What is elementary number theory

In this class, we go through a buffet of results in elementary number theory. Some highlights are:

  • modular arithmetic
  • quadratic reciprocity
  • primitive roots
  • public key cryptography

What can you expect from this course

  • develop appreciation for classical number theory
  • work on your proof writing skills
  • learn about the connection between number theory and modern technologies

What I expect from you

  • skim notes before watching the videos
  • watch videos, and do the exercises at the end
  • if anything is not making sense, ask in class, or by e-mail

How to study

  • review definitions
  • do practice problems
  • invent your own problems
  • review proofs of theorems (do they make sense?)
  • summarize proofs of theorems

Assessment information

Tentatively (this may change based on feedback from AQAC)

  • 50% final exam
  • 20% first coursework exam
  • 20% second coursework exam
  • 10% assignments (5 assignments, drop the lowest marks)

Calendar

Week Topics Evaluation
1 Divisibility, gcd (review)  
2 Linear diophantine equations, modular arithmetic Assignment 1 given
3 Arithmetic functions (Euler \(\phi\)-function, divisor function, etc.) Assignment 1 due
4 Polynomials Assignment 2 given
5 Primitive roots Assignment 2 due
6 Quadratic residues I Exam 1
7 Quadratic residues II Assignment 3 given
8 Introduction to cryptography Assignment 3 due
9 Elliptic curves over finite fields Assignment 4 given
10 Elliptic curves II Exam 2
11 Continued fractions Assignment 4 due, Assignment 5 given
12 Pell’s equation Assignment 5 due
13 revision