## MA211Half UnitAlgebra and Number Theory

This information is for the 2020/21 session.

Teacher responsible

Prof Graham Brightwell

Availability

This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

Pre-requisites

Students must have completed Introduction to Abstract Mathematics (MA103) and Mathematical Methods (MA100).

Course content

The aim of this course is to continue (from MA103) the study of abstract algebraic structures. There are two main strands in the course. First, we develop further the theory of groups, using permutation groups as a key example. We investigate the important concepts of normal subgroups and quotient groups. Secondly, we introduce rings, and study factorisation in rings, where we also look at some connections with number theory. Groups: Review of basic group theory; permutations and permutation groups; homomorphisms; conjugation, normal subgroups and quotient groups; the first isomorphism theorem for groups. Rings: basic properties of rings and examples (including polynomial rings, matrix rings, and number rings); subrings, ideals and ring homomorphisms; divisibility in integral domains; greatest common divisors; Euclidean rings and unique factorisation; applications to number theory; principal ideal domains.

Teaching

This course is delivered through a combination of classes and lectures, totalling a minimum of 30 hours across Michaelmas Term.  This year, this teaching will be delivered through a combination of lectures released as online videos and face-to-face or virtual classes.

Formative coursework

Written answers to set problems will be expected on a weekly basis.

A Book of Abstract Algebra, Charles C Pinter, (Dover, 2nd edition, 2010);

Introduction to Algebra, Peter J Cameron (OUP 1988);

Rings, Fields and Groups: Introduction to Abstract Algebra, Reg Allenby (Butterworth-Heinemann, 2nd edition 1991).

Assessment

Exam (80%, duration: 2 hours) in the summer exam period.
Coursework (20%) in the MT.

Important information in response to COVID-19

Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Mathematics

Total students 2019/20: 31

Average class size 2019/20: 10

Capped 2019/20: No

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

• Self-management
• Problem solving
• Application of information skills
• Communication
• Application of numeracy skills
• Specialist skills