School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2020/21 Last Updated: 30 May 2020

MAT-20025 - Abstract Algebra

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MAT-10047 Algebra

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This module introduces and studies the abstract algebraic structure known as a group. Starting with the axiomatic and theoretical foundations, the module progresses, through a study of subgroups, to the proof of one of the most important theorems in Group Theory, Lagrange's Theorem. The module also examines applications of group theory, and the often beautiful way in which it interacts with geometry and number theory. It concludes with a preliminary exploration of other, closely related algebraic structures, namely rings and fields.

This module provides develops material required for a large number of Level 6 options.

This module provides develops material required for a large number of Level 6 options.

The module aims to provide students with their first rigorous treatment of group theory as an axiomatic system, as well as exploring applications to geometry and number theory. It also aims to expose students, at an introductory level, to other algebraic structures such as rings and fields.

define and identify abstract algebraic structures and concepts including equivalence relations, binary operations, rings, fields and permutations: 1,2,3

1,2,3

1,2,3

select and apply concepts of group theory to mathematical problems: 3

state and prove theorems involving groups, rings and fields: synthesise theoretical material and concepts to solve problems:

1,2,3

1,2,3

select and apply concepts of group theory to mathematical problems: 3

state and prove theorems involving groups, rings and fields: synthesise theoretical material and concepts to solve problems:

Lectures: 36 hours

Tutorials: 12 hours

Preparation for continuous assessment: 24 hours

Independent study: 76 hours

Unseen Examination: 2 hours

Tutorials: 12 hours

Preparation for continuous assessment: 24 hours

Independent study: 76 hours

Unseen Examination: 2 hours

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Take-home assignments

Two equally weighted take-home, written assignments. Each assignment consists of a set of questions with pre-allocated space for written solutions. The assignments are set at regular intervals across the semester. Students should expect to spend 12 hours across the semester on their assignments.¿

Two class tests.

Two class tests to assess both theoretical and practical aspects of the module. The class tests are equally weighted. Each class test will last 40 minutes.

2-hour unseen examination

The examination paper will consist of no less than five and not more than eight questions all of which are compulsory.