Math 115: Introduction to Number Theory

Summer 2008

Instructor: Anthony Varilly-Alvarado

Office: 941 Evans

Office hours: Monday 1-2:30pm and Wednesday 1-2:30pm in 941 Evans.

Email: varilly at math.berkeley.edu

Lectures: MTuWTh 10am-12pm in 6 Evans

Description: We will be mainly concerned with the study of prime numbers. These are the ``building blocks'' of whole numbers. We will study notions of divisibility, congruences (public key cryptography), quadratic reciprocity and arithmetic functions. This material corresponds roughly to chapters 1--4 of the book. After that, depending on how much time we have left we will either study some analytic number theory (I would write up notes for this) or some algebraic number theory (Chapter 9 of the book), depending on people's interests.

Handouts:

Syllabus

Sample Midterm Questions; Midterm Solutions

Sample Final Questions (Updated 8/8 at 1:46pm)

Homework:

Due 6/26: Pages 17-20, problems 1,3(a)-(d),7,13,14,20,24,43.

Due 7/1: Homework 2

Due 7/3: Pages 28-29, Problems 3 and 8 (use congruences to make your life easier), Page 57, Problems 5, 20, 23.

Due 7/8: Pages 56-60, Problems 14, 17, 18, 27, 28, 45 Page 63, Problems 5, Pages 71-74, Problems 3, 7, 19

Due 7/10: Pages 72-74: 20, 26, 29, Page 86: 2, 3, 4.

Due 7/15: Page 72: 21, Page 82: 5, 6, Page 91: 2, 4, 9, 10, 11, Page 96: 1.

Due 7/17: Pages 96-97: 2, 3, 6, Pages 106-107: 2, 5, 8.

Due 7/22: None. Study for the Midterm.

Due 7/24: Pages 119-121: 4, 10, Pages 126-128: 1, 5, 10.

Due 7/29: Pages 135-137: 8(c)-(f), 9, 10, 11, 13, 23. Pages 140-142: 4(a),(d),(f), 6, 9, 10, 23.

Due 7/31 Pages 147-150: 3, 5, 6, 14, 21.

Due 8/5 Pages 184-188: 9, 13, 18, 30 Pages 191-193: 6, 8, 15, 16, 19. Page 195: 3

Due 8/7 Pages 195-197: 6, 16, 17. Page 414: 3, 5. Also, solve and hand in the following problem

Due 8/12 (Optional--Extra credit): Page 419: 1, 3, Page 423: 2, Page 245: 1 Pages 427-428: 1, 2, 4, 6. (I decided to scratch the extra problem. You have enough work as it is.)