Math 202A – Fall 2010

Introduction to Topology and Analysis

Instructor: Atilla YILMAZ

Contact info: atilla@math

Teaching assistant: Hung TRAN

Lectures: MWF 10:10 am - 11:00 am, 70 EVANS

Office hours: Wednesdays 11:00 am -12:00 pm and 1:00 pm - 3:00 pm, 796 EVANS

Prerequisites: Math 104 or equivalent, plus familiarity with basic set theory and linear algebra.

Required Text: G. B. Folland, Real Analysis, Second Edition, Wiley Interscience, 1999.

Recommended Reading: H. L. Royden, Real Analysis, Third Edition, Prentice Hall, 1988.

Syllabus: Chapters 1-5 of Folland. (Measures; integration; signed measures and differentiation; point set topology; elements of functional analysis.) Additional topics if time permits.

Grading: Homework 40%, midterm exam 20%, final exam 40%.

Important dates: If the midterm exam date is problematic for you, please contact the instructor as soon as possible.

• Friday, August 27: First lecture
• Monday, September 6: No lecture
• Friday, October 15: No lecture
• Monday, October 18: Midterm exam
• Friday, November 26: No lecture
• Friday, December 3: Last lecture
• Monday, December 13: Final exam

Make-up policy:

• There will be no make-up exams. If you miss the midterm exam, then the final exam will determine 60% of your grade.
• If you miss the final exam, your final exam grade will be zero.

Homework policy:

• Weekly homework will be posted to this page every Friday. You will hand in your homework at the end of the following Friday lecture. Late homework will not be accepted. There will be no exceptions. However, the lowest three of your homework grades will be dropped.
• The problems will be chosen from Folland.

Typos: Please click here for a list of errata for the textbook. Some of the typos appear in exercises. Please make sure that you correct them.

Homework problems:

• Due September 10: (from Folland, 2nd edition) exercises 1, 3, 4, 5 from Chapter 1. (I decided not to assign exercise 2.)
• Due September 17: (from Folland, 2nd edition) exercises 8, 12, 14, 17 from Chapter 1.
• Due September 24: (from Folland, 2nd edition) exercises 18, 23, 27, 30 from Chapter 1.
• Due October 1: (from Folland, 2nd edition) exercises 4, 7, 11, 13, 16 from Chapter 2.
• Due October 8: (from Folland, 2nd edition) exercises 20, 21, 23, 26, 28c, 28d from Chapter 2.
• Due October 22: (from Folland, 2nd edition) exercises 32, 33, 42, 46, 50 from Chapter 2. (See the errata sheet for corrections regarding exercise 50.)
• Due October 29: (from Folland, 2nd edition) exercises 2, 3, 4, 6 from Chapter 3. (See the errata sheet for a correction regarding exercise 6.)
• Due November 5: (from Folland, 2nd edition) exercises 10, 11, 12, 17 from Chapter 3.
• Due November 12: (from Folland, 2nd edition) exercises 22, 24, 25, 26 from Chapter 3.
• Due November 19: (from Folland, 2nd edition) exercises 30, 31, 32, 39, 42 from Chapter 3.
• Due December 3: (from Folland, 2nd edition) exercises 2, 3, 6, 7, 8, 10 from Chapter 4. (On November 24, I will assign another set of problems which will also be due December 3.)
• Also due December 3: (from Folland, 2nd edition) exercises 17, 21, 24, 26, 29 from Chapter 4.
• Not to be turned in: (from Folland, 2nd edition) exercises 38, 39, 61, 63 from Chapter 4.