**Final Projects**

- Tuesday May 3, 2016
- 8:00-8:30

*Sets of measure zero. The 1/3 Cantor set. The Cantor function.*

Michael Sanchez, Jason Baker, Kyle Henke - 8:40-9:10

*Characterization of Riemann Integrable functions: continuous almost everywhere (except on a set of measure zero).*

Duc Nguyen

- 8:00-8:30
- Thursday May 5, 2016
- 8:00-8:30

*Completeness of metric spaces.*

Justin Campbell, Matt Robinson - 8:40-9:10

*Weierstrass Approximation Theorem.*(Section 14.8).

Peterson Moyo and Cindi Goodman

- 8:00-8:30
- Thursday May 12, 2016
- 7:40-8:10

*Ultrametric.*

Hanna Butler, Zach Stevens, Marshall Branderburg - 8:20-8:50

*Fourier series.*

Sarka Blahnik - 9:00-9:30

*Tempered distributions.*

Lionel Fiske, Cairn Overturf

- 7:40-8:10

**Homework 8 (due on Thursday April 28, 2016):** Do at least 5 problems
(Exercises 6.1.4 and 6.4.1 count like just one problem).

**Homework 7 (due on Thursday April 14, 2016)**

**Homework 6 (due on Thursday April 1st, 2016)**

**Homework 5 (due Tuesday March 8, 2016):** Do one exercise per section (4 total).

** Homework 4 (due Tuesday March 1st, 2016):**
Problems from Book II 3rd edition Chapter 1 (in earlier editions this is
Chapter 12). Do at least 4 of the given exercises.

** Homework 3 (Due Tuesday Feb 16, 2016)**

- Section 11.4: Exercise 11.4.2 (if f is continuous, positive, and Riemann
integrable, and it integral is zero then f must be zero).

- Section 11.6: Exercise 11.6.3 (integral test for series).

- Section 11.9: Exercise 11.9.2 (two antiderivatives of the same function must be equal up to a constant).

**Homework 2 (Due on Thursday Feb 4th, 2016)**

- Section 11.3: Exercise 11.3.5 (show only that upper Riemann integral is equal to the infimum of the upper Riemann sums).

- Section 11.4: Exercise 11.4.1 (a) and (d) only (integration laws: linearity and precursor of monotonicity).

**Homework 1 (due on Tue 1/26/2016):**
Exercises from Tao's Book I (hardcover edition), Chapter 11 on Riemann Integration:

- Exercise 11.1.2 (intersection of two bounded intervals is
a bounded interval),

- Exercise 11.1.4 (P1#P2 is a partition and a common refinement for both P1 and P2)
- Exercise 11.2.2 (only show if f,g are piecewise constant (p.c.) on I then max(f,g) is p.c. on I),
- Exercise 11.2.4(g)(h) (laws of p.c. integration).

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Last updated: January 29, 2016