- Department: Mathematics
- Credit value: 20 credits
- Credit level: H
- Academic year of delivery: 2024-25
- See module specification for other years: 2023-24
Number theory studies the properties of one of the most basic mathematical objects known to humankind. In doing so, it utilises an unusually wide variety of methods and proofs, many of which are surprisingly deep. This course will introduce some of the fundamental problems in this subject, ranging from determining whether a number is a square modulo p or not, to finding the most accurate approximation to real numbers with continued fractions.
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
- None
Occurrence | Teaching period |
---|---|
A | Semester 2 2024-25 |
Number theory studies the properties of one of the most basic mathematical objects known to humankind. In doing so, it utilises an unusually wide variety of methods and proofs, many of which are surprisingly deep. This course will introduce some of the fundamental problems in this subject, ranging from determining whether a number is a square modulo p or not, to finding the most accurate approximation to real numbers with continued fractions.
By the end of the module, students should be able to:
1. Demonstrate facility with the unusually wide variety of methods and proofs which appear in number theory.
2. Apply algorithms taught in the course in specific calculations.
3. Demonstrate the ability to reason in a rigorous, precise and logical manner.
Congruences and residues
Primitive roots and quadratic reciprocity
Sum of squares
Multiplicative functions and average orders
Continued fractions and Pell’s equations
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
None
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Rose, A Course in Number Theory, Oxford University Press.