MA 42: Number Theory, Spring 2012

Instructor

  • Reinier Bröker

    • Times and Places

    Text book

    A friendly introduction to Number Theory by Joseph Silverman. This book is available in the Brown bookstore. Note: we will be using the third edition of the book. The fourth edition is scheduled to be printed in January 2012. Any edition of the book will do actually, just note that the homework listed below refers to the third edition.

    Contents

    Topics include Pythagorean Triples, greatest common divisors, The Chinese remainder theorem, the RSA public key cryptosystem, quadratic reciprocity, Pell's equation. As the only way to really learn mathematics is by doing it, you will be expected to work on problem sets every week. You should also plan to read selections from the text in preparation for each class.

    Grading

    Your grade is based on the homework, midterms and final. I will weigh these as follows. Homework: 20%, Midterm: 20% each, Final: 40%.

    Exams

    First midterm: Thursday March 1st, in class. Topics: Chapters 1-12. (Note: no calculators are allowed on any exam.)

    Second midterm: Thursday April 5th, in class. Topics: Chapters 12-22.

    Final: Thursday May 10, 2pm -- 5pm, Room: Barus and Holley 141. Topics: Chapters 1-27, 37, 39, 40 (no Pell's equation). Practice final

    Homework

    Due date Exercises
    2-2-2012 1.3, 2.1, 2.2
    2-9-2012 3.2, Compute the gcd of your birthday and phone number, 6.1, 7.5
    2-16-2012 7.4, 8.3, 9.2
    2-23-2012 10.1(a), 10.3(a), 11.1, 11.5 (b,c)
    3-1-2012 no homework. Here is a midterm. (Don't hand in your solutions, please.)
    3-8-2012 12.2, 13.5, 15.4, 15.5
    3-15-2012 16.1(a), 17.1, 18.1, 18.2, 19.1
    3-22-2012 21.2, 21.4, 21.6
    4-3-2012 22.1, 22.2, 22.3, 22.4(a), 23.1
    4-10-2012 no homework due
    4-19-2012 24.1, 25.1, 25.3, 26.3, 27.4 (hint: prove directly that if m = a^2+b^2, then -1 is a square modulo p_i, don't use fancy formulas)
    4-26-2012 Exercises
    5-3-2012 39.7, 40.1 (a,b), 40.2(a)

    Additional Info

    Here are two links to additional notes and a free book that you can consult.