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# Number Theory - MAT00085H

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• Department: Mathematics
• Module co-ordinator: Dr. Evgeniy Zorin
• Credit value: 20 credits
• Credit level: H
• Academic year of delivery: 2024-25
• See module specification for other years: 2023-24

## Module summary

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.

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## Module will run

Occurrence Teaching period
A Semester 2 2024-25

## Module aims

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.

## Module learning outcomes

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.

## Module content

• Congruences and residues

• Primitive roots and quadratic reciprocity

• Sum of squares

• Multiplicative functions and average orders

• Continued fractions and Pell’s equations

## Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Closed exam : Number Theory
3 hours 100

None

### Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Closed exam : Number Theory
3 hours 100

## Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.