Fall 2024
Math 25: Number Theory
E-mail: salim.tayou@dartmouth.edu,
Office: Kemeny Hall 341.
Schedule:
- Meeting times: Monday-Wednesday-Friday 10:10 AM-11:15 AM.
- X-hour: Thursday, block 10X (12:15 - 1:05 p.m.).
- Room: 307 in Kemeny Hall.
- First/last meeting: Monday, September 16th/ Monday, November 18th, 2024.
- Office hours: See Canvas or by appointment, in Kemeny Hall 341.
Syllabus:
The great mathematician C. F. Gauss once wrote, "Mathematics is the queen of sciences and number theory is the queen of mathematics." Number theory is the part of mathematics dealing with the integers and certain generalizations. Topics include modular arithmetic, unique factorization into primes, linear Diophantine equations, and Fermat's Little Theorem. Discretionary topics may include cryptography, primality testing, partition functions, multiplicative functions, the law of quadratic reciprocity, and other historically interesting problems.
Textbook:
- David M. Burton, "Elementary Number Theory" (7th edition).
Prerequisites:
Math 8, or equivalent. If you are unsure about your preparation, please talk to the instructor!
Grading:
Homework will be assigned weekly. The solutions can either be scanned or typed and uploaded on Canvas. Late homework can only be accepted under special circumstances. Collaborative work on homework is accepted but you must write your own solution as well as the names of the collaborators. The Grade will be based on reading (5%), weekly homework (25%), a midterm (20%), an in class final exam (30%), and a take-home final exam (20%). See policy on Canvas for collaborative work on homework.
Learning Outcomes:
By the end of this course, you should be able to:
- Understand of the basic structures of number theory: define terms, explain their significance, and apply them in context;
- Solve mathematical problems: utilize abstraction and think creatively; and
- Write clear mathematical proofs: recognize and construct mathematically rigorous arguments.