**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