MATH 401/501 - HOMEWORK PROBLEMS - Fall 2010

Homework 1 (due Mon Jan 30, 2012---> Wed Feb 1):
For the first two problems assume arithmetic and whatever you know about inequalities:

(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.

Exercises from Tao's Book. For this problems you can only assume results and exercises prior to the given exercise (if you are going to use a previous result, make sure you state it, of course if it has not been proved in class and is not one of the other homework problems, you can attempt to prove those intermediate results, but this is not required):

(3) 2.3.1. (p.32 2nd ed, p.36 1st ed) (multiplication is commutative)

(4) 2.2.3(c)(d)(e) [p.29 2nd ed, p.33 1st ed] (Properties of order)

(5) 2.3.5 [p.32 2nd ed, p.36 1st ed] (Euclidean Algorithm)

Homework 2 (due Mon Feb 06, 2012---> Wed Feb 08):
(1) Section 3.1: Exercise 3.1.6 first half of (f), (g) and second half of (h) (p.46 2nd ed, p.51 1st ed)

(2) Section 3.3: Exercises 3.3.2, 3.3.5, 3.3.7 [p.55-56 2nd ed, p.63 1st ed]

Homework 3 (due Mon Feb 13, 2012):
(1) Section 3.4 Exercise 3.4.2 (p.61 2nd ed, p.68 1st ed)

(2) Section 3.6 Exercises 3.6.2, 3.6.5, 3.6.9 [p.72 2nd ed, p.82 1st ed]

(3) Bonus (to be written on a separate page that I will grade):
Section 3.6 Exercise 3.6.6 [p.72 2nd ed, p.82 1st ed]

Homework 4 (due Mon Feb 20, 2012 if you want it graded before the exam):
(1) Section 4.1 Exercises 4.1.2, 4.1.3, 4.1.6 (p.80 2nd ed, p.92 1st ed)

(2) Section 4.2 Exercise 4.2.6 (p.85 2nd ed, p.98 1st ed)

(3) Section 4.3 Exercise 4.3.2 (b)(c)(f)(g)

(4) Section 4.4 Exercise 4.4.1 (p92 2nd ed, p.106 1st ed)

Review for Midterm 1 - exam was on Fri Feb 24, 2012

Homework 5 (due Fri March 7, 2012):
(1) Section 5.2 Exercises 5.2.1, 5.2.2 [p.101 2nd ed];

(2) Section 5.3 Exercises 5.3.2, 5.3.5 [p.109-110 2nd ed];

(3) Section 5.4 Exercise 5.4.1 [p.115 2nd ed].

Homework 6 (due Fri March 23, 2012):
Section 5.4 Exercises 5.4.3, 5.4.5, 5.4.7 [p.115 2nd ed].

Homework 7 (due Wed March 28, 2012):
(1) Section 5.5 Exercise 5.5.1 (p.120 2nd ed).

(2) Section 5.6 Exercises 5.6.1(e), 5.6.2(d) (p.124 2nd ed).

(3) Section 6.1 Exercises 6.1.5, 6.1.8(b)(e) (p. 131-132 2nd ed).

Bonus 6.1.8(g).

Homework 8 (due Monday April 16)
Section 6.4: problem 6.4.7 (p. 146 2nd ed).

Section 6.5: problem 6.5.3 (p. 148 2nd ed).

Second Midterm Take home due on April 13, 2012
Read and do all exercises in Section 7.2

Homework 9 (due Monday April 30) try 4 out of the following problems
Section 9.3: problem 9.3.5 (p. 226 2nd ed).

Section 9.4: problem 9.4.7 (p. 230 2nd ed).

Section 9.6: problem 9.6.1 (p. 237 2nd ed).

Section 9.7: problem 9.7.2 (p. 239 2nd ed).

Section 9.8: problem 9.8.2 (p. 241 2nd ed).

Section 9.9: problem 9.9.3, 9.9.6 (p. 248 2nd ed).

For bonus points you can try: 9.3.4, 9.8.5.