Math 152 - Topics in Number Theory - Spring 2006

| General Info | Schedule | (Up) Dates | Homework | Further Reading | Handouts |

General Information

Meeting Time MWF 11-11:50
Location 380-380W (basement, Math building 380)
Professor Ben Brubaker (brubaker@math.stanford.edu)
Office: 382-F (2nd floor, Math building 380)
Office Phone: 3-4507
Office Hours: Wed. 2-5, or by appointment.
Course
Assistant
Kazim Buyukboduk (kazim@math.stanford.edu)
Office: 380-U1 (Basement, Math building)
Office Hours: Tues., Thurs. 5:30-7 pm
TextbookPrimes of the Form x^2+ny^2, by David Cox
Grade
Breakdown
2 Midterms -- 25 % each, Final Project -- 25 %, Homework -- 25%
Course
Content
We'll follow the book closely throughout the course, supplementing with extra topics where it is necessary to fill in the background for more advanced sections. Along the way, we'll discover the basics of congruences and modular arithmetic, quadratic reciprocity and higher reciprocity laws, quadratic forms, genus theory, and even the rudiments of class field theory. (You shouldn't know what any of those words mean yet, but by the end of the quarter, have a working knowledge of all of them and why they are important.)
Prerequisites There aren't any specific prerequisites for this course. We will build up to most of the more difficult concepts together in lecture. Some familiarity with proofs and abstract mathematical thinking is useful, but can be developed over the course of the quarter.

Announcements & Dates

  • There's a typo in Homework 4: the left-hand side of the last problem should read f(la/p) NOT f(a/p). This corrected version should match your notes from class. Again, f(z) = e^{2 \pi i z} - e^{-2 \pi i z}.
  • Important Dates
    • Sunday, April 23: Add deadline
    • Wednesday, April 26: In-Class Exam 1
    • Sunday, April 30: Drop deadline
    • Friday, June 2: In-Class Exam 2
    • Wednesday, June 14th: Final Projects Due (Noon Sharp)

Further Reading:

Good Textbooks on Number Theory

  • Joseph Silverman, A Friendly Introduction to Number Theory -- friendly indeed, and very well written. Expands on basic concepts you might find to be too terse in Cox's book.
  • Ireland and Rosen, A Classical Introduction to Modern Number Theory -- A Springer Graduate Text in Mathematics series book, but starts off very slow and builds to very sophisticated math. The number of chapters you can read and understand in this book is a very good measure of your understanding of algebraic number theory.

Solutions and Handouts:

  • Final Project Instructions
  • Solutions to Midterm 2
  • Basics of Groups, Rings, and Fields, a handout mainly discussing groups and explaining the proof given at the end of class on Monday, April 10, for Fermat's Little Theorem. Groups, and also fields, will be mentioned later in the course, so this is probably worth reading if you have never seen these abstract concepts defined before.