MAU23101 Introduction to number theory
| Module Code | MAU23101 |
|---|---|
| Module Title | Introduction to number theory |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Pierre-Yves Bienvenu |
| Module Prerequisites | N/A |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 1.
- Continuous assessment contributes 15% towards the overall mark.
- Re-assessment, if needed, consists of 100% exam.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- State and prove some standard theorems in number theory.
- Use standard theorems to solve problems in number theory including some classes of Diophantine equations.
Module Content
- Divisibility and factorisation of integers: prime numbers, gcd and lcm, Euclidean algorithm, Bézout's theorem, multiplicative functions such as sums of divisors.
- Arithmetic in the ring Z/nZ and the field Z/pZ, Euler's totient function, Chinese remainder theorem, multiplicative order and primitive roots.
- Sums of squares, quadratic forms, discriminant, class number.
- Continued fractions, expansion of rationals and quadratic irrationals, Diophantine approximation, Pell-Fermat equations.
Recommended Reading
- A course in computational number theory by Bressoud and Wagon.
- A classical introduction to modern number theory by Ireland and Rosen.
- The higher arithmetic by Harold Davenport.
- Primes of the form x2 + ny2 by David Cox.