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Modules

6CCM224b Introduction to Number Theory

Lecturer: Dr James Newton

Advice/Help for this module is also available from: Dr Mahesh Kakde

Semester: 1

Credit Level: 6   Credit Value: 15

Programmes:

Mathematics BSc/MSci (or with Year Abroad)
Mathematics with Statistics BSc (or with Year Abroad)
Mathematics with Management and Finance BSc (or with Year Abroad)
Mathematics and Philosophy BSc (or with Year Abroad)
Mathematics and Philosophy BA (or with Year Abroad)
Mathematics and Physics BSc/MSci (or with Year Abroad)
Mathematics and Computer Science BSc
Graduate Diploma

Aims and objectives:

The aim of this module is to give an introduction to elementary number theory and to further develop the algebraic techniques met in ‘Introduction to Abstract Algebra’. By introducing several new concepts in the concrete setting of rational integers, this module is a good preparation for more demanding modules in number theory and algebra.

Syllabus:

Review of divisibility, prime numbers and congruences. Residue class rings, Euler’s φ-function, primitive roots. Quadratic residues and quadratic reciprocity law. Irrational and transcendental numbers. Sums of squares. Some Diophantine equations. If time permits we will also learn about the ‘AKS’ algorithm for primality testing.

Teaching arrangements:

Three hours of lectures and occasional one-hour tutorials which will be announced in advance.

Prerequisites:

Introduction to Abstract Algebra (4CCM121A or 5CCM121B)

Summative Assessments:

Type WeightMarking Model
2hr written examination 90% Model 2
Class Test 10% Model 5

For students who fail the module at the first attempt, reassessment will be based entirely on the written exam. 

Formative assessments:

Problem sheets will be given out every week (from second week onwards), and work handed in will be marked and returned to you. Solutions will be discussed in tutorials.

Suggested reading/resources (link to My Reading Lists)

 


19 September 2018
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