### MATH 401/501 - HOMEWORK PROBLEMS - Fall 2006

Homework 1 (due 8/31/06) : (1) Show by induction that
1+4+9+16+...+ n^2 = n(n+1)(2n+1)/6.
(2) Exercises from Tao's Book: (p.33) 2.2.1; (p.36) 2.3.1.

Homework 2 (due 9/5/06): Exercises from Tao's Book:
(p.33) 2.2.2, 2.2.3;
(p.36) 2.3.2, 2.3.4, 2.3.5.

Homework 3 (due 9/12/06): Exercises from Tao's Book:
(p.52) 3.1.8, 3.1.9, 3.1.10;
(p.63) 3.3.2, 3.3.3, 3.3.4.

Homework 4 (due 9/19/06): Exercises from Tao's Book:
(p.63) 3.3.7;
(p.69) 3.4.2 (check 3.4.5);
(p.75) 3.5.4, 3.5.5 (you can substitute these problems by the harder problems 3.5.7 and 3.5.10);
(p. 82) 3.6.1, 3.6.9 (you can substitute these problems by the harder problems 3.6.6 and 3.6.10).

Homework 5 (due 9/28/06): Exercises from Tao's Book:
(p.92) 4.1.5, 4.1.6 (think about 4.1.8);
(p.98) 4.2.2., 4.2.4, 4.2.6;
(p.102) 4.3.5;
(p.106) 4.4.1.

Homework 6 (due 10/3/06): Exercises from Tao's Book:
(p.102) 4.3.2;
(p.114) 5.1.1

Homework 7 (due 10/10/06): Exercises from Tao's Book:
(p.117) 5.2.1, 5.2.2;
(p.127) 5.3.4, 5.3.5;

Homework 8 (due 10/17/06 Tuesday after Fall Break): Exercises from Tao's Book:
(p.133) 5.4.4 (Hint: 5.4.3 might be useful), 5.4.8;
(p.139) 5.5.1

Homework 9 (due 10/24/06): Exercises from Tao's Book:
(p.139) 5.5.1, 5.5.4;
(p.144) 5.6.2, 5.6.3

Homework 10 (due 10/31/06 Halloween!): Exercises from Tao's Book:
(p.152) 6.1.6, 6.1.8, 6.1.9

Homework 11 (due 11/7/06): Exercises from Tao's Book:
(p.169) 6.4.5, 6.4.6, 6.4.7, 6.4.9, 6.4.10 (two of these are examples of sequences that you must construct, they are not hard);
(p.171) 6.5.1;
(p.175) 6.6.3, 6.6.5.

Homework 12 (due 11/14/06): Exercises from Tao's Book:
(p.188) 7.1.5;
(p.195) 7.2.5, 7.2.6;
(p.200) 7.3.2;
You can replace the first four of the above problems by 7.1.3* and 7.1.4* (p. 188) (or replace two for one of them).
(p.207) 7.5.1, 7.5.2, 7.5.3.

Homework 13 (due 11/21/06): Exercises from Tao's Book:
(p.249) 9.1.1, 9.1.9, 9.1.13;
(p.253) 9.2.1;
(p.260) 9.3.1;
(p.265) 9.4.3, 9.4.4.

Homework 14 (due 11/28/06): Exercises from Tao's Book:
(p.273) 9.6.1;
(p.276) 9.7.2;
(p.278) 9.8.4, bonus 9.8.5* (Read and think: 9.8.1 and 9.8.2);
(p.286) 9.9.5.

Last Homework 15 (due 12/05/06): Exercises from Tao's Book:
(p.295) 10.1.6;
(p.298) 10.2.2 or 10.2.3, and 10.2.7;
(p.299) 10.3.2 or 10.3.3;
(p.302) 10.4.2;
(p.305) 10.5.2.