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

Homework 1 (due 2/3/09) : (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.
Bonus Problems (due during Week 2/3/09): Exercise 2.2.4 (p.33): Verify the trichotomy law
Exercise 2.3.5 (p.36): Verify the division algorithm. Verify the uniqueness of the quotient and the reminder (as stated the algorithm requires to prove only the existence).

Homework 2 (due 2/10/09) :
Section 3.1 (p.51-52): 3.1.2, 3.1.9, 3.1.10.
Write carefully the induction proof of: if a set has n elements then its power set has 2^n elements.
Bonus Problems (due during Week 2/10/09): 3.3.2, 3.3.3

Homework 3 (due 2/17/09) :
Section 3.3 (p.63): 3.3.6, 3.3.7.
Section 3.4 (p.68-70): 3.4.4, 3.4.5.
Section 3.6 (p.82-83): 3.6.4
Bonus Problems (due during Week 2/17/09): 3.5.5, 3.5.10, 3.6.6

Homework 4 (due 2/25/09) :
Section 4.1 (p.92): 4.1.3, 4.1.5 (think about 4.1.8)
Section 4.2 (p.98): 4.2.1, 4.2.2, 4.2.6 (notice typo: reals=rationals)
Section 4.3 (p.102): 4.3.1
Section 4.4 (p.106): 4.4.1

Midterm 1 on Thursday February 26, 2009
Exam will cover Chapters 2, 3 and 4. It will be an open book exam.
Tuesday and Wednesday Feb 24-25, 2009 we will review for the exam.

Homework 5 (due Tuesday 3/10/09) :
Section 4.3 (p.102): 4.3.2, 4.3.3-4.3.4
Section 4.4 (p.106): 4.4.2

Homework 6 (due Tuesday 3/24/09) :
Section 5.1 (p.114): 5.1.1 (note correction)
Section 5.2 (p.117): 5.2.1
Section 5.3 (p.127): 5.3.2, 5.3.4, 5.3.5
(Bonus) Section 5.4 (p.133): Choose at least one from 5.4.3, 5.4.4, 5.4.5

Homework 7 (due Thursday 4/2/09) :
Section 5.5 (p.139): 5.5.1
Section 5.6 (p.144): 5.6.1 (bonus), 5.6.3
Section 6.1 (p.152): 6.1.5

Homework 8 (due Thursday 4/9/09) :
Section 6.1 (p.152): 6.1.8(e)(g)(h)
Section 6.3 (p.160): 6.3.3
Section 6.4 (p.169): 6.4.3, 6.4.5
Section 6.6 (p.175): 6.6.5

Homework 9 (due Thursday 4/16/09) :
Section 6.7 (p.178): 6.7.1
Section 7.1 (p.189): 7.1.4
Section 7.2 (p.195): 7.2.1, 7.2.4
Section 7.3 (p.200): 7.3.2
Section 7.5 (p.207): 7.5.2, 7.5.3

Homework 10 (due Thursday 4/30/09) :
Section 9.1 (p.249): 9.1.9, 9.1.14, 9.1.15
Section 9.4 (p.265): 9.4.5
Section 9.5 (p.269): 9.5.1
Section 9.6 (p.273): 9.6.1
Section 9.7 (p.276): 9.7.2
Section 9.8 (p.278-279): 9.8.2
Section 9.9 (p.285-286): 9.9.5

Last Homework 11 (due Thursday 5/7/09) :
Section 10.1 (p.294-295): 10.1.4 (d)(g), 10.1.5-10.1.6
Section 10.2 (p.298): 10.2.5, 10.2.7
Section 10.3 (p.299-300): 10.3.2-10.3.3
Section 10.4 (p.302-302): 10.4.1