Math 471: Number Theory

This course is an introductory course in elementary number theory. We will explore divisibility, prime numbers, cryptography, congruences, arithmetic functions, and Diophantine equations.

Text: An Introduction to the Theory of Numbers by Niven, Zuckerman, and Montgomery.

Policy Sheet

Instructor

Dan Yasaki, LGRT 1116, (413) 545-6016, yasaki@math.umass.edu

Office hours: Tuesdays 10:00-11:00 AM and Wednesdays 9:00-10:00 in LGRT 1116

Useful Links

• TUG: Getting started in LaTeX:
• UMASS: More LaTeX documentation:
• PARI homepage: Although you can get by with Mathematica or Maple for much of what we will do, Pari/GP has a few advantages. It is designed for number theory, so it is fast and does LOTS of things. It is also free. A quick gp example A sample gp file
• SPARK:
• SPIRE:
• ASCII encoder/decoder: Type your favorite message in [TEXT], hit ENCODE, and see the ASCII codes in the [DEC/CHAR] box. For us, the important use is the other way. Paste your list of 2 digit numbers in [DEC/CHAR] and hit DECODE to see the text.

Grading

• Problem Sets:
  • Problem Set 1: Due Friday, September 14 Solutions
  • The problems for Problem Set 1. Apologies for any typos.
  • Problem Set 2 with hints: Due Friday, September 21 Solutions
  • The problems for Problem Set 2. Apologies for any typos. By this point I hope everyone has a book. This is the last time I will do this.
  • Problem Set 3 with hints: tex file Due Monday, October 1. Late assignments not accepted. Solutions
  • Problem Set 4 with hints: tex file Due Monday, October 8. This one is proof heavy, so get started early if you do not like proofs. Solutions
  • Test question: secret.txt This will not be collected, but will give the answer to one of the questions on Test 1.
  • Problem Set 5 with hints: tex file Due Monday, October 22. Solutions
  • Problem Set 6 with hints: tex file Due Monday, October 29. Solutions
  • Problem Set 7 with hints: tex file Due Monday, November 5. Solutions
  • Problem Set 8 with hints: tex file Due Wednesday, November 28. Solutions
  • Problem Set 9 with hints: tex file Due Wednesday, December 5. Solutions
• Tests/Quizzes:
  • Quiz 1 : RSA exercise. The answer is 471.
  • Test 1 is on Friday, October 12. It will cover Chapter 1 (except 1.4) and Chapter 2 through (and including) 2.5. Study your definitions and major theorems. Review 1 Solutions
  • Test 1 answers tex file
  • Quiz 2 tex file : Hensel and Columbus.
  • Test 2 will cover 2.6--2.8 and 3.1--3.3. Study your definitions. Vocab etc. tex file Solutions
    It is in class on Friday, November 30.
  • This is an extra assignment to get a glimpse of one question from the test. Secret
  • Test 2 answers
• Extra Credit:
  • Pell tex file
• Final exam:
  • The final exam is cumulative Final Review tex file It is Tuesday, December 18 at 8:00AM in LGRC A301. (Not our usual room!) The linked review sheet has some sample problems, as well as last semester's final. Last semester, we covered p-adic numbers instead of continued fractions, so be sure to study also continued fractions and Pell equations. The plan is to have a non-zero portion of the test be (hard) computational so that you have to do it at home.
  • Final exam #1 Pell equation
    Final exam #2 RSA question tex file
    For #1, the x-value of the solution gives the location of the easier to memorize question/answer. For #2, the decrypted number gives the location. For example, if the answer is 123, then go to
    www.math.umass.edu/~yasaki/Courses/Math_471/123.pdf