Math 250 -- Spring 2024

Number Theory
Amherst College

Syllabus
Homework
Math Links
Lecture Room: Seeley Mudd 014
Lecture Time: TuTh 11:30-12:50
Final Exam: TBA
Instructor: David Zureick-Brown ("DZB")
Office: Seeley Mudd 502
Phone: (413) 542-2595
Email: dzureickbrown@amherst.edu

Text: "A Friendly Introduction to Number Theory" 4th ed., by Joseph H. Silverman
Office Hours: Mondays 4:15-5:15 (in person)
Wednesday 2:30-3:30 (zoom)
Wednesday 3:30-5:30 (in person)
pythagorean
About this course:

Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.

--Leonhard Euler

The mathematician Pascal admires the beauty of a theorem in number theory; it's as though he were admiring a beautiful natural phenomenon. Its marvellous, he says, what wonderful properties numbers have. It's as though he were admiring the regularities in a kind of crystal.

--Ludwig Wittgenstein

Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is.

-- Paul Erdos
Topics:

An introduction to the theory of rational integers; divisibility, the unique factorization theorem; congruences, quadratic residues. Selections from the following topics: cryptology; Diophantine equations; asymptotic prime number estimates; continued fractions; algebraic integers. Here is an official pdf of the syllabus for this course.

Homework

The homework assignments are available at this link, and will be updated regularly.

Assignments should be turned in via Gradescope, as a single file. The gradescope code is available at the top of the assignments pdf.