**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

**Reading Assignment:** Section 3.2.

**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

Return to: Department of Mathematics and Statistics, University of New Mexico

Last updated: April 21, 2009