**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.

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Last updated: Sep 4, 2006