### MATH 401/501 - HOMEWORK PROBLEMS - Fall 2010

Homework 1 (due Th 9/2/10):
(1) Show by induction that
1+4+9+16+...+ n^2 = n(n+1)(2n+1)/6.
(2) Show by induction that n^2 <= 2^n for all n>3.
(3) Exercise from Tao's Book: (p.32 2nd ed, p.36 1st ed) 2.3.1.

Homework 2 (due Th 9/9/10):
Exercises from Tao's Book: 2.2.3(c)(d)(e) [p.29 2nd ed, p.33 1st]; and 2.3.5 [p.32 2nd ed, p.36 1st ed]

Homework 3 (due Th 9/16/10):
Exercises from Tao's Book: 3.1.6(f)(g)(h) [p.46 2nd ed, p.51 1st ed. Do only the first equality for (f) and (h)];
3.3.2, 3.3.5, 3.3.7 [p.55-56 2nd ed, p.63 1st ed]
and 3.4.2 [p.61 2nd ed, p.68 1st ed]

Homework 4 (due Th 9/23/10):
Exercises from Tao's Book: 3.5.4 [p.66 2nd ed, p.75 1st ed. Do only the first set equality];
3.6.4(e), 3.6.5, 3.6.9 and you can do 3.6.6 as a bonus [p.71 2nd ed, p.82 1st ed]

Homework 5 (due Th 9/30/10):
Exercises from Tao's Book: 4.1.2, 4.1.3, 4.1.5, 4.1.6 [p.80 2nd ed, p.92 1st ed.];
4.2.4, 4.2.6 [p.85 2nd ed, p.98 1st ed]

Homework 6 (due Tu 10/12/10):
Exercises from Tao's Book: 4.3.2, 4.3.3(c), 4.3.4 (b) [p.89 2nd ed, p.102 1st ed.];
4.4.1, 4.4.2 (bonus) [p.92 2nd ed, p.106 1st ed]
5.1.1 (bonus) [p.99 2nd ed, p.114 1st ed.]

Homework 7 (due Th 10/21/10):
Exercises from Tao's Book: 5.2.1, 5.2.2 [p.101 2nd ed, p.? 1st ed.];
5.3.2, 5.3.5 [p.109-110 2nd ed, p.? 1st ed]

Homework 8 (due Th 10/28/10):
Exercises from Tao's Book: 5.4.3, 5.4.5 [p.115 2nd ed, p.? 1st ed.];
5.5.1 [p.120 2nd ed, p.? 1st ed]
5.6.2 (bonus) [p.124 2nd ed, p.? 1st ed]

Homework 9 (due Th 11/04/10):
Exercises from Tao's Book: 6.1.5, 6.1.6 (bonus), 6.1.8 [p.131-132 2nd ed, p.? 1st ed.];
6.3.3 [p.138 2nd ed, p.? 1st ed]
5.4.8 (bonus) [p.115 2nd ed]

Homework 10 (due Th 11/18/10):
Exercises from Tao's Book: 6.4.3, 6.4.5 [p.146 2nd ed]
6.5.1 [p.148 2nd ed]
6.6.3, 6.6.4 [p.151 2nd ed]
6.7.1 (bonus) [p.153 2nd ed]

Homework 11 (due Wed 11/24/10):
Exercises from Tao's Book: 9.3.4, 9.3.5 (continuous version of equeeze test, not sure if this is in first edition) [p. 226 2nd edition]
9.4.2, 9.4.3 or 9.4.4, 9.4.5 [p.230 2nd edition]

Homework 12 (due Th 12/2/10):
Exercises from Tao's Book: 9.6.1 [p. 237 2nd edition]
9.7.2 [p. 239 2nd edition]
9.8.4, 9.8.5 (Bonus) [p. 241 2nd edition]
9.9.2 [p. 248 2nd edition]

Homework 13 (due Fr 12/10/10) starred (*) problems ask for examples:
10.1.4 (d)(g)(h), 10.1.5*, 10.1.6* (p.256 2nd ed),
10.2.2*, 10.2.3*, 10.2.5 (Mean Value Theorem) (p.258-259 2nd ed),
10.3.2*, 10.3.3* (p.260 2nd ed),
10.4.1 (p. 263 2nd ed).

Here are practice problems for the final (pdf file).