Institution : College of Science at Zulfi, Majmaah University. Academic Department : Department of Mathematics. Programme : Bachelor degree of mathematics. Course : Group Theory Math 343 Course Coordinator : Dr Rabah Kellil Programme Coordinator : Dr Rabah Kellil Course Specification Approved Date : 20/ 12 / 1435 H

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A. Course Identification and General Information 1 - Course title : Group Theory. Course Code: MATH343 2. Credit hours : (3+1) 3 - Program(s) in which the course is offered: Bachelor degree of Mathematics 4 – Course Language : English.

5 - Name of faculty member responsible for the course: Dr Rabah Kellil 6 - Level/year at which this course is offered : 6th 7 - Pre-requisites for this course (if any) :

MATH231 8 - Co-requisites for this course (if any) :

............................................................. 9 - Location if not on main campus :

)............................................................. ( 10 - Mode of Instruction (mark all that apply) A - Traditional classroom √ What percentage? 90 %

B - Blended (traditional and online) What percentage? ……. %

D - e-learning What percentage? ……. %

E - Correspondence What percentage? ……. %

F - Other √ What percentage? 10 %

Comments : ...........................................................................................................

B Objectives

What is the main purpose for this course? The student should be at the end of the course be familiar with abstract structures. Should have a good background on the different Group Axioms and can work with the simplest examples of groups. He should know all the principals on symmetric groups. Should apply Lagrange's Theorem, construct Cyclic , Conjugacy classes and apply the class equation. He should be able to apply the isomorphism theorems and Cayley's Theorem. The p-groups, Cauchy’s Theorem, Sylow’s Theorems will be applied to determine the different subgroups of a given group when it is possible or at least their nature. Burnside’s theorem, Dihedral groups, Quaternion's groups will be an illustration of particular groups and the student should be able to master. Briefly describe any plans for developing and improving the course that are being implemented : The course is self contained and doesn’t need to be changed. However the part (Burnside’s theorem, Dihedral groups, Quaternion's groups) can be deleted as it can be developed in a specialised course in Master’s degree studies.

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C. Course Description

1. Topics to be Covered List of Topics No. of

Weeks Contact Hours

Definitions and examples of groups , subgroups, Lagrange’s theorem.

2 8h

Normal subgroups, quotient (or factor) groups, cyclic groups,

1 4h

Mid-term 1 50mn. homomorphism, Isomorphism’s theorems, Automorphism, Cayley ‘s theorem and its generalization

2 8h

Simple groups Symmetric groups Sn

and properties, Group action on a set, Classes equation. 2 8h

Mid-term 2 50mn p-groups, Cauchy’s theorem, Solow's theorems 2 8h External and internal product of groups, 1 4h Burnside’s theorem, Dihedral groups, Quaternion's groups,

2 8h

Groups of automorphisms of a finite and infinite groups.

2 8h

Final Exam 2h 2. Course components (total contact hours and credits per semester):

Lecture Tutorial Laboratory Practical Other: Total

Contact Hours 39 13 ............ ............ 4 56

Credit ............ ............ ............ ............ ............ 4Credits Hours .

3. Additional private study/learning hours expected for students per week. 6

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4. Course Learning Outcomes in NQF Domains of Learning and Alignment with Assessment Methods and Teaching Strategy

NQF Learning Domains And Course Learning Outcomes

Course Teaching Strategies

Course Assessment

Methods 1.0 Knowledge 1.1 State the axioms defining a group. We first introduce new

notions, give examples from the simple ones (numbers sets) to those related to matrices, functional sets, we establish the attached properties, we give and prove different theorems related to those notions. Finally we construct new examples and concepts. To well fix the principal facts, homework is proposed.

-MCQ on principal theorems -Proving additional notions that can been elaborated from the general study -In general we introduce a short question to control the ability of the student to make the relationship between all the parts of the course.

1.2 Deduce simple statements from these axioms. 1.3 Provide examples of groups. 1.4 Determine the image and the kernel of a group

homomorphism. 1.5 State, prove and apply some of the classical theorems of

elementary Group Theory. 1.6 State, prove and apply some of the classical theorems of

symmetric groups and be able to deduce the table of any symmetric group and to decompose a permutation as a product of cycles of disjoint support and then to determine the order and the inverse of the given permutation.

1.7 Classify finitely generated Abelian groups.

2.0 Cognitive Skills 2.1 The ability to recognize a group structure. Explanations and examples

given in lectures. Short questions and discussion during the tutorial class+ short quizzes.

2.2 The ability to design new groups, to define their subgroups and to distinguish the normal ones.

Guidance and supervision of the work developed in tutorial classes.

..................

2.3 The ability to make calculus with any permutation and to extract its principal properties.

By using many examples ..................

2.4 To compare two group structures using the isomorphism theorems.

We use Isomorphism Theorems

..................

2.5 To discover that a group can be seen as a geometrical object (the action of a group on a set and representation).

Some examples ..................

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NQF Learning Domains And Course Learning Outcomes

Course Teaching Strategies

Course Assessment

Methods 2.6 To understand that a finite group can be seen as a

subgroup of the well known symmetric group Sn for a certain n.

Apply Cayley’s theorem to particular construction

..................

3.0 Interpersonal Skills & Responsibility 3.1 The ability to use MAPLE to solve some question relative to

subgroups of finite group We show that MAPLE can solve many mathematical problems and show how MAPLE works.

..................

3.2 The ability to write a mathematical text in word. We explore the different sub-packages of the software.

..................

3.3 .................. .................. 3.4 .................. .................. 3.5 .................. .................. 3.6 ..................................................................... .................. .................. 4.0 Communication, Information Technology, Numerical 4.1 The ability to communicate using computer We show that MAPLE can

solve many mathematical problems and show how MAPLE works. We explore the different sub-packages of the software.

.................. 4.2 - The ability to write a document in send it to whom it concerns

and with different text editor with respect to the document. ..................

4.3 ..................................................................... .................. .................. 4.4 ..................................................................... .................. .................. 4.5 ..................................................................... .................. .................. 4.6 ..................................................................... .................. .................. 5.0 Psychomotor 5.1 The ability to work on a computer .................. To control the

document produced by the student, the results obtained for the exercises proposed.

5.2 The ability to write a document in some text editor as word. ..................

5.3 .................. .................. 5.4 ..................................................................... .................. .................. 5.5 ..................................................................... .................. .................. 5.6 ..................................................................... .................. .................. 5. Schedule of Assessment Tasks for Students During the Semester:

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Assessment task Week Due Proportion

of Total Assessment

1 Midterm exams 3. 15.

2 Midterm exams 10 15

3 Final exams 15 60

4 Home Works MCQ and Quizzes. 2, 4,6,8,12 10.

5 ......................................................................... ................ ....................

6 ......................................................................... ................ ....................

7 ......................................................................... ................ ....................

8 ......................................................................... ................ ....................

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D. Student Academic Counseling and Support Assumed by the Academic Advising Unit of the College E. Learning Resources 1. List Required Textbooks : - Group theory, W.R. Scott, Dover, 2010, ISBN 0486653773, 13: 9780486653778. - Introduction to Group Theory, Oleg Bogopolski, TU Dortmund, Germany, 2008, ISBN 978-3-03719-041-8

2. List Essential References Materials : ............................................................. ............................................................. ............................................................

3. List Recommended Textbooks and Reference Material : 1. For general group theory, my favorite reference is Rotman's book.

2. For arithmetic groups (here there is some overlap with answer 3), I like Dave Witte Morris's book on the subject (it's not in print yet, but it is available on his webpage).

3. For some particular view of groups as a geometric object , the favorite references are Bourbaki's volume on the subject and Mike Davis's "The Geometry and Topology of Coxeter Groups".

4. For geometric group theory, in addition to the wonderful book of Bridson and Haefliger that Henry mentioned, I like Pierre de la Harpe's book on the subject (mostly for the amazing bibliography).

5. For the symmetric group, I really like G. D. James's "The Representation Theory of the Symmetric Groups".

4. List Electronic Materials : ..........................................

5. Other learning material : Next my home page on University e-learning system. ......................................................... .... ............................................................

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F. Facilities Required 1. Accommodation

1 class room for 25 students. 1 Mathematical Lab with 25 computers equipped with MAPLE software

2. Computing resources 1 Mathematical Lab with 25 computers equipped with MAPLE software ............................................................. ............................................................

3. Other resources ............................................................. .. ........................................................... ............................................................

G Course Evaluation and Improvement Processes 1 Strategies for Obtaining Student Feedback on Effectiveness of Teaching: Made by the evaluation and examination committee of the college ............................................................. ............................................................

2 Other Strategies for Evaluation of Teaching by the Program/Department Instructor : ............................................................. ............................................................. ............................................................

3 Processes for Improvement of Teaching : ............................................................. ............................................................. ............................................................

4. Processes for Verifying Standards of Student Achievement ............................................................. ............................................................. ............................................................

5 Describe the planning arrangements for periodically reviewing course effectiveness and planning for improvement :

Each semester the results of the students are studied to determine eventually the part of the course which need to be improved, changed or to be more illustrated. ............................................................. ............................................................

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Course Specification Approved

Department Official Meeting No ( ….. ) Date … / …. / ….. H

Course’s Coordinator Department Head Name : Dr Rabah Kellil. Name : .......................... Signature : ........................... Signature : .......................... Date : …./ … / …… H Date : …./ … / …… H