Number Theory – Mathematics 0420
Brown University – Spring, 2010
Professor Joseph Silverman

Text A Friendly Introduction to Number Theory  (3rd edition) by Joseph H. Silverman, Prentice-Hall, ISBN 0131861379
     Click here to download Chapters 1–3.
     Click here to download the extra material for Chapter 8.
     Click here to download the new versions of Chapters 23–24.
Office Mathematics Department, Kassar House, Room 202
Phone 863-1124
Email jhs@math.brown.edu
Web Site www.math.brown.edu/~jhs/MA0042/MA0042HomePage.html
Office Hours Monday 2:30–3:30pm and Friday 9:00–9:50am, and by appointment.
(Or just drop by. I tend to be in on MWF and not on TTh.)

Reading Period and Exam Period Office Hours
No class and no office hours Mon May 3 – Fri May 7
Review Session: Mon May 10, 11:00–11:50am, Wilson 101
Office Hour: Mon May 10, 2:30–3:30pm, Kassar 202
Office Hour: Thurs May 13, 1:00–2:00pm, Kassar 202
Course Time MWF 11:00–11:50 (D Hour)
Course Location Wilson Hall 101
Recitation/ Homework Sessions Mondays, 7:00–8:00pm, Barus-Holley 141
Homework I will keep a list of reading and homework assignments on the following web page:
Click here to go to the Math 0420 Homework Page.
Problem Sets NOTE: The problem sets are challenging. Don't leave them until the last minute! We will be moving rapidly. In order to learn the material, it is very important to DO THE HOMEWORK WHEN IT IS ASSIGNED.
RULES: Homework must be stapled. All problems must be clearly labeled. Late homework will not be accepted under any circumstances. (One or two missing homeworks is unlikely to affect your grade, and it's an imposition on the grader to have to go back and grade late homeworks.)
Note on Using Computers in Math 0420 Computers are a useful tool that can be used to generate data for making conjectures and to perform computations that would be tedious to do by hand. However, they are not a replacement for understanding. So for example, you might use a computer to compute the greatest common divisor of two large numbers, but you should be sure that you understand how the computer is doing the computation.
Computer Package for Math 0420 I tend to use a computer program called PARI-GP to do number theory calculations. The good news about PARI is that it is free and very fast and powerful at doing number theoretic computations. The bad news is that it's not tremendouly user friendly. If you're computer savvy, you can download PARI here:
Click here to go to the PARI home page.

Another way to use PARI to do short calculations is to use the SAGE web site. You'll need to create a (free) account. Then you'll be able to type one or more PARI commands and type Shift-Return to perform the computation.

As an alternative, I have written a web page number theory calculator that you can use for Math 0420. It is not as versatile as PARI and it can only handle numbers up to about 16 digits, (and it does not warn you when the numbers get too big, it just gives the wrong answer). However, it it is very easy to use.
Click here for an online number theory calculator.

Dates to Remember: There will be two in-class hour exams and a final exam.

Hour Exam #1

Friday, February 26

Click to download Exam 1 Solutions.

Hour Exam #2

Wednesday, April 7

Click to download Exam 2 Solutions.

Final Exam

Saturday, May 15
Exam Group 17

Time 2:00-5:00pm
Barus-Holley 168

Grading: The course grade will be determined on the following basis:

Problem Sets

20%

Hour Exams (22.5% each)

45%

Final Exam

35%

Syllabus (Tentative):

  1. Pythagorean Triples
  2. Divisibility, greatest common divisors, and linear equations
  3. The fundamental theorem of arithmetic
  4. Congruences, Fermat's little theorem ap-1=1 (mod p), and Euler's formula aφ(m)=1 (mod m)
  5. The Chinese remainder theorem
  6. Powers, roots, and the RSA public key cryptosystem
  7. Squares modulo p and quadratic reciprocity
  8. Pell's equation and Diophantine approximation
  9. Binomial coefficients
  10. Fibonacci numbers and linear recurrences
  11. Continued fractions and Pell's equation
  12. Additional topics as time permits

Go to Professor Silverman's Home Page.