Course overview
This course is an introduction to the study of whole numbers, with particular emphasis on the study of prime numbers. Once considered the province of pure mathematics, and devoid of applications, number theory is today central in cryptography, and in making e-commerce viable. One of the oldest sub-areas of mathematics, some of the methods developed 2,500 years ago are still in use today, but this course will be a modern introduction to the subject. We will focus on four main areas: basic study of prime numbers (divisibility, primality), congruences, continuous fractions, and applications to solving integer equations.
- Modular Arithmetic
- Applications
Course learning outcomes
- Solve a variety of problems in elementary number theory using appropriate techniques.
- Investigate the existence of integer solutions to algebraic equations using congruence methods.
- Use logical arguments to prove number theoretic results.
- Perform computations using continued fractions.
- Demonstrate skills in communicating mathematics.
Degree list
The following degrees include this course