Real Analysis

Math 230A, Fall 2010

Disclaimer: Probability of errors within files is non-trivial.

Real Analysis, by Walter Rudin

Date Content Homework Solutions
Wed 9/1/10

Rudin
Ch. 1, pp 1-5

Lecture Notes

Motivation for Example 1.1

HW 1

HW 1b

1.1 p. 21 #1 - 7

HW 1, Week 1 Practice Problems
(posted 9/13/10)

Week 2
Mon 9/6/10
Labor Day    
Wed 9/8/10

Rudin
Ch. 1, pp 5, 7, 8, 17-21
Construction of R.

Lecture Notes

HW 2

 

HW 2, Week 2 Practice Problems
(posted 9/15/10)

Week 3
Mon 9/13/10

Rudin
Ch. 1, p. 9, 19
Thm 1.20, Thm 1.21

Lecture Notes

   
Wed 9/15/10

Rudin
Ch. 1, p11, 12, 16
Matrix representation of complex numbers

Lecture Notes

   
Week 4
Mon 9/20/10

Rudin
Ch. 1, p16
Thm 1.37
Young's Ineq, Holder's Ineq., Minkowskie Ineq.
Ch. 2, pp 24, 25

Lecture Notes

HW 3 HW 3, Week 3 Practice Problems
(posted 9/24/10)
Wed 9/22/10

Rudin
Ch. 2 p. 25
Defn 2.4 finite, countable, ...

Lecture Notes

Inequalities Study Guide

HW 4 HW 4, Week 4, Practice Problems
(posted 10/4/10)
Week 5
Mon 9/27/10

Review for Exam
Defn cardinality, "≤"

Lecture Notes

HW 5 HW 5, Week 5, Practice Problems
(posted 10/4/10)
Wed 9/29/10 Exam 1    
Week 6
Mon 10/4/10

Rudin
Ch. 2 pp 26-30
Thms 2.8, 2.12, 2.13, 2.14
Schroder-Bernstein Thm

Lecture Notes

HW 6 HW 6, Week 6, Practice Problems
(posted 10/11/10)
Wed 10/6/10

Rudin
Ch. 2 pp 30, 32
Defn 2.15, 2.18, Thm 2.20
cardA < cardP(A)

Lecture Notes

   
Week 7
Mon 10/11/10

Rudin
Ch. 2 pp 32 - 24
Defn 2,18, Thms 2.19, 2.22, 2.23, 2.24

Lecture Notes

HW 7 HW 7, Week 7, Practice Problems
(posted 10/29/10)
Wed 10/13/10

Rudin
Ch. 2 pp 34, 35
Thm 2.24, 2.27, Defn 2.26
Cantor Set

Lecture Notes

   
Week 8
Mon 10/18/10

Rudin
Ch. 2 pp 35 - 37
Defn 2.31, 2.32, Thm 2.30, 2.33, 2.34

Lecture Notes

HW 8 HW 8, Week 8, Practice Problems
(posted 10/26/10)
Wed 10/20/10

Rudin
Ch 2 pp 37, 38
Thms 2.35, 2.36, 2.37

Lecture Notes

   
Week 9
Mon 10/25/10

Rudin
Ch 2 p 40
Thm 2.41

Lecture Notes

HW 9 HW 9, Week 9, Practice Problems
(posted 10/30/10)
Wed 10/27/10

Rudin
Ch 2 pp 41 - 43
Thms 2.43, 2.47, Defn 2.45 Connected Sets

Lecture Notes

   
Week 10
Mon 11/1/10
Review for Exam 2    
Wed 11/3/10 Exam 2    
Week 11
Mon 11/8/10

Rudin
Ch 3pp 47 - 50
Defn 3.1, Thms 3.2, 3.3

Lecture Notes

   
Wed 11/10/10

Rudin
Ch 3 pp 50-52
Thms 3.4, 3.5, 3.6, 3.7
Defn Subsequence, Cauchy Sequence

Lecture Notes

HW 10 HW 10, Week 11, Practice Problems
(posted 11/24/10)
Week 12
Mon 11/15/10

Rudin
Ch 3 pp 53 - 55
Thms 3.11, 3.14
Defns Monotonic, Complete Metric Space

Lecture Notes

   
Wed 11/17/10

Rudin
Ch 3pp 56, 57
Defn Upper/Lower Limit
Thms 3.17, 3.19, 3.20

Lecture Notes

HW 11

HW 11b

HW 11, Week 12, Practice Problems

HW 11b, Week 12, Rudin Exercises

Week 13
Mon 11/22/10

Rudin
Ch 3 pp 58 - 61
Defn 3.21, Thms 3.22, 3.23, 3.24, 3.45, 3.25, 3.26

Lecture Notes

   
Wed 11/24/10

Rudin
Ch 3 pp 61 - 66
Thms 3.27, 3.28, 3.29, 3.31, 3.32, 3.33, 3.34

Lecture Notes

HW 12

HW 12b

HW 12, Week 13, Rudin Exercises

HW 12, Week 13, Practice Problems

Week 14
Mon 11/29/10

Rudin
Ch 3 pp 68 - 69
Thms 3.37, 3.39, Defn 3.38

Lecture Notes

   
Wed 12/1/10

Rudin
Ch 3pp 71 - 75
Thms 3.43, 3.44, 3.48, 3.50

Lecture Notes

HW 13 HW 13, Week 14, Practice Problems
Week 15
Mon 12/6/10

Rudin
Ch 3 pp 75 - 78
Thms 3.50, 3.55

Lecture Notes

   
Wed 12/8/10      
Mon 12/13/10 Final Exam 3:00pm