MATH 450. Real Analysis.

COURSE SYLLABUS FALL 2011

Instructor: Azer Akhmedov

Office: Minard Hall, 428K

E-mail: azer.akhmedov@ndsu.edu

Office Hours: MW 2:00PM-2:50PM (or by appointment)

Phone: 231 8078.

CLASS MEETS: MWF 1:00PM-1:50PM, Dolve, Room 202.

TEXTBOOK: APOSTOL, Mathematical Analysis, 2nd Edition.

COURSE DESCRIPTION: real numbers, completeness, open and closed sets,

Bolzano-Weierstrass Theorem, coverings, Heine-Borel Theorem, compactness, metric

spaces, Cauchy sequences, limit of a function, continuity, uniform continuity, fixed point

theorem for contractions, derivatives, Taylor’s Theorem, infinite series, convergence

tests, sequences of functions, pointwise convergence, uniform convergence and

differentiation, bounded variation, curves and paths.

COURSE OBJECTIVE: The course is designed to give an introduction to the topics

that are presented but not proved rigorously in Calculus classes, and to provide

background required for more advanced courses in mathematics.

HOMEWORK:

The homeworks are assigned bi-weekly and are due every other Friday in class. These

assignments will be posted on Blackboard, in the section Assignments.

In order to fully understand the material covered in lecture, you are strongly encouraged

to work on all the homework problems. If you have difficulties with any of the homework

problems please see me as soon as possible.

EXAMS: There will be two in-class Midterm Exams and a cumulative Final Exam.

Books and calculators are not allowed in exams. You may use one 8”x10” notecard. The

exams are scheduled as follows

MIDTERM 1. – Friday, September 30th.

MIDTERM 2. – Wednesday, November 09th

.

FINAL EXAM – TBA

GRADING: For each student individually, I will choose the better of the following two

grading schemes:

SCHEME 1. Exam 1 – 15%, Exam 2 – 15%, HWK – 30%, Final – 40%

SCHEME 2. Exam 1 – 20%, Exam 2 – 20%, HWK – 30%, Final – 30%

COURSE POLICIES

ACADEMIC HONESTY: All work in this course must be completed in a manner

consistent with NDSU University Senate Policy, Section 335: Code of Academic

Responsibility and Conduct (http://www.ndsu.nodak.edu/policy/335/htm).

SPECIAL ACCOMODATIONS: The Americans with Disabilities Act requires that

reasonable accommodations be provided for students with disabilities or other special

needs. Students eligible for special accommodations are strongly encouraged to share

their concerns or requests with me at the beginning of the semester, or as soon as

possible. I will be happy to make appropriate arrangements.

CLASS ATTENDANCE: Class attendance is generally expected. If you cannot attend

a particular lecture, make sure that you stay informed regarding the information provided

during that lecture.

EXAMS: The three midterm exams and the final exam are to be written individually,

any collaboration is prohibited. There will be no makeup Final Exam. Makeup tests for

midterm exams will be given only in case of a legitimate (documented) excuse. The

student is required to inform me at least one week in advance if makeup is necessary.