Math 470/770: Real Analysis II, Spring 2012
Instructor: Sergei Ovchinnikov, TH 931, office hours: TuTh 7:00-8:00, 11:00 - 12:00, phone: 81387, e-mail: sergei@sfsu.edu (please restrict the use of email and voicemail only to important matters).
Textbook: An Introduction to Analysis, Forth Edition, by William Wade.

Prerequisite: MATH 370 with a grade of C or better.

Bulletin Description: Sequences and series of functions, uniform convergence, real-analytic functions, metric spaces, open and closed sets, compat and connected sets, continuous functions. (Paired with MATH 770. Students who have completed MATH 770 may not take MATH 470 for credit.)

Course Objectives: The principal aim of Real Analysis II is for students to learn how to carry out a rigorous analysis of the convergence of infinite series of numbers and functions. They are expected to understand and apply the major theorems involving metric spaces. Students learn to solve problems using the concepts of analysis. They present their solutions as rigorous proofs written in correct mathematical English. Students will be able to devise, organize and present brief (half-page) solutions based on definitions and theorems of analysis.

Course Requirements: Students will submit written homework on a regular basis. Homework assignments will require student to read the text or other sources, provide proofs or counter-examples of propositions, explore examples, and make conjectures. Beyond the work required in MATH 470, students in MATH 770 will be required to write a paper on an approved advanced topic that makes use of multi-variable analysis. MATH 470 and 770 are paired. Students who have completed one of the two for credit may not take the other course for credit.

Evaluation of Students: Students will be graded on their ability to devise, organize and present in correct mathematical English rigorous solutions to assignments and problems on exams. While instructors may design their own methods of evaluating student performance, these methods include in-class examinations and homework assignments.

Course Outline:

  1. Chapter 7. Infinite Series of Functions (Sections 1 - 4)
  2. Chapter 10. Metric Spaces (Sections 1 - 6)
  3. Chapter 11. Differentiability on R^n (Sections 1 - 6)
Homework is the most important part of your studies. Homework assignments will be given on a regular bases. The homework grades will count 70% of your grade.

There will be three midterms (one per chapter) and no final exam.

Policy on make-ups: Make-up exams will be given for serious documented reasons or by a prior arrangement.

Students with disabilities who need reasonable accommodations are encouraged to contact the instructor. The Disability Programs and Resource Center (DPRC) is available to facilitate the reasonable accommodations process. The DPRC is located in the Student Service Building and can be reached by telephone (voice/TTY 415-338-2472) or by email (dprc@sfsu.edu).

Dropping, Withdrawing & Grading Option Procedures

Academic Senate Policy on the Observance of Religious Holidays see also InterfaithCalendar

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