### MATH 402/502 - HOMEWORK PROBLEMS - Spring 2007

Homework 0: Do (or redo) the final exam for Math 401/501 Fall 2006. Solutions Final 401/501 due to Matthew Straughn.

Team/individual work 1: Properties of Riemann Integrals from Tao's book I, Chapter 11.
Theorem 11.4.1 (a,b,c) Linear Properties due to Matthew Straughn.
Theorem 11.4.3 Closed under min due to Peterson Moyo and Joshua Abrams.
Theorem 11.4.1 (g) Closed under extension due to Jorge Piovesan.
Theorem 11.4.1 (h) Closed under restriction due to Hyunjung Ra and Brian Nease.
Exercise 11.4.2 Solution due to Sara Pollock.
Exercises 11.5.1: Bounded piecewise continuous functions are integrable by Dave Flores and Amanda Towsend.
Exercises 11.6.3, 11.6.4 and 11.6.5: Integral test by Anatoly Kobozev.
Exercise 11.10.1: Integration by parts by Teresa Evans.

Homework 1 (due 2/15/07): Solutions compiled by Matthew Straughn.
Exercises from Tao's Book II:
(p.398-99) 12.1.3, 12.1.5, 12.1.6, 12.1.12, 12.1.15.

Homework 2 (due 2/22/07): Solutions compiled by Matthew Straughn.
Exercises from Tao's Book II:
(p. 405) 12.2.3, 12.2.4;
(p. 408) 12.3.1;
(p. 411) 12.4.7.

Homework 3 (due 3/1/07): Solutions compiled by Matthew Straughn.
Exercises from Tao's Book II:
(p. 417-19) 12.5.4, 12.5.5, 12.5.12, 12.5.13

Team/individual work 2:
Integration exercise in Analysis qualifying Jan 2007 Solution compiled by Matthew Straughn.
Topology Tao's book II, Chapter 12.
(p.412) 12.4.8 Completion of metric spaces by Josh Beach.
(p. 418) 12.5.10 Totally bounded (Josh Beach).

Homework 4 (due 3/9/07): Solutions Exercises from Tao's Book II:
(p. 417-19) Choose four out of:
(p. 422) 13.1.4
(p.425-426) 13.2.4, 13.2.6, 13.2.8, 13.2.9-13.2.11

Homework 5 (due 3/27/07): Solutions Exercises from Tao's Book II (choose 4 out of the following):
(p. 429) 13.3.5, 13.3.6
(p.432) 13.4.1, 13.4.2, 13.4.7*, 13.4.9
(p. 448-449) 14.2.1, 14.2.2

Homework 6 (due 4/3/07): Solutions Exercises from Tao's Book II (choose 4 out of the following):
(p. 452) 14.3.3, 14.3.4, 14.3.5, 14.3.8
(p.455) 14.4.3*
(p. 458) 14.5.3
(p. 460) 14.6.1
(p. 472) 14.7.2*

Homework 7 (due 4/17/07): Exercises from Tao's Book II (choose 4 out of the following):
(p. 540) 17.1.2, 17.1.4
(p. 552) 17.3.4
(p. 555) 17.4.3*, 17.4.4, 17.4.5
(p. 558) 17.5.1

Homework 8 (due 5/1/07): Exercises from Tao's Book II:
(p. 560-61) 17.6.1-17.6.4, 17.6.8
(p. 567) 17.7.1, 17.7.3

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Last updated: Feb 15, 2007