School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2019/20 Last Updated: 20 November 2019

MAT-10047 - Algebra

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This module is intended to help students with the transition from the methods based approach of A level to the higher levels of rigour and understanding expected at degree level. It begins by discussing mathematical statements and various strategies of proof. This is followed by a short exposition of naive set theory. The remainder of the module covers the algebraic development of number systems and their properties followed by the fundamental topics in matrix and vector algebra, providing a solid introduction to algebra at degree level.

This module aims to provide students with a solid foundation in Algebra for the ¿degree-level study of pure mathematics. The module will emphasise the need for care and rigour in presenting formal mathematical arguments and will provide students with knowledge of many key topics in pure mathematics which are needed for study beyond FHEQ Level 4.

state clearly the key definitions and theorems covered in the module: 1,2,3

2,3

perform arithmetic and theoretical calculations with matrices, vectors and complex numbers: 1,2,3

derive and apply (in specific examples) the key theorems covered in the module: 1,2,3

apply module concepts and theoretical material to develop mathematical and logical arguments:

2,3

perform arithmetic and theoretical calculations with matrices, vectors and complex numbers: 1,2,3

derive and apply (in specific examples) the key theorems covered in the module: 1,2,3

apply module concepts and theoretical material to develop mathematical and logical arguments:

72 hours lectures

24 hours tutorial classes

200 hours private study

2 hour unseen examination

2 hour class test

24 hours tutorial classes

200 hours private study

2 hour unseen examination

2 hour class test

None

Class Test

Unseen 2-hour¿ class test set during the module.

Take-home assignment

Approximately four 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 two semesters. Students should expect to spend 12 hours across the academic year on their assignments.

2-hour unseen examination

Unseen 2-hour end of module examination. The examination paper will consist of no less than five and not more than eight questions, all of which are compulsory.