 Second order equations TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

13 Nonlinear second order equatios TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

14 Nonlinear second order equatios TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

15 Canonical form TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

16 Final exam

Recommended or

Required Reading

1. Differential Equations, Shepley L. Ross, John Wiley & Sons, New York, 1974.

2.Lectures on Differential Equations ,Ersan Akyıldız,Yılmaz Akyıldız,Şafak Alpay,Albert Ekip,Ali

Yazıcı,Matematik Vakfı,2000.

3. Adi Diferensiyel Denklemler , Mehmet Çağlıyan,Nisa Çelik,Setenay Doğan, Nobel Yayınları,2007. 4. Modern Uygulamalı Diferensiyel Denklemler, Yaşar Pala, Nobel Yayınları, 2006

Assesements



Assignment 1 20

Project -


Seminar -

Quizzes -

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 1 5 5

Project - -



Study/Laboratory/Trip and Observation) - -

Mid-terms 2 7.5 15






Learning

Outcomes

Programme Outcomes


LO1 3 3 3 3 3 3

LO2 4 4 4 4 4 4

LO3 5 5 5 5 5 5

LO4 3 3 3 3 3 3

LO5 5 5 5 5 5 5

LO6 2 2 2 2 2 2

LO7 4 4 4 4 4 4

LO8 3 3 3 3 3 3



Course Unit Title PRINCIPLES OF ATATÜRK AND HISTORY OF TURKISH REVOLUTION I

Course Unit Code TAR 301




Allocated 4




Year of Study 3


delivered 5

Name of Lecturer







Work Placement NONE


To criticize the reasons of the Ottoman collapse, Balkan Wars, WWI, dynamics of the National

Struggle. To get students to explain well the concepts like revolution and reform. Additionally

to summarize political developments in completed phase of Turkish Revolution and

establishment process of new state, Ataturk Revoluitons in the political and social fields

Learning Outcomes


1) Acquires a knowledge of the sources belonging to the Principles of Atatürk

2) Apprehends the renovation movements in Ottoman State

3) Apprehends the historical origins of Atatürk?s Principles

4) Understands the state structure of Turkish Republic

5)Apprehends the Turkish case in 21th century

6) To be able to identify historical roots of Turkish Revolution, to claim consciously Ataturk?s

revolutions

7) To be able to interpret by energy which take from Turkish history and Turkish National

Struggle, student claims his state and nation.

Course Contents

Events, thoughts and principles in the rise and development process of Modern Turkey.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1

Content and aim of history of Ataturk

Principles and Revolution - Concepts like

reform

Explaining Method, Questioning Method

2 The structure of Ottoman Empire and its

dissolution reasons - Recovery and

reform efforts in the state Explaining Method, Questioning Method

3

Constitutional development and

intellectual transactions in the state -

The Ottoman geopolitics and foreign

policy


4 The administration of CUP and last phase

- WWI and the Ottoman Empire Explaining Method, Questioning Method

5 Mid-Term Exam

6

Mondros Armistice and Occupations,

Paris Peace Conference - National

Independence Determination and

Mustafa Kemal


7 Mustafa Kemal?s opinions and his pass

to Anatolia - Period of the Congress Explaining Method, Questioning Method

8 Occupation of Istanbul and reactions -

Opening Turkish Grand National

Assembly (TGNA) and its features Explaining Method, Questioning Method

9

First activities of the TGNA and first

codes - Reactions to TGNA, internal

rebellions, opposite groups, the press in

the National Struggle


10 National Struggle Fronts (south and

southeast) - National Struggle Fronts

(east) and the Armenian Question Explaining Method, Questioning Method

11

National Struggle Fronts (west), first

occupations and national army -

Establishment of regular army and

financial sources of the National Struggle


12

Treaty of Sevres and its impact on

Turkish Nation - Fronts in the National

Struggle, Inonu I-II, Sakarya and Great

Attack


13

Political aspect of National Struggle,

Mudanya Armistice, Lozan Peace

Conference, Foreign policy in the Ataturk

period - Revolutions in the political,

educational, cultural, jurisprudence and

social fields


14 Principles of Atatürk (Republicanism,

Nationalism, Populism, Secularism,

Etatism, revolutionism) Explaining Method, Questioning Method




16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 3 45

Assignments 2 15 30

Project




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title THEORY OF COMPLEX FUNCTIONS I





Allocated 7




Year of Study 3


delivered 5

Name of Lecturer







Work Placement NONE

Objectives of the Course System of complex numbers and constitution of complex functions

Learning Outcomes


1) Recognize the difference between complex numbers and reel numbers.

2) Understand the cartesian and polar form of complex numbers

3) Integer and rational power of complex numbers

4) Understand the limit, continuity and derivative rules of complex numbers

5) Explain analitic consept

6) Apply properties of basic functions

7) explain properties of complex numbers

Course Contents

Definition of complex numbers, argument of complex numbers, integer and rational powers of

complex numbers, exponential phrases and logarithm, complex and irrational powers of complex

numbers, some basic functions, limit and continuity of complex functions

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Definition of complex numbers and basic

information Explaining Method, Questioning Method

2 Cartesian and polar form of complex

numbers Explaining Method, Questioning Method

3 Exponential phrases and logarithm Explaining Method, Questioning Method

4 Exponential phrases and logarithm Explaining Method, Questioning Method

5 Mid-Term Exam

6 Complex and irrational powers of complex

numbers Explaining Method, Questioning Method

7 Geometric presentation some sets Explaining Method, Questioning Method

8 Basic topologic consepts in E Explaining Method, Questioning Method

9 Extended complex numbers and Riemann

Sphere Explaining Method, Questioning Method

10 Mid-Term Exam

11 Extended complex numbers and Riemann

Sphere Explaining Method, Questioning Method

12 Some basic Functions Explaining Method, Questioning Method

13 Some basic Functions Explaining Method, Questioning Method

14 Gheometric presentation of complex

functions Explaining Method, Questioning Method

15 Limit and continuity of complex functions Explaining Method, Questioning Method

16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 3 45

Assignments 2 15 30

Project




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title COMPUTER PROGRAMMING I


Type of Course Unit OPTİONAL



Allocated 5




Year of Study 3


delivered 5

Name of Lecturer







Work Placement NONE

Objectives of the Course The aim of this course is to introduce computer programming with a character-based

programming (C/C++) and to give some information about algorithm, codding and the flow

charts.

Learning Outcomes


1) He / she sees general concepts about computer programming.

2) He/ she has the ability to use the related materials about mathematics, constructed on

competency, achieved in secondary education and also has the further knowledge equipment. 3)He / she understands the logic of creating an algorithm.

4)He/ she follows up the knowledge of mathematics and has the competency of getting across

with his (or her) professional colleagues within a foreign language. 5) He/ she has the knowledge of computer software information as a mathematician needs.

6) He/ she has scientific and ethic assets in the phases of congregating, annotating and

announcing the knowledge about mathematics. 7) He/ she uses the ability of abstract thinking.

Course Contents

Introduction to programming systems, the concept of algorithm, flow charts, the structure of

the program of C++, data types, constants and variables, operators, input and outputs

commands, compare commands, loops, ordering and array concept, defining and using a

function, file operations, classes and introduction of visual programming.

W

eek

ly D

etail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Introduction to programming systems

and visual studio environment Explaining Method, Questioning Method

2 The concept of algorithm, flow charts Explaining Method, Questioning Method

3 The structure of the program of C++,

defining a variable Explaining Method, Questioning Method

4 Commands for input and output data Explaining Method, Questioning Method

5 Mid-Term Exam

6 Structural control statements Explaining Method, Questioning Method

7 Loops Explaining Method, Questioning Method

8 Linear Diophantine equations Explaining Method, Questioning Method

9 Orderings and arrays Explaining Method, Questioning Method

10 Two-dimensional arrays (matrices) Explaining Method, Questioning Method

11 To define and to use a function Explaining Method, Questioning Method

12 Classes Explaining Method, Questioning Method

13 Data files Explaining Method, Questioning Method

14 Euler?s Theorem Explaining Method, Questioning Method

15 Files applications Explaining Method, Questioning Method

16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 3 45

Assignments 2 15 30

Project




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title NUMBER THEORY I





Allocated 5




Year of Study 3


delivered 5

Name of Lecturer







Work Placement NONE

Objectives of the Course The objective of this course is giving the background of number theory that is connected with

many areas of mathematics.

Learning Outcomes


1Evaluating the fundamental notions, theories and data with academic methods, he/ she

determines and analyses the encountered problems and subjects, exchanges ideas, improves

suggestions propped up proofs and inquiries..

2) He/ she has the ability to use the related materials about mathematics, constructed on

competency, achieved in secondary education and also has the further knowledge equipment. 3) He/ she has the competency of executing the further studies of undergraduate subjects

independently or with shareholders. 4He/ she follows up the knowledge of mathematics and has the competency of getting across

with his (or her) professional colleagues within a foreign language.

5) He/ she has the knowledge of computer software information as a mathematician needs.

6) He/ she has scientific and ethic assets in the phases of congregating, annotating and

announcing the knowledge about mathematics. 7) He/ she uses the ability of abstract thinking.

Course Contents

Introduction, Divisibility, Prime numbers, The greatest common divisor, Euclidean algorithm, The

fundamental theorem of arithmetics, Linear Diophantine equations, Congruances, Linear

congruances, Chinese Remainder Theorem, Wilson Theorem, Euler?s Theorem, Primitive roots.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Introduction Explaining Method, Questioning Method

2 Divisibility Explaining Method, Questioning Method

3 Prime numbers Explaining Method, Questioning Method

4 The greatest common divisor Explaining Method, Questioning Method

5 Mid-Term Exam

6 Euclidean algorithm Explaining Method, Questioning Method

7 The fundamental theorem of arithmetics Explaining Method, Questioning Method

8 Linear Diophantine equations Explaining Method, Questioning Method

9 Congruences Explaining Method, Questioning Method

10 Linear congruences Explaining Method, Questioning Method

11 Linear congruences Explaining Method, Questioning Method

12 Chinese Remainder Theorem Explaining Method, Questioning Method

13 Wilson Theorem Explaining Method, Questioning Method

14 Euler?s Theorem Explaining Method, Questioning Method

15 Primitive roots Explaining Method, Questioning Method

16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 3 45

Assignments 2 15 30

Project




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title REAL ANALYSIS

Course Unit Code OMAT 405







Year of Study 4


delivered 7

Name of Lecturer RESEARCH ASISTAN OF MATHEMATIC DEPARTMENT



Prerequisities and co-requisities ANALYSIS I-II-III-IV



Work Placement NONE


The purpose of this course is to teach bases of Real Valuable Function Theory, to recognise

infinite sets, measurable sets, measurable functions and Lebesque integral and to do operation

regarding these.

Learning Outcomes

1)He/She is able to define infinite sets and concept of countable infinity

2) He/She is able to explain limit and densify point, open and closed sets and structure of these

3) He/She is able to calculate measurement of open and closed sets and inside and out

measurement of finite sets

4) He/She is able to understand measurable functions and its properties

5) He/She is able to calculate Lebesque integral of a funtion

6) He/She is able to compare beregnet Lebesque integral with Riemann integral

Course Contents

Algebra, Sigma algebra, measurable sets, measurement of Lebesque, measurable sets,

measurable functions, Lebesque integral of finite and infinite mesurable functions and Compare

Lebesque integral with Riemann integral

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Infinite sets, Countable infinity, comparing

of sets Telling, explanation and question-answer

2

Point sets, point of limit, open sets, closed

sets and structures of these sets, densify

points

Telling, explanation and question-answer

3 Measurable sets and measurement of open

sets Telling, explanation and question-answer

4

İnside and out measurement of finite sets,

measurable sets and class of measurable

sets


5 FIRST EXAM

6 Vitali theorem and its results Telling, explanation and question-answer

7 Measurable functions and its properties Telling, explanation and question-answer

8 Measurable function sequences and

convergence in measurement Telling, explanation and question-answer

9 Structure of measurable functions Telling, explanation and question-answer

10 SECOND EXAM

11 Lebesque integral of finite functions Telling, explanation and question-answer

12 Proprties of Lebesque integral Telling, explanation and question-answer

13 Relations of Lebesque integral with

Riemann integral Telling, explanation and question-answer

14 Generating primitive function again Telling, explanation and question-answer

15 FINAL EXAM

16

Recommended or

Required Reading

1] Yıldız, Abdullah; Kevser Özden Reel analiz , I,P.Natanson.tercüme 2005 Yıldız T.Üniversitesi

yayınları.

[2] Reel Analiz, Mustafa Balcı, Ankara, 1988

[3] Reel Analiz, Ali Dönmez, Seçkin, 2001

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 1 10 10

Project - - -




Mid-terms 2 7,5 15






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title TECHNICAL ENGLISH I





Allocated 5




Year of Study 3


delivered 5

Name of Lecturer







Work Placement NONE

Objectives of the Course To teach students english used for mathematics and english meanings of mathematical terms

Learning Outcomes


1) Construct basic english knowledge

2) Understand the difference of technical texts

3) Identify english meanings of mathematical terms.

4) Understand most used templates in articles and issues

5) translate a mathematical text from english to turkish and turkish to english.

Course Contents Translation of technical texts

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts Week

TOPICS


1 Basic English Knowledge Explaining Method, Questioning Method




5 Mid-Term Exam


7 Technical English Knowledge Explaining Method, Questioning Method



10 Mid-Term Exam


12 Translation Explaining Method, Questioning Method




16 Final Exam

Recommended or

Required Reading

Lecture Notes

Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 1 15

Assignments 2 10 20

Project - -




- -

Mid-terms 2 7,5 15






Learning



LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title VECTORAL ANALYSIS





Allocated 5




Year of Study 3


delivered 5

Name of Lecturer







Work Placement NONE

Objectives of the Course Examination of the relations between coordinate systems and basic analysis knowledge

Learning Outcomes


1) Have enough knowledge about coordinate systems

2) Understand rotation of coordinate systems.

3) Learn continuity of vectoral functions and concept of directional derivative

4) Understand gren and stokes theorems

5) Learn Gauss theorem and applying it to differential equations.

6) Comprehend meaning of Gradient and Divergance.

Course Contents

Vectoral algebra, coordinate systems in space, rotation of coordinate systems in plane and space,

vectoral functions and the limit of vectoral functions, continuity and derivative of vectoral

functions, directional derivative, Green theorem, stokes theorem, gauss theorem, differential forms.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Vectoral algebra Explaining Method, Questioning Method

2 Coordinate system in space Explaining Method, Questioning Method

3 Rotation of coordinate systems in plane

and space Explaining Method, Questioning Method

4 Equations of plane and straight line Explaining Method, Questioning Method

5 Mid-Term Exam

6 Vectoral functions and their limits Explaining Method, Questioning Method

7 Continuity and derivative in vectoral


8 Directional derivative Explaining Method, Questioning Method

9 Gradient Explaining Method, Questioning Method

10 Mid-Term Exam

11 Divergance Explaining Method, Questioning Method

12 Green and Stokes Theorems Explaining Method, Questioning Method

13 Conservative fields, Gauss theorem Explaining Method, Questioning Method

14 Applications of Pysical and differential

equations Explaining Method, Questioning Method

15 Differential forms Explaining Method, Questioning Method

16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 1 15

Assignments 2 10 20

Project




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title ABSTRACT ALGEBRA II





Allocated 6




Year of Study 3


delivered 6

Name of Lecturer







Work Placement NONE

Objectives of the Course Helping to learning of the information about ring an structure of ideal

Learning Outcomes


1) Identify division rings

2) Understand homomorphism, prime and maksimal ideals.

3) Apply isomorphism theorems

4) Identify field extensions and apply them

5) evaluate roots of polinomials

6) Understand transandant numbers

Course Contents

Quotient rings, homeomorphisms in rings, prime and maximal ideals, isomorphism theorems,

polinom rings, prime factorisation, field extensions, algebraic numbers, transendent numbers,

galois hypotesis, roots of polinoms.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Quotient rings Explaining Method, Questioning Method

2 Quotient rings Explaining Method, Questioning Method

3 Homeomorphisms in rings Explaining Method, Questioning Method

4 Prime and maximal ideals Explaining Method, Questioning Method

5 Mid-Term Exam

6 Isomorphism theorems Explaining Method, Questioning Method

7 Fields Explaining Method, Questioning Method

8 Polinom rings Explaining Method, Questioning Method

9 Prime factorisation Explaining Method, Questioning Method

10 Mid-Term Exam

11 Field extensions Explaining Method, Questioning Method

12 Algebraic numbers Explaining Method, Questioning Method

13 Transandant numbers Explaining Method, Questioning Method

14 Drawings which can’t make with a

callipers Explaining Method, Questioning Method

15 Galois hypotesis Explaining Method, Questioning Method

16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 3 45

Assignments 2 15 30

Project




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title PARTIAL DIFFERENTIAL EQUATIONS II








Year of Study 4


delivered 8

Name of Lecturer



Prerequisities and co-requisities Differential equation course is recommended.


Programme Components NO

Work Placement NO


To solve the partial differential problems arising in science.

Learning Outcomes

1) At the and of this course you will be able to recognize and clasify PDEs

2) At the and of this course you will be able to solve first order linear and nonlinear PDEs.

3) At the and of this course you will be able to clasifie 2nd order PDEs.

4) At the and of this course you will be able to solve second order linear equations.

5) At the and of this course you will be able to obtain solution by reducting canonical form

Course Contents PDEs, first order equations, linear equatios, nonlinear equations, high order equations, linear

second order equations, nonlinear second order equatios, canonical form

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 PDEs TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

2 PDEs TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES


QUESTION TECHNIQUES


QUESTION TECHNIQUES

5 Midterm exam


QUESTION TECHNIQUES


QUESTION TECHNIQUES


QUESTION TECHNIQUES


QUESTION TECHNIQUES

10 Midterm exam


QUESTION TECHNIQUES


QUESTION TECHNIQUES

13 Linear and nonlinear second order equatios TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES


QUESTION TECHNIQUES


QUESTION TECHNIQUES

16 Final exam

Recommended or

Required Reading

Course notes

Assesements



Assignment 1 20

Project -


Seminar -

Quizzes -

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 1 5 5

Project - -




Mid-terms 2 7.5 15






Learning

Outcomes

Programme Outcomes


LO1 3 3 3 3 3

LO2 4 4 4 4 4

LO3 5 5 5 5 5

LO4 4 4 4 4 4

LO5 5 5 5 5 5

LO6 2 2 2 2 2

LO7 4 4 4 4 4

LO8 3 3 3 3 3



Course Unit Title PRINCIPLES OF ATATÜRK AND HISTORY OF TURKISH REVOLUTION II

Course Unit Code TAR 302




Allocated 2




Year of Study 3


delivered 5

Name of Lecturer







Work Placement NONE


To criticize the reasons of the Ottoman collapse, Balkan Wars, WWI, dynamics of the National

Struggle. To get students to explain well the concepts like revolution and reform. Additionally

to summarize political developments in completed phase of Turkish Revolution and

establishment process of new state, Ataturk Revoluitons in the political and social fields

Learning Outcomes


1) Acquires a knowledge of the sources belonging to the Principles of Atatürk

2) Apprehends the renovation movements in Ottoman State

3) Apprehends the historical origins of Atatürk?s Principles

4) Understands the state structure of Turkish Republic

5)Apprehends the Turkish case in 21th century

6) To be able to identify historical roots of Turkish Revolution, to claim consciously Ataturk?s

revolutions

7) To be able to interpret by energy which take from Turkish history and Turkish National

Struggle, student claims his state and nation.

Course Contents

Events, thoughts and principles in the rise and development process of Modern Turkey.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1

Content and aim of history of Ataturk

Principles and Revolution - Concepts like

reform


2 The structure of Ottoman Empire and its

dissolution reasons - Recovery and

reform efforts in the state Explaining Method, Questioning Method

3

Constitutional development and

intellectual transactions in the state -

The Ottoman geopolitics and foreign

policy


4 The administration of CUP and last phase

- WWI and the Ottoman Empire Explaining Method, Questioning Method

5 Mid-Term Exam

6

Mondros Armistice and Occupations,

Paris Peace Conference - National

Independence Determination and

Mustafa Kemal


7 Mustafa Kemal?s opinions and his pass

to Anatolia - Period of the Congress Explaining Method, Questioning Method

8 Occupation of Istanbul and reactions -

Opening Turkish Grand National

Assembly (TGNA) and its features Explaining Method, Questioning Method

9

First activities of the TGNA and first

codes - Reactions to TGNA, internal

rebellions, opposite groups, the press in

the National Struggle


10 National Struggle Fronts (south and

southeast) - National Struggle Fronts

(east) and the Armenian Question Explaining Method, Questioning Method

11

National Struggle Fronts (west), first

occupations and national army -

Establishment of regular army and

financial sources of the National Struggle


12

Treaty of Sevres and its impact on

Turkish Nation - Fronts in the National

Struggle, Inonu I-II, Sakarya and Great

Attack


13

Political aspect of National Struggle,

Mudanya Armistice, Lozan Peace

Conference, Foreign policy in the Ataturk

period - Revolutions in the political,

educational, cultural, jurisprudence and

social fields








16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 3 45

Assignments 2 15 30

Project




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title THEORY OF COMPLEX FUNCTIONS II





Allocated 6




Year of Study 3


delivered 6

Name of Lecturer







Work Placement NONE

Objectives of the Course Serial presentation of analytic functions. Evaluation of some complex and real integrals by aid of

residual theorem

Learning Outcomes


1) Classification of curves.

2) Calculate integrals in complex plane.

3) Explain cauchy integral theorem and its results.

4) Calculate serial expansions of functions around non-analytic points.

5) Classify singular points.

6) Calculate complex integrals with residual theorem.

7) Calculate some real integrals with complex methods.

Course Contents Complex functions, Analytic functions, Curve in complex plane, Line integral, Line integral of

analytic functions, Sequences of complex numbers, Function sequences, Power series

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts Week

TOPICS


1 Complex functions Explaining Method, Questioning Method

2 Complex functions Explaining Method, Questioning Method

3 Analytic functions Explaining Method, Questioning Method

4 Analytic functions Explaining Method, Questioning Method

5 Mid-Term Exam

6 Curve in complex plane Explaining Method, Questioning Method

7 Line integral Explaining Method, Questioning Method

8 Line integral Explaining Method, Questioning Method

9 Line integral of analytic functions Explaining Method, Questioning Method

10 Mid-Term Exam

11 Sequences of complex numbers Explaining Method, Questioning Method

12 Sequences of complex numbers Explaining Method, Questioning Method

13 Function sequences Explaining Method, Questioning Method

14 Power series Explaining Method, Questioning Method

15 Power series Explaining Method, Questioning Method

16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 3 45

Assignments 2 15 30

Project




Mid-terms 2 15 30






Learning



LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title COMPUTER PROGRAMMİNG II








Year of Study 3


delivered 6

Name of Lecturer






Work Placement NONE

Objectives of the Course Teaching the computer programming and showing the importance of using the computer

programming in mathematics.

Learning Outcomes

1.Comprehension the objective of programming

2.To be forming algorithms

3.Coding the algorithms with Basic language

4.To be forming algorithms of arithmetic problems

5.Comprehension the fluence control command

Course Contents Computer programming , Comprehension how is working the computer , Forming algorithms

for some mathematical problems , Coding with the Basic language

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Logic of programming Telling-explanation and Application

2 Forming algorithms Telling-explanation and Application

3 Fundementals of Basic language Telling-explanation and Application

4 Writing some easy programs in the Basic

language Telling-explanation and Application

5 Midterm exam

6 To codify fundemental mathematic

problems in the Basic language Telling-explanation and Application

7 Fluence controll commands Telling-explanation and Application

8 Control structures Telling-explanation and Application

9 Continue the control structures Telling-explanation and Application

10 Midterm exam

11 Commands Telling-explanation and Application

12 Loops Telling-explanation and Application

13 Sequences Telling-explanation and Application

14 Continue to sequences Telling-explanation and Application

15 Final exam

Recommended or

Required Reading

Lecture notes,Programlama sanatı algoritmalar-Rifat Çölkesen ,Quick Basic ile Bilgisayar Programlama-

Bülent Altunkaynak

Assesements



Assignment 2 20

Project


Seminar

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100






15

3

45



15

1

15

Assignments

2

14

28

Project




Mid-terms

2

7

14

Final examination

1

14

14

Total Work Load 35 39

116

Total Work Load / 30 (h) - -

3.86

ECTS Credit of the Course - -

4


Learning

Outcomes

Programme Outcomes


LO1 4 4 4 5 4 4 5

LO2 4 4 4 5 4 4 5

LO3 4 4 4 5 4 4 5

LO4 4 4 4 5 4 4 5

LO5 4 4 4 5 4 4 5



Course Unit Title METRIC SPACES

Course Unit Code OMAT310







Year of Study 3


delivered 6

Name of Lecturer RESEARCH ASSISTANT OF MATHEMATIC DEPARTMENT






Work Placement NONE

Objectives of the Course By using known concepts, analysing about Metric spaces and Topologic spaces and hence

getting backround for Functional Analysis which will be get further.

Learning Outcomes

1)He/She is able to remember concepts which are learned before(Sets, Functions, Continuity

ect)

2)He/She is able to adapt these concepts to Metric spaces, Normed spaces and Topologic spaces

3)He/She is able to make an opinion about distance between any two points

4)He/She is able to define open sets and open sphere

5)He/She is able to realize relations between Metric spaces and general Topologiz spaces

6)He/She is able to adapt a problem in Metric spaces to Topologic spaces

7)He/She is able to have abstract thinking ability

Course Contents

Sets, Functions, Finite sets, Countable sets, Ranking correlation, Absulate value and some

important inequalities, Number sequences, Continuity, Linear spaces, Metric spaces, Normed

spaces, Sub metric spaces and normed sub spaces, Open and closed sets in Metric spaces, Open

and closed sets in Sub metric spaces, Neigbourhood ve aggregation points, equivalent metrics,

Convergene of sequences in Metric spaces, Continuity of functions in Metric spaces,

Convergence and continuity in normed spaces and also introduction to Topologic concepts and

properties of Topologic spaces. W

eek

ly D

etail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1

Sets, Functions, Finite sets, Calculable sets

and Ranking correlation, Absolute value

and Some important inequalities


2 Number sequences, Continuity, Linear

spaces Telling, explanation and question-answer

3 Metric spaces, Normed spaces, Sub metric

spaces and Sub normed spaces Telling, explanation and question-answer

4 Open and closed sets in (X,d) metric space Telling, explanation and question-answer

5 FIRST EXAM

6

Open and closed sets in sub metric spaces,

Contiguities and aggregation points,

Equivalent metric


7

Convergence of sequences in metric

spaces, Continuity of functions in metric

spaces, Convergence and continuity in

normed spaces


8 Exact metric spaces Telling, explanation and question-answer

9 Compact metric spaces Telling, explanation and question-answer

10 SECOND EXAM

11 Correlativity, Continuity in correlative

metric spaces Telling, explanation and question-answer

12

Topologic spaces,Inside, out, limit and

aggregation points of a set in topologic

spaces


13 Convergence and Continuity in topologic

spaces Telling, explanation and question-answer

14 Bases and Contiguities in topologic spaces Telling, explanation and question-answer

15 FINAL EXAM

16

Recommended or

Required Reading

[1] Turgut BAŞKAN, İ. N. CANGÜL, Osman BİZİM, Metrik Uzaylar ve Genel Topolojiye Giriş

Vipaş A.Ş. BURSA, 2000.

[2] “Metrik uzaylar ve topoloji” Seyit Ahmet KILIÇ, Musa ERDEM, Vipaş A.Ş.,BURSA,1999.

[3] “Genel topoloji” Cemil YILDIZ, Kalkan matbaacılık, ANKARA,2002.

Assesements



Assignment 2 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 2 8 16

Project - - -




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title NUMBERS THEORY II








Year of Study 3


delivered 6

Name of Lecturer






Work Placement NONE

Objectives of the Course Transferring various applications in Number Theory to students

Learning Outcomes

1.Comprehension and apply the Wilson Theorem

2. Comprehension and apply the Fermat theorem

3. Comprehension and apply the Euler theorem

4. Comprehension and apply the special numbers

5.Comprehension the Kriptology

Course Contents

Wilson theorem,Applications of the Wilson theorem,Fermat theorem ,Application of Fermat

theorem,Euler theorem ,Application of Euler theorem,Primitive roots and indexes,Quadratic

residual,Special numbers ,Applications of special numbers,Continuous fractions,Applications

of continuous fractions ,Kriptology theory I , Kriptology theory II. Applications of Kriptology

theory

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Wilson theorem Telling and explanation

2 Various applications of Wilson theorem Telling and explanation

3 Fermat theorem Telling and explanation

4 Various applications of Fermat theorem Telling and explanation

5 Midterm exam

6 Euler theorem Telling and explanation

7 Various applications of Euler theorem Telling and explanation

8 Primitive roots and indexes Telling and explanation

9 Quadratic residual Telling and explanation

10 Midterm exam

11 Special numbers and their applications Telling and explanation

12 Continuous fractions and their applications Telling and explanation

13 Introduction to Kriptology theory Telling and explanation

14 Applications of Kriptology theory Telling and explanation

15 Final exam

Recommended or

Required Reading

Lecture notes,Soyut cebir ve sayılar teorisi-M.Bayraktar,Sayılar teorisi-H.Hilmi Hacısalihoğlu

Assesements



Assignment 1 10

Project


Seminar

Mid-terms 2 90

Total 100


Grade 50


TOTAL 100






15

3

45



15

2

30

Assignments

1

10

10

Project




Mid-terms

2

15

30

Final examination

1

15

15

Total Work Load 34 45

130


4.33


4


Learning

Outcomes

Programme Outcomes


LO1 4 5 5 5 5 4

LO2 4 5 5 5 5 4

LO3 4 5 5 5 5 4

LO4 4 5 5 5 5 4

LO5 4 5 5 5 5 4



Course Unit Title TECHNİCAL ENGLISH II








Year of Study 3


delivered 6

Name of Lecturer






Work Placement NONE

Objectives of the Course The purpose is recognition of english terms used in Mathematic and some proper english terms

Learning Outcomes

1.Comprehension the advance level mathematical terms

2. Comprehension the advance level english structures

3.Make translation in basic mathematical disciplines

4.Make translation from English to Turkish

5. Make translation from Turkish to English

Course Contents

Translation of scientific articles from English to Turkish

Translation of technical articles from English to Turkish

Translation of English lecture notes

Wee

kly

Det

ail

ed

Cou

rse

Con

ten

ts

Week

TOPICS


1 Mathematical terms Telling and explanation

2 Continue to mathematical terms Telling and explanation

3 English patterns Telling and explanation

4 Translation from Abstract algebra Telling and explanation

5 Midterm exam

6 Article translation from Abstract algebra Telling and explanation

7 Translation from the book of Differential

Equations Telling and explanation

8 Article translation related to Differential

Equations Telling and explanation

9 Translation from the book of Differential

Geometry Telling and explanation

10 Midterm exam

11 Article translation related to Differential

Geometry Telling and explanation

12 Translation of Complex Analysis Telling and explanation

13 Translation of Functional Analysis Telling and explanation

14 Translation of Numerical Analysis Telling and explanation

15 Final exam

Recommended or

Required Reading

Lecture notes

Assesements



Assignment 2 20

Project


Seminar

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100






15

3

45



15

1

15

Assignments

2

10

20

Project




Mid-terms

2

7,5

15

Final examination

1

15

15

Total Work Load 35 36,5

110


3.66


4


Learning

Outcomes

Programme Outcomes


LO1 5 5 4 5

LO2 5 5 4 5

LO3 5 5 4 5

LO4 5 5 4 5

LO5 5 5 4 5



Course Unit Title INTRODUCTION TO TOPOLOGY II








Year of Study 2


delivered 4




Prerequisities and co-requisities INTRODUCTION TO TOPOLOGY I



Work Placement NONE


The aim of this course is to give the fundamental concepts of topology and the methods of

proof. Besides, the other aims are to discuss the advanced topological concepts, to discover the

relations between topology and the other disciplines and to learn topics about compact spaces,

local compact spaces, connected spaces, separation axioms convergence, countability.

Learning Outcomes

1) He/She is able to define compactness in topologic space,

2) He/She is able to compare the compactness in classical analysis with compactness in

topologic space,

3) He/She is able to prove fundamental theorems in compact topologic space,

4) He/She is able to define countable compactness and sequentially compactness,

5) He/She is able to prove the theorems related to countable compactness and sequentially

compactness,

6) He/She is able to define the concepts of the connected spaces,

7) He/She is able to solve the problems by the aid of the concepts of the connected spaces

8) He/She is able to classify topologic spaces,

Course Contents Compact spaces, local compact spaces, sequentially compactness, countable compactness,

connected spaces, separation axioms, convergence, countability.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Compact topological spaces [1] Pages 89-107

2 Local compact spaces [1] Pages 107-109

3 Compactness [1] Pages 109-112

4 Countable compactness, sequentially

compactness [1] Pages 112-120

5 FIRST EXAM

6 Connected spaces [1] Pages 120-126

7 Connectedness on the reel line, some

applications of connected spaces [1] Pages 126-131

8 Local connected spaces [1] Pages 131-139

9 Separation Axioms,T0-spaces, T1-spaces [1] Pages 139-143

10 SECOND EXAM

11 Regular spaces and T3-spaces [1] Pages 143-145

12 Normal spaces and T4-spaces [1] Pages 145-152

13 Urysohn Lemma, Tietze Extension

Theorem [1] Pages 152-157

14 Convergence, nets, subnets, convergence

of nets [1] Pages 157-170

15 FINAL EXAM

16

Recommended or

Required Reading

1] Gürkanlı A. Turan, Genel Topoloji, Samsun, 1993.




[1] Gürkanlı A. Turan, Genel Topoloji, Samsun, 1993.




Assesements



Assignment 2 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 2 4 8

Project - - -




Mid-terms 2 10 20






Learning



LO1 4 3 3 5

LO2 4 3 3 5

LO3 4 3 3 5

LO4 4 3 3 5

LO5 4 3 3 5

LO6 4 3 3 5

LO7 4 3 3 5

LO8 4 3 3 5



Course Unit Title COMPLEX ANALYSIS I


Type of Course Unit Compulsory

Level of Course Unit Bachelor (First Cycle)





Year of Study 4


delivered 7

Name of Lecturer

Mode of Delivery FORMAL EDUCATION


Prerequisities and co-requisities Advised to take the Analysis IV



Work Placement NO


To introduce Complex numbers, their notations and properties and introduction of the complex

functions theory. The conceptions of limit,continuity,complex differentation and entire

functions and theorems related with these and applications.Complex sequences and series.

Fundamental functions and to analysis their properties.

Learning Outcomes

1.At the and of this course you will be able to define Complex numbers

2. At the and of this course you will be able to define topology of the complex plane

3.At the and of this course you will be able to define Complex sequences and series

4. At the and of this course you will be able to define complex functions,limit,continuity and

derivative of these functions

5. At the and of this course you will be able to define ,Cauchy-Riemann equations

Course Contents

Complex numbers,topology of the complex plane,Complex sequences and series,complex

functions,limit,continuity and derivative of these functions,Cauchy-Riemann equations,Entire

functions,Exponential, logarithmic,trigonometric and hyperbolic functions.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Complex numbers TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

2 Topology of the complex plane TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

3 Topology of the complex plane TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

4 Complex sequences and series TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

5 Midterm Exam

6 Complex sequences and series TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

7 Complex functions TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

8 Complex Limit TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

9 Complex continuity TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

10 Midterm Exam

11 Cauchy-Riemann equations TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

12 Exponential functions TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

13 Trigonometric and hyperbolic functions TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES


QUESTION TECHNIQUES


QUESTION TECHNIQUES

16 Final Exam

Recommended or

Required Reading

1.R.V.Churchill and J.W.Brown, Complex Variables and Applications, McGraw-Hill Series in Higher

Mathematics, New York, 1990.

2.M.R.Spiegel,Complex Variables, Schaum’s Outline Series in Mathematics-Statistics, McGraw-Hill

Series, New York, 1964.

3.R.P.Boas, Invitation to Complex Analysis, The Random House, New York,.1987,

4.A.Kaya, Karmaşık Degişkenler ve Uygulamalar, çeviri: R.VChurchill, Milli Eğitim Bakanlığı

Yayınları, İstanbul, 1989.

5.T.Başkan, Kompleks Fonksiyonlar Teorisi, Vipaş A.Ş., Yayın sıra no:38, Dördüncü Baskı, Bursa,

Assesements



Assignment 5 20

Project -


Seminar -

Quizzes -

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 5 10 50

Project - -




Mid-terms 2 7.5 15






Learning

Outcomes

Programme Outcomes


LO1 3 3 3 3 3

LO2 4 4 4 4 4

LO3 5 5 5 5 5

LO4 2 2 2 2 2

LO5 4 4 4 4 4

LO6 5 5 5 5 5

LO7 3 3 3 3 3

LO8 3 3 3 3 3



Course Unit Title DIFFERENTIAL GEOMETRY





Allocated 6




Year of Study 3


delivered 5

Name of Lecturer







Work Placement NONE

Objectives of the Course The goal of this lesson is to develop knowledge about differential geometry of eager students.

Learning Outcomes


1) Identify afine space, topological space and metric space concepts

2) Construct a jacobian matrice

3) Identify frenet vectoral spaces, oscilator, normal rectifian planes

4) Identify curvature sphere, tangent space, vector fields and cotangent space

5) Understand directional derivative, covariant derivative and apply

6)Identify gradient functions, divergance functions and rotational functions

Course Contents

Affine space, Euclides space, Topological space, metric space

Jacobian matrice and differentiable functions, Curves theorem, frenet vector spaces

Oscillator, normal and rectifian planes, Curvatures of curves, curvature circle

Curvature sphere, Tangent spaces, cotangent spaces, Directional derivative, covariant derivative

Gradient functions, divergance function, Rotational functions, Convection forms, structure

equations

Wee

kly

Det

ail

ed

Cou

rse

Con

ten

ts

Week

TOPICS


1 Affine space Explaining Method, Questioning Method

2 Euclides space Explaining Method, Questioning Method

3 Topological space, metric space Explaining Method, Questioning Method

4 Jacobian matrice and differentiable


5 Mid-Term Exam

6 Curves theorem, frenet vector spaces Explaining Method, Questioning Method

7 Oscillator, normal and rectifian planes Explaining Method, Questioning Method

8 Curvatures of curves, curvature circle Explaining Method, Questioning Method

9 Curvature sphere Explaining Method, Questioning Method

10 Mid-Term Exam

11 Tangent spaces, cotangent spaces Explaining Method, Questioning Method

12 Directional derivative, covariant derivative Explaining Method, Questioning Method

13 Gradient functions, divergance function Explaining Method, Questioning Method

14 Rotational functions Explaining Method, Questioning Method

15 Convection forms, structure equations Explaining Method, Questioning Method

16 Final Exam

Recommended or Lecture Notes

Required Reading

Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100








Assignments 2 15 30

Project




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title FUNCTIONAL ANALYSIS I








Year of Study 4


delivered 7

Name of Lecturer



Prerequisities and co-requisities Mathematical analysis I, II, III and IV should be taken.



Work Placement NO

Objectives of the Course To teach the notions of metric spaces. To introduce vector sapces, normed vector spaces,

Banach spaces, inner product spaces and Hilbert spaces. To teach their properties.

Learning Outcomes

1. At the and of this course you will be able to learn metric spaces, convergence, Cauchy

sequence, completeness. At the and of this course you will be able to understand the

completion of metric spaces and the seperability.

2. At the and of this course you will be able to understand vector spaces, normed vector spaces,

inner product spaces and Hilbert spaces with their basic properties.

3. At the and of this course you will be able to have knowledge about the completion of normed

spaces, complete and uncomplete normed spaces.

4. At the and of this course you will be able to prove the theorem related to Cauchy Schwarz

inequality, the notion of orthogonality and orthonormal sets.

5. At the and of this course you will be able to prove some theorem on approximation in Hilbert

spaces, and investigates the application areas of these theorems.

6. At the and of this course you will be able to understand the relations between these spaces.

Course Contents Metric spaces. Vector spaces. Normed vector spaces. Banach spaces. Inner product and Hilbert

sapces. Basic properties of these spaces.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Vector spaces TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

2

Metric spaces

TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

3

Metric spaces


QUESTION TECHNIQUES

4 Normed vector spaces TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

5 Midterm exam

6 Banach spaces TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

7 Banach spaces TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

8 Inner product TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

9 Hilbert spaces TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

10 Midterm exam

11 Hilbert spaces TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

12 Dual spaces TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

13 Basic properties of these spaces TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES


QUESTION TECHNIQUES


QUESTION TECHNIQUES

16 Final exam

Recommended or

Required Reading

“Fonksiyonel Analiz” Mustafa Bayraktar, Erzurum,1996

“Fonksiyonel Analiz” Binali Musayev ve Murat Alp, Balcı yayınları, 2000

“Fonksiyonel Analiz” Seyit Ahmet Kılıç,

Functional Analysis with applications” B. Choudhary and S. Nanda, Willey Eastern limited,19991.

Assesements



Assignment 1 20

Project -


Seminar -

Quizzes -

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 1 20 20

Project - -




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1 3 3 3 3 3

LO2 4 4 4 4 4

LO3 5 5 5 5 5

LO4 2 2 2 2 2

LO5 4 4 4 4 4

LO6 5 5 5 5 5

LO7 3 3 3 3 3

LO8 3 3 3 3 3



Course Unit Title NUMERICAL ANALYSIS I








Year of Study 4


delivered 7

Name of Lecturer RESEARCH ASSISTANT OF MATHEMATIC DEPARMENT



Prerequisities and co-requisities ANALYSIS I-II-III-IV, LİNEAR ALGEBRA I-II, COMPUTER PROGRAMME



Work Placement NONE

Objectives of the Course The aim of this course to introduce basic numerical methods which are used in some places of

Mathematic

Learning Outcomes

1)He/She is able to understand numerical methods for non-linear equations systems

2) He/She is able to understand numerical methods for eiagen vector and eiagen value problems

3) He/She is able to get a new outlook

4) He/She is able to learn to solve problems by means of different methods

5) He/She is able to use computer more effectively in Mathematic

Course Contents

Numerical methods for non-linear equations and equation systems, Solutions of linear equation

systems directly and by using consecutive methods, Numerical methods for eaigen vector and

eiagen value problems.

Wee

kly

Det

ail

ed

Cou

rse

Con

ten

ts

Week

TOPICS


1 Errors and Computer Arithmetic Telling, explanation and question-answer

2 Numerical methods for non-linear

equations: Fixed point Iteration Telling, explanation and question-answer

3

Numerical methods for non-linear

equations: Newton method and

convergence



equations: Regula Falsi method Telling, explanation and question-answer

5 FIRST EXAM


equations: Bisection method Telling, explanation and question-answer

7 Newton and simple Iteration for solution of

non-linear equations systems Telling, explanation and question-answer

8

Linear equations systems: Gauss

Elimination Method and Gauss Jordan

Method


9 Linear equation systems: LU

decomposition method Telling, explanation and question-answer

10 SECOND EXAM

11 Consecutive methods for linear equation

systems: Jacobi method Telling, explanation and question-answer

12 Consecutive methods for linear equation

systems: Gauss -Siedel method Telling, explanation and question-answer

13 Chracteristic value problems: Faddiev-

Leverrier method Telling, explanation and question-answer

14 Chracteristic value problems: Vianello

iterative approximation method Telling, explanation and question-answer

15 FINAL EXAM

16

Recommended or

Required Reading

[1]Applied Numerical Analysis, Curtis F. ,Patrick O. Wheatly, Addison-Wesley Publishing Company,

Canada,1984.

[2]Fen ve Mühendislik için Nümerik Analiz,Doç.Dr. Mustafa Bayram,Aktif Yayınevi, 2002,İstanbul

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100






15 3 45



15 3 45

Assignments 1 10 10

Project - - -




- - -

Mid-terms 2 7,5 15






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title APPLIED MATHEMATICS


Type of Course Unit Compulsory

Level of Course Unit Bachelor (First Cycle)


Theoretical (hour/week) -



Year of Study 4


delivered 7

Name of Lecturer



Prerequisities and co-requisities NO



Work Placement NO


Provide information about the main application areas of mathematics, to develop new

mathematical models and methods of broad utility to science and engineering; and

to make fundamental advances in the mathematical and physical sciences themselves

Learning Outcomes

1.At the and of this course you will be able to define Laplace and inverse Laplace

transformation

2.At the and of this course you will be able to apply characteristic of Laplace and inverse

Laplace transformation to diferensiel equations

3.At the and of this course you will be able to do mass accounts with the help of multi-storey

integrals

4. At the and of this course you will be able to use Guldin theorems and its applications

5. At the and of this course you will be able to use Fourier series and its applications

Course Contents

Definition of the Laplace and inverse Laplace transformation , its characteristics, its

applications to the diferensiel equations,work account making in the force fields,mass with the

help of multi-storey integrals, finding moment of the center of gravity and inaction, Guldin

theorems and its applications, Fourier series and its applications

Wee

kly

Det

ail

ed

Cou

rse

Con

ten

ts

Week

TOPICS


1 Definition of the Laplace and inverse

Laplace transformation


QUESTION TECHNIQUES

2 Definition of the Laplace and inverse



QUESTION TECHNIQUES

3 Characteristics of the Laplace and inverse



QUESTION TECHNIQUES

4 Characteristics of the Laplace and inverse



QUESTION TECHNIQUES

5 MİDTERM EXAM

6

Application of the Laplace and inverse

Laplace transformations to the diferensiel

equations


QUESTION TECHNIQUES

7

Application of the Laplace and inverse

Laplace transformations to the diferensiel

equations


QUESTION TECHNIQUES

8 Work account making in the force fields TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

9 Work account making in the force fields TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

10 MİDTERM EXAM

11

Mass with the help of multi-storey

integrals, finding moment of the center of

gravity and inaction


QUESTION TECHNIQUES

12 Finding moment of the center of gravity

and inaction,


QUESTION TECHNIQUES

13 Guldin theorems and its applications TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

14 Fourier series and its applications TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

15 Fourier series and its applications TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

16 FİNAL EXAM

Recommended or

Required Reading

A. Altın, Uygulamalı Matematik Ders Notları

B.İ. Yaşar, Uygulamalı Matematik

M.R. Spiegel, Laplace Transforms (Schaum's Outline Series)

E. Altan, Yüksek Matematiğe Giriş I ve II

E. C. Young, Vector and Tensor Analysis

N. Piskunov, Differential and Integral Calculus

B.M.Budak-S.V.Fomin, Multiple Integrals Field Theory and Series

M. R. Spiegel, Advanced Calculus (Schaum's Outline Series)

B. J. Rice, Applied Analysis for Physics and Engineers

C.R.Wylie, Advanced Engineering Mathematics

Assesements



Assignment 1 20

Project -


Seminar -

Quizzes -

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 1 15 15

Project - -




Mid-terms 2 7.5 15






Learning

Outcomes

Programme Outcomes


LO1 3 3 3 3 3

LO2 4 4 4 4 4

LO3 5 5 5 5 5

LO4 2 2 2 2 2

LO5 5 5 5 5 5

LO6 2 2 2 2 2

LO7 4 4 4 4 4

LO8 3 3 3 3 3



Course Unit Title BOUNDARY VALUE PROBLEMS








Year of Study 4


delivered 7

Name of Lecturer RESEARCH ASSISTANT OF MATHEMATIC DEPARTMENT






Work Placement NONE

Objectives of the Course Creating backround for Initial and Boundary Value Problems

Learning Outcomes

1)He/She is able to know Initial and Boundary Value Problems

2) He/She is able to know Basis existence and unique Theorem for Boundary Value Problems

3) He/She is able to relaise Initial Value Problems

4) He/She is able to attain knowledge abour Sturm Theory and Sturm Lioville Problem

5) He/She is able to make expansion of a function in terms of sequences of Orthogonal

Functions

Course Contents

Initial Value Problems, Existence and Uniques for Initial Value Problems, Boundary Value

Problems of second digit and some existence Theorems, Sturm Theory, Sturm Lioville

Problem, Orthogonal of characteristic functions, Expansion of a function in terms of sequences

of Orthonormal functions.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Initial Value Problems Telling, explanation and question-answer

2 Initial Value Problems Telling, explanation and question-answer

3 Basis existence and unique Theorem for

Initial Value Problems Telling, explanation and question-answer

4 Basis existence and unique Theorem for

Initial Value Problems Telling, explanation and question-answer

5 FIRST EXAM

6 Sturm Theory Telling, explanation and question-answer

7 Sturm Theory Telling, explanation and question-answer

8 Sturm Lioville Problem Telling, explanation and question-answer

9 Sturm Lioville Problem Telling, explanation and question-answer

10 SECOND EXAM

11 Orthogonal of characteristic functions Telling, explanation and question-answer

12 Orthogonal of characteristic functions Telling, explanation and question-answer

13 Expansion of a function in terms of

sequences of Orthonormal functions. Telling, explanation and question-answer

14 Expansion of a function in terms of

sequences of Orthonormal functions. Telling, explanation and question-answer

15 FINAL EXAM

16

Recommended or

Required Reading

1] S. L. Ross, Differential Equations, John Wiley, New York, 1974.

[2] W. Boyce and R. Diprima, Elementary Differential Equations and Boundary Value Problems, Wiley,

New York, 1969.

[3] P. B: Bailey, L. F. Shampine and P. E. Waltman, Nonlinear Two Point Boundary Value Problems,

Academic Pres, New York, 1968.

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100






15 3 45



15 3 45

Assignments 1 10 10

Project - - -




- - -

Mid-terms 2 7,5 15






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title FOURIER ANALYSES





Allocated 6




Year of Study 2


delivered 3

Name of Lecturer







Work Placement NONE

Objectives of the Course Explain and understand properties of fourier sequences and series

Learning Outcomes


1) Identify iner product spaces

2) Calculate the norm of a function

3) Understand fourier series and basic properties

4) Practice with fourier series

5) Calculate fourier integral

6) Understand the application areas of fourier analysis

Course Contents

Basic information, Inner product spaces, Norm of a function

Sets of orthogonal functions, Fourier series, Convergence of fourier series

Calculation of fourier series, Various fourier series, Various fourier series

Convergence properties, Perseval equation, Some convergence theorems, Applications of fourier

integrals

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Basic information Explaining Method, Questioning Method

2 Inner product spaces Explaining Method, Questioning Method

3 Norm of a function Explaining Method, Questioning Method

4 Sets of orthogonal functions Explaining Method, Questioning Method

5 Mid-Term Exam

6 Fourier series Explaining Method, Questioning Method

7 Convergence of fourier series Explaining Method, Questioning Method

8 Calculation of fourier series Explaining Method, Questioning Method

9 Various fourier series Explaining Method, Questioning Method

10 Mid-Term Exam

11 Various fourier series Explaining Method, Questioning Method

12 Convergence properties Explaining Method, Questioning Method

13 Perseval equation Explaining Method, Questioning Method

14 Some convergence theorems Explaining Method, Questioning Method

15 Applications of fourier integrals Explaining Method, Questioning Method

16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






1 10 10



- -

Assignments - -

Project - -




Mid-terms 2 7,5 15



Total Work Load / 30 (h) 4.33

ECTS Credit of the Course 6


Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title Integral Equations








Year of Study 4


delivered 7







Work Placement NONE

Objectives of the Course Teach Basic Theory of Integral Equation,method of Solutions and Applications of Integral Equations.

Learning Outcomes

1) Demonstrate basic knowledge of Mathematics, its scope, application, history,

problems, methods, and usefulness to mankind both as a science and as an

intellectual discipline

2) Relate mathematics to other disciplines and develop mathematical models for

multidisciplinary problems

3)Continuously develop their knowledge and skills in order to adapt to a rapidly

developing technological environment

4)Develop mathematical, communicative, problem-solving, brainstorming skills.

5)Demonstrate sufficiency in English to follow literature, present technical

projects and write articles.

Course Contents

Linear Integral Equations

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Fredholm equations. Concept of integral equations.


2

Fredholm operator and its degree. Iterated kernel. Method of successive approximations.


3

Volterra equation. Concept of resolvent. Integral equations with degenerated kernels.


4

General case of Fredholm equation. Conjugate Fredholm equation. Fredholm theorems. Resolvent. The case of several independent variables.


5 FIRST EXAM

6

The case of several independent variables. Equations with weak singularity. Continuous solutions of integral equations.


7 Riesz-Schauder equations. Telling, explanation and question-answer

8

Method of successive approximations for equations with conjugate bounded operators. Completely continuous operators.


9

Solution of Riesz-Schauder equations. Extension of Fredholm theorems. Symmetric integral equations. Symmetric kernels. Fundamental theorems on symmetric equations.


10

Theorem on existence of a characteristic constant. Hilbert-Schmidt theorem. Solution of symmetric integral equations


11 Bilinear series. Telling, explanation and question-answer

12 Boundary value problem for an ordinary differential equation.


13

Boundary value problem for an ordinary differential equation. Characteristic constants and proper functions of an ordinary differential operator. Proof the Fourier method


14

. Green function for the Laplace operator. Proper functions of the problem on vibrations of a membrane.


15 FINAL EXAM

16

Recommended or

Required Reading

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 1 10 10

Project - - -




Mid-terms 2 7,5 15






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title PLANE GEOMETRY I








Year of Study 4


delivered 7







Work Placement NONE

Objectives of the Course İntroducing basic concepts of Geometry and investigating special Theorems

Learning Outcomes

1)He/She is able to remember basic concepts of Geometry

2) He/She is able to learn Thales’s relations, Save’s Theorem and Menalaüs’s Theorem

3) He/She is able to undestand the relations of bisecting angle and median and Theorems of

bisecting angle and median

4) He/She is able to learn the properties of right trianle, isosceles triangle, equilateral triangle

and Pythagoras’s Theorem

5) ) He/She is able to understand area in trianle and circle-area relations of trianle

Course Contents

Basic concepts, angles , triangles, Thales’s relations, Save’s Theorem, Memalaüs’s Theorem,

median relations in triangle, the theorem of median, bisecting angle and its relations in triangle,

theorem of internal bisecting angle, triangles with respect to angles, triangles with respect to

sides, right trianle, isosceles triangle, equilateral triangle, Pythagoras’s Theorem, Ökhlid’s

relations, isosceles right triangle, area in triangle, circle-area relations in triangle.

Wee

kly

Det

ail

ed

Cou

rse

Con

ten

ts

Week

TOPICS


1 Basic concept and angles Telling, explanation and question-answer

2 Thales’ relations, Save’s theorem and

Menalaüs’s theorem Telling, explanation and question-answer

3 Median relations and theorem of median in

triangle Telling, explanation and question-answer

4 Bisecting angle relations and theorem of

bisecting triangle Telling, explanation and question-answer

5 FIRST EXAM

6 Theorem of internal bisecting angle and its

application in triangle Telling, explanation and question-answer

7 Triangles with respect to angles and

Triangles with respect to sides Telling, explanation and question-answer

8 Right trianle, isosceles triangle and

equilateral triangle Telling, explanation and question-answer

9 Pythagoras’s Theorem Telling, explanation and question-answer

10 SECOND EXAM

11 Ökhlid’s relation Telling, explanation and question-answer

12 Area of triangle and its applications Telling, explanation and question-answer

13 Circle of triangle and its applications Telling, explanation and question-answer

14 Circle-area relation of triangle Telling, explanation and question-answer

15 FINAL EXAM

16

Recommended or

Required Reading

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 1 10 10

Project - - -




Mid-terms 2 7,5 15






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title COMPLEX ANALYSIS II








Year of Study 4


delivered 8

Name of Lecturer



Prerequisities and co-requisities Advised to take the Complex Analysis I



Work Placement NO


To give a perspective on the topics of Integrations on complex plane,Complex power series,

Taylor and Laurent series,Classification of the singular points and Residue theorem, Calculation

of some real integrals with complex methods,The Argument principle

Learning Outcomes

1) At the and of this course you will be able to categorize the curves.

2 At the and of this course you will be able to calculate integral on complex plane.

3) At the and of this course you will be able to interpret the Cauchy-integral theorem and its

corollories.

4) At the and of this course you will be able to calculate serial expansions of functions

5) At the and of this course you will be able to categorize the singular points

6) At the and of this course you will be able to calculate the complex integrals by using Residue

theorem. with complex methods

7) At the and of this course you will be able to calculate the some real integrals by applying

complex methods.

Course Contents

Integration on complex plane, Complex power series, Taylor and Laurent series, classification

of the singular points and Residue theorem, Calculation of some real integrals with complex

methods,The Argument principle.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Integration on complex plane TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

2 Integration on complex plane TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

3 Complex power series TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

4 Complex power series TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

5 Midterm Exam

6 Taylor and Laurent series TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

7 Taylor and Laurent series TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

8 Classification of the singular points and

Residue theorem


QUESTION TECHNIQUES

9 Classification of the singular points and

Residue theorem


QUESTION TECHNIQUES

10 Midterm Exam

11 Calculation of some real integrals with

complex methods


QUESTION TECHNIQUES

12 Calculation of some real integrals with

complex methods


QUESTION TECHNIQUES

13 The Argument principle TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES


QUESTION TECHNIQUES


QUESTION TECHNIQUES

16 Final Exam

Recommended or

Required Reading

1.R.V.Churchill and J.W.Brown, Complex Variables and Applications ,McGraw-Hill Series in Higher

Mathematics, New York,1990.

2.M.R.Spiegel, Complex Variables, Schaum’s Outline Series in Mathematics-Statistics, McGraw-Hill



4.A.Kaya, Karmaşık Degişkenler ve Uygulamalar, çeviri:R.VChurchill, Milli Eğitim Bakanlığı Yayınları,

İstanbul, 1989. 5.T.Başkan, Kompleks Fonksiyonlar Teorisi, Vipaş A.Ş., Yayın sıra no:38, Dördüncü Baskı, Bursa, 2000.

Assesements



Assignment 5 20

Project -


Seminar -

Quizzes -

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 5 10 50

Project - -




Mid-terms 2 7.5 15






Learning



LO1 3 3 3 3 3

LO2 4 4 4 4 4

LO3 5 5 5 5 5

LO4 2 2 2 2 2

LO5 4 4 4 4 4

LO6 5 5 5 5 5

LO7 3 3 3 3 3

LO8 3 3 3 3 3



Course Unit Title DIFFERENTIAL GEOMETRY II





Allocated 6




Year of Study 3


delivered 5

Name of Lecturer







Work Placement NONE

Objectives of the Course The goal of this lesson is to develop knowledge about differential geometry of eager students.

Learning Outcomes


1) Define the concept of the curve,

2) Construct the Frenet frame of the curve,

3) Formulate the curvatures of the curve,

4) Categorize the tangent spaces at a point of the curve,

5) Calculate algebraic invariants of the curve,

6) Define and characterizes the types of the curves,

7) Cefine surfaces and hypersurfaces,

8) Calculate algebraic invariants of the surface,

Course Contents

Affine space, Euclides space, Topological space, metric space

Jacobian matrice and differentiable functions, Curves theorem, frenet vector spaces

Oscillator, normal and rectifian planes, Curvatures of curves, curvature circle

Curvature sphere, Tangent spaces, cotangent spaces, Directional derivative, covariant derivative

Gradient functions, divergance function, Rotational functions, Convection forms, structure

equations

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Surfaces , parametric curves of surface Explaining Method, Questioning Method

2 Tangent space of curve Explaining Method, Questioning Method

3 Differentiable function Explaining Method, Questioning Method

4 Directional derivative, vector field,

covariant derivative Explaining Method, Questioning Method

5 Mid-Term Exam

6 Gauss curvature and mean curvature Explaining Method, Questioning Method

7 Gauss curvature and mean curvature Explaining Method, Questioning Method

8 Planar and umbilic point Explaining Method, Questioning Method

9 Basic forms Explaining Method, Questioning Method

10 Mid-Term Exam

11 Gauss transform Explaining Method, Questioning Method

12 Metric and integral above surface Explaining Method, Questioning Method

13 Asymptotic and geodesic curve Explaining Method, Questioning Method

14 Congruent curves Explaining Method, Questioning Method

15 Congruent curves Explaining Method, Questioning Method

16 Final Exam

Recommended or


Assesements



Assignment 2 20

Mid-terms 2 80

Total 100



Grade

2 50


Success Grade 1 50

Total 100






15 3 45



15 3 45

Assignments 2 15 30

Project




Mid-terms 2 15 30






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title FUNCTIONAL ANALYSIS II








Year of Study 4


delivered 8

Name of Lecturer



Prerequisities and co-requisities Functional analysis I should be taken.



Work Placement NO


To teach the notions of operator theory. To transform a given problem to an operator equation.

To investigate existance, uniqueness and stability of the solution of an operator equation.

Classification of operators. To analyse the solution methods

Learning Outcomes

1) At the and of this course you will be able to distinguish linear and nonlinear operators.

2) At the and of this course you will be able to learn the classifications such as the concepts for

an operator of being bounded, continuous and compact.

3) At the and of this course you will be able to understand the solution of an operator equation.

4) At the and of this course you will be able to evaluate the solutions of integral equations,

differential equations and algebraic equations.

5) At the and of this course you will be able to understand the advantages of Hilbert spaces for

operators by using the properties of Hilbert spaces.

Course Contents Linear spaces. Dual spaces. Adjoint operators. Compact sets. Compact linear operator. Hilbert

adjoint operators on Hilbert spaces. The notions of spectrum and resolvant.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Linear spaces TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

2 Linear spaces TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES


QUESTION TECHNIQUES


QUESTION TECHNIQUES

5 Midterm Exam

6 Adjoint operators TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

7 Adjoint operators TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

8 Compact sets TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

9 Compact sets TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

10 Midterm Exam

11 Compact linear operator TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

12 Compact linear operator TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

13 Hilbert adjoint operators on Hilbert spaces TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES


QUESTION TECHNIQUES


QUESTION TECHNIQUES

16 Final Exam

Recommended or

Required Reading

1.R.V.Churchill and J.W.Brown, Complex Variables and Applications ,McGraw-Hill Series in Higher

Mathematics, New York,1990.

2.M.R.Spiegel, Complex Variables, Schaum’s Outline Series in Mathematics-Statistics, McGraw-Hill



4.A.Kaya, Karmaşık Degişkenler ve Uygulamalar, çeviri:R.VChurchill, Milli Eğitim Bakanlığı Yayınları,

İstanbul, 1989.

5.T.Başkan, Kompleks Fonksiyonlar Teorisi, Vipaş A.Ş., Yayın sıra no:38, Dördüncü Baskı, Bursa, 2000.

Assesements



Assignment 5 20

Project -


Seminar -

Quizzes -

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 5 10 50

Project - -




Mid-terms 2 7.5 15






Learning

Outcomes

Programme Outcomes


LO1 3 3 3 3 3

LO2 4 4 4 4 4

LO3 5 5 5 5 5

LO4 2 2 2 2 2

LO5 4 4 4 4 4

LO6 5 5 5 5 5

LO7 3 3 3 3 3

LO8 3 3 3 3 3



Course Unit Title NUMERICAL ANALYSIS II


Type of Course Unit ELECTİVE






Year of Study 4


delivered 8

Name of Lecturer






Work Placement NO


To Investigate, Discrete Structure Error Analysis, to Introduce Theorical and Applied

Informations About Error Analysis, Finite Difference, Difference Equations, Enterpolation,

Regression, Numerical Derivative and Integration, Numerical Solution to Differential Equation

Learning Outcomes

1) At the and of this course you will be able to investigate beheviour of discrete structure.

2) At the and of this course you will be able to learn error analysis.

3) At the and of this course you will be able to investigate non-linear equations.

4) At the and of this course you will be able to investigate non-linear equation systems.

5) At the and of this course you will be able to learn finite difference

Course Contents

Discrete Structure Error Analysis, Introduce Theorical and Applied Informations About Error

Analysis, Finite Difference, Difference Equations, Enterpolation, Regression, Numerical

Derivative and Integration, Numerical Solution to Differential Equation Systems, Numerical

Solution to Algebrical Equation Systems

Wee

kly

Det

ai

led

Cou

r

se

Con

t

ents

Week TOPICS


1 Discrete Structure Error Analysis TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

2 Discrete Structure Error Analysis TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

3 Introduce Theorical and Applied

Informations About Error Analysis


QUESTION TECHNIQUES

4 Introduce Theorical and Applied

Informations About Error Analysis


QUESTION TECHNIQUES

5 Midterm exam

6 Finite Difference TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

7 Finite Difference TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

8 Difference Equations TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

9 Difference Equations TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

10 Midterm exam

11 Enterpolation, Regression TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

12 Enterpolation, Regression TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

13 Numerical Solution to Differential

Equation Systems


QUESTION TECHNIQUES


Equation Systems


QUESTION TECHNIQUES


Equation Systems


QUESTION TECHNIQUES

16 Final exam

Recommended or

Required Reading

Course notes

Assesements



Assignment 1 20

Project -


Seminar -

Quizzes -

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 1 10 10

Project - -




Mid-terms 2 7.5 15






Learning

Outcomes

Programme Outcomes


LO1 3 3 3 3 3

LO2 4 4 4 4 4

LO3 5 5 5 5 5

LO4 2 2 2 2 2

LO5 5 5 5 5 5

LO6 2 2 2 2 2

LO7 4 4 4 4 4

LO8 3 3 3 3 3



Course Unit Title Axiomatic Geometry








Year of Study 4


delivered 7







Work Placement NONE


To construct system of axioms with their properties of “consistency” and “independency”, to develop ones ability towards systematic thinking, by examining all results which will be obtained from system of axioms at nearlinear spaces, projective spaces and Afin spaces and example of spaces satisfying these axioms

Learning Outcomes

1) He/She defines the basic concepts of motion geometry,

2) He/She compares structure of affine space with structure of Euclidean space,

3) He/She proves and interprets the theorems related to Euclidean space isometries,

4) He/She defines and classify the motions,

5) He/She solves the problems related to transformation groups,

6) He/She classify the isometries,

Course Contents

Axiomatic systems, near‐linear spaces, linear spaces, de Brujin‐Erdös theorem, commutative property, hyperplanes, projective spaces, subplanes, projective planes, affine planes, embedding of the affine plane into projective plane.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 The Affine Spaces Telling, explanation and question-answer

2 Affine Coordinate Systems Telling, explanation and question-answer

3 Affine transformation, Affine Group Telling, explanation and question-answer

4 Affine Subspaces Telling, explanation and question-answer

5 FIRST EXAM

6 Euclidean Spaces, Euclidean Coordinate

Systems Telling, explanation and question-answer

7 Euclidean Subspaces, Isometries Telling, explanation and question-answer

8 Introductory to transformation Telling, explanation and question-answer

9 Motions of Euclidean Space Telling, explanation and question-answer

10 Types of motions of plane, Translations Telling, explanation and question-answer

11 Rotations Telling, explanation and question-answer

12 Translations and Rotations resultant Telling, explanation and question-answer

13 Reflections, Telling, explanation and question-answer

14 Transflections. Telling, explanation and question-answer

15 FINAL EXAM

16

Recommended or

Required Reading

Assesements



Assignment 1 %20

Project NONE NONE


Seminar NONE NONE

Quizzes NONE NONE

Mid-terms 2 %80

Total 100


Grade %50


TOTAL 100








Assignments 1 10 10

Project - - -




Mid-terms 2 7,5 15






Learning

Outcomes

Programme Outcomes


LO1

LO2

LO3

LO4

LO5

LO6

LO7

LO8



Course Unit Title DİSCRETE MATHEMATİCS


Type of Course Unit ELECTIVE

Level of Course Unit BACHELOR(FIRST CYCLE)





Year of Study 4


delivered 8

Name of Lecturer






Work Placement NO


Math topics covered in this course various courses related to computer engineering

infrastructure constitutes the foundation of mathematics. Computer-related courses in general

are included in all programs with different content.

Learning Outcomes

1)At the and of thıs course you will be able to constitue System of Integers

2) At the and of thıs course you will be able to express Peano postulates

3) At the and of thıs course you will be able to express Fermat and chinese remainder theorems

4) At the and of thıs course you will be able to express Groups, Homomorphisms

5) At the and of thıs course you will be able to define mod congruence relation

Course Contents

System of Integers: Peano postulates. Noether order. Induction principle. Divisibility. Primes.

Relative primality. mod congruence relation. Fermat and chinese remainder theorems.

Generalized permutations and combinations. Stirling numbers. Generating functions:

Recurrence relations. Algebraic structures: Groups. Homomorphisms. Group codes. Polya s

method of enumeration. Rings . Galois fields. Cyclic codes.

Wee

kly

Det

ail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 System of Integers TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

2 Peano postulates TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

3 Noether order TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

4 Induction principle TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

5 Midterm exam

6 Divisibility TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

7 Relative primality TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

8 Mod congruence relation TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

9 Fermat and chinese remainder theorems TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

10 Midterm exam

11 Generalized permutations and

combinations


QUESTION TECHNIQUES

12 Stirling numbers TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

13 Recurrence relations TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES


QUESTION TECHNIQUES


QUESTION TECHNIQUES

16 Final exam

Recommended or

Required Reading

1) C.L.Liu, "Elements of Discrete Mathematics", McGraw Hill, 1987.

2) K.H. Rosen, "Discrete Mathematics and Its Applications", McGraw Hill, 1998.

3) H.F.Mattson.Jr., "Discrete Mathematics with Applications", John Wiley and Sons, 1993.

4) D.F.Stanat and D.F.McAllister, "Discrete Mathematics in Computer Science", Prentice Hall,1977.

5) R. P. Grimaldi, "Discrete and Combinatorial Mathematics", Addison - Wesley, 1985.

Assesements



Assignment 1 20

Project -


Seminar -

Quizzes -

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 1 10 10

Project - -




Mid-terms 2 7.5 15






Learning

Outcomes

Programme Outcomes


LO1 3 3 3 3 3

LO2 4 4 4 4 4

LO3 4 4 4 4 4

LO4 3 3 3 3 3

LO5 4 4 4 4 4

LO6 4 4 4 4 4

LO7 3 3 3 3 3

LO8 2 2 2 2 2



Course Unit Title INTRODUCTION TO CRYPTOLOGY








Year of Study 4


delivered 8

Name of Lecturer



Prerequisities and co-requisities Linear algebra and Algebra



Work Placement NO

Objectives of the Course Students should be able to demonstrate an understanding of some legal and socio-ethical issues

surrounding cryptography and overview of some of the classical cryptosystems

Learning Outcomes

1) At the and of this course you will be able to will be able to have an overview of some of the

classical cryptosystems

2 )At the and of this course you will be able to explain the fundamentals of cryptography, such

as encryption, digital signatures and secure hashes

3 )At the and of this course you will be able to select appropriate techniques and apply them to

solve a given problem.

4) At the and of this course you will be able to design and evaluate security protocols

appropriate for a given situation.

5) At the and of this course you will be able to demonstrate an understanding of the

mathematical underpinning of the cryptography.

Course Contents Algebraic structure, techniques of cryptography

Wee

kly

Det

ail

ed

Cou

rse

Con

ten

ts

Week

TOPICS


1 Classical cryptosystems TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

2 Classical cryptosystems TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

3 Fundamentals of cryptography TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

4 Fundamentals of cryptography TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

5 Midterm exam

6

Appropriate techniques and apply them to



QUESTION TECHNIQUES

7

Appropriate techniques and apply them to



QUESTION TECHNIQUES

8

Design and evaluate security protocols



QUESTION TECHNIQUES

9




QUESTION TECHNIQUES

10 Midterm exam

11




QUESTION TECHNIQUES

12 Algebraic structure TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

13 Algebraic structure TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

14 Mathematical underpinning of the

cryptography


QUESTION TECHNIQUES

15 Mathematical underpinning of the

cryptography


QUESTION TECHNIQUES

16 Final exam

Recommended or

Required Reading

Course notes

Assesements



Assignment 1 20

Project -


Seminar --

Quizzes -

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 1 10 10

Project - -




Mid-terms 2 7.5 15






Learning

Outcomes

Programme Outcomes


LO1 3 3 3 3 3

LO2 4 4 4 4 4

LO3 5 5 5 5 5

LO4 4 4 4 4 4

LO5 4 4 4 4 4

LO6 3 3 3 3 3

LO7 4 4 4 4 4

LO8 3 3 3 3 3



Course Unit Title MEASURE THEORY








Year of Study 4


delivered 8

Name of Lecturer



Prerequisities and co-requisities Analysis I-II-III-IV should be taken.



Work Placement NO


To teach the fundamental notions of the thoery of functions with a real variable. Infinite sets,

measurable sets, measurable functions, Lebesgue integral, the space of square integrable

functions.

Learning Outcomes

1) At the and of this course you will be able to define infinite sets, countable infinity,

continuum, and ordering of sets.

2) At the and of this course you will be able to explaine limit point, closed and open sets, and

accumulation point.

3) At the and of this course you will be able to calculate the measure of open and closed sets,

and the inner and outer measures of bounded sets.

4) At the and of this course you will be able to translate measurable functions and their

properties, and convergence in measure.

5 At the and of this course you will be able to calculate the Lebesgue integral of a function and

compare the Lebesgue integral with Riemann integral.

Course Contents Fundamental notions and theorems of the theory of functions with a real variable.

The analysis of the concepts of measure and integral. W

eek

ly D

etail

ed C

ou

rse

Con

ten

ts

Week

TOPICS


1 Fundamental notions of functions with a

real variable


QUESTION TECHNIQUES

2 Fundamental notions of functions with a

real variable


QUESTION TECHNIQUES

3 Fundamental theorems of functions with a

real variable


QUESTION TECHNIQUES

4 Fundamental theorems of functions with a

real variable


QUESTION TECHNIQUES

5 Midterm exam

6 The measure of open and closed sets TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

7 The measure of open and closed sets TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

8 Measurable functions TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

9 Measurable functions TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

10 Midterm exam

11 Lebesgue integral TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

12 Lebesgue integral TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES

13 Riemann integral TELL- STATEMENT METHOD ,ANSWER

QUESTION TECHNIQUES


QUESTION TECHNIQUES


QUESTION TECHNIQUES

16 Final exam

Recommended or

Required Reading

Course notes

Assesements



Assignment 1 20

Project -


Seminar -

Quizzes -

Mid-terms 2 80

Total 100


Grade 50


TOTAL 100








Assignments 1 10 10

Project - -




Mid-terms 2 7.5 15






Learning

Outcomes

Programme Outcomes


LO1 4 4 4 4 4

LO2 4 4 4 4 4

LO3 5 5 5 5 5

LO4 2 2 2 2 2

LO5 4 4 4 4 4

LO6 5 5 5 5 5

LO7 3 3 3 3 3

LO8 3 3 3 3 3


individual course description...kadıoğlu e. kamali m.-genel matematik,robert a.adams-calculus,...

Documents