Number Theory
Time and place:
9:30am–10:45am TR Nebraska Hall W106.
Office hours
- Tuesday 2–3pm
- Wednesday 10–11am
- Friday 2–3pm
Problem sets
Worksheets
Midterm #2
Midterm #1
Textbook:
There is no required textbook for the course. I will post lecture notes from the class here. Recommended texts covering similar material are
- A friendly introduction to number theory by Joseph Silverman
- Elementary number theory and its applications by Kenneth Rosen
Course content:
In this class, we will cover the fundamentals of number theory. Possible topics include
- Pythagorean triples
- Euclidean algorithm and linear diophantine equations
- congruences and the Chinese Remainder Theorem
- unit groups, Fermat's Little Theorem, and Euler's Theorem
- primitive roots and discrete logarithms
- quadratic reciprocity
- sums of two squares
- primes in arithmetic progressions, the zeta function, and L-functions
- continued fractions and rational approximations of real numbers
- Pell's equation
- elliptic curves
We will explore this material through in-class group work and exercise sets. This content will build on Math 310 topics like the division algorithm, Euclidean algorithm, congruences, rings, and proof by induction.
How to succeed in this class:
- Start working on homework sets early. It takes a lot of time to figure out and properly write a proof.
- Read the notes before class and review the lecture notes after class. We will devote a large portion of class to groupwork, so lecture will be fast, and some parts of the material will be relegated to your reading outside of class.
- Carefully commit the definitions and important theorems to memory. Proving something without knowing the relevant definitions is like eating soup with a fork.
- Don't let early material slip by unmastered. If you don't understand something early in the class or haven't perfected a skill, do not ignore it and hope that it goes away. We will build off of these skills throughout the rest of the course.
- Utilize office hours, and not just for homework problems. My office hours are time set aside specifically for you to talk to me about the course material. You can stop by during any office hour without an appointment or any heads-up. You can also write to ask about meeting me at a different time if you cannot meet me during the regularly scheduled office hours.
I am confident that you (yes, you!) can succeed in this class if you are willing to work hard in and outside of class and you follow the tips above.