Math 202B - Intro to Topology and Analysis - Spring 2014

Coordinates

Lectures: MWF 9:00-10:00, Room 70 Evans Hall


Instructor: Michael Christ 809 Evans Hall, 642-2143. mchrist@berkeley.edu

Office hours: M 10:30--11:30, T 10-11 in 809 Evans


Course assistant: Thanh Vu, vqthanh@berkeley.edu, 1041 Evans Hall. Office hours T 1-2, F 11-12.


Text, syllabus, prerequisites, dates: See course policies announcement. 
Problem Sets
  1. Problem Set 1  (due Wednesday 1/29).
  2. Problem Set 2  (due Wednesday 2/5).
  3. Problem Set 3  (due Friday 2/14).
  4. Problem Set 4  (due Wednesday 2/19).
  5. Problem Set 5  (due Wednesday 2/26).
  6. Problem Set 6  (due Wednesday 3/5).
  7. Solutions for problem sets 1 through 6, and 9, are now posted at the designated location.
  8. Problem Set 7  (due Friday 3/14).
  9. Problem Set 8  (due Wednesday 3/19).
  10. Problem Set 9  (due Wednesday 4/2).
  11. Problem Set 10  (due Wednesday 4/9).
  12. Problem Set 11  (due Wednesday 4/16).
  13. Problem Set 12  (due Wednesday 4/23).
  14. Problem Set 13  (due Friday 5/2).
Lecture Notes
  1. Topic 1: Products of measure spaces
  2. Topic 2: Lebesgue measure and integration on Euclidean space of dimension greater than one
  3. Topic 3: Normed vector spaces
  4. Topic 4: Baire's Theorem, and applications
  5. Topic N+1: The Riesz Representation Theorems This also includes the conclusion of the discussion of the dual of L^p.
  6. Topic N+2: Fourier Analysis: Convolution
  7. Topic N+3: Fourier Transform
  8. Topic N+4: Pointwise Convergence of Fourier Series
  9. Topic N+5: Averages, Differentiation of Integrals, and the Maximal Function

Reading assignments
  1. Folland sections 2.5 and 2.6.
  2. Section 2.7 (Little class time will be devoted to this section, so please do read it.)
  3. Sections 5.1 and 5.2
  4. Section 5.3
  5. Section 5.4
  6. Section 5.5
  7. Sections 6.1 and 6.2
  8. Section 7.1.
  9. Sections 7.2 and 7.3.
  10. Sections 8.1 and 8.2.
Exam info
  • Solutions for midterm exam
  • 2013 Final Exam (for use as a sample or practice exam)
  • Solutions for final exam
  • The final exams are graded. Scores (out of 102) were 97, 92, 89. 88, 86, 83, 80, 76, 69, 66, 62, 54, 46, 31. Course grades have been submitted (2 A+, 4A, 2A-, 3B+, 3B).


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