INSTRUCTOR: Ralph Greenberg, Padelford C-553
543-7648, greenber@math.washington.edu
OFFICE HOURS: Tuesday 11:00 - 1:00
Additional office hours will be announced in class. If the times
are inconvenient, please make an appointment by e-mail.
TEXT: An Introduction to the Theory of Numbers, 5th Edition
Niven, Zuckerman, and Montgomery
GRADING: Homework will be important part of this course and will count 40% of
the grade.
There will be two exams during the quarter, each counting 30% of
the grade. The second exam may be given on Monday, March 14th, 2:30 - 4:20.
This course will cover a variety of different topics in the theory
of numbers. After a review of some of the basic theorems in chapter
1 and the first few sections of chapter 2, we will prove a fundamental
theorem concerning the existence of primitive roots when the modulus is
a prime. (Sections 2.7, 2.8.)
The theory of quadratic residues. (Sections 3.1, 3.2.) We will give at least one proof of the famous Law of Quadratic Reciprocity.
Approximation of irrational numbers by rational numbers and the theory of continued fractions. (Chapter 7.) One of the interesting applications will be the solution of a certain Diophantine equation called "Pell's equation." (Section 7.8.)
Quadratic Fields. (Chapter 9.) It is especially interesting to see how the law of quadratic reciprocity is related to the primes in quadratic fields. (Section 9.7). Pell's equation is related to units in quadratic fields. (Section 9.6).
Other topics to be covered if time permits, or in Math 415:
Primes in arithmetic progressions. (Section 8.4.)
Elliptic curves. (Sections 5.6, 5.7.)