School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2020/21 Last Updated: 25 February 2021

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 żdegree-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: 2,4

3,4

perform arithmetic and theoretical calculations with matrices, vectors and complex numbers: 1,2,3,4

derive and apply (in specific examples) the key theorems covered in the module: 1,2,3,4

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

3,4

perform arithmetic and theoretical calculations with matrices, vectors and complex numbers: 1,2,3,4

derive and apply (in specific examples) the key theorems covered in the module: 1,2,3,4

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

Learning/teaching comprises 72 hours video lectures, 20 hours flipped examples classes, and 4 hours for class test and examination.

Independent study comprises 20 hours for online assignments, 80 hours preparation for examples classes, 20 hours preparation for class test and exam, and 84 hours consolidation of lecture material.

Independent study comprises 20 hours for online assignments, 80 hours preparation for examples classes, 20 hours preparation for class test and exam, and 84 hours consolidation of lecture material.

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On-line assignment

A take-home, written assignments to be submitted on-line. The assignment consists of a set of questions with pre-allocated space for written solutions.Students should expect to spend 10 hours on this assignment.

On-line, open book Class Test

An alternative class test designed to be completed in 2 hours by a well prepared student. The test is on-line and will be open book.

On-line assignment

A take-home, written assignments to be submitted on-line. The assignment consists of a set of questions with pre-allocated space for written solutions.Students should expect to spend 10 hours on this assignment.

Open book alternative examination

An alternative class test designed to be completed in 2 hours. The test is on-line and will be open book. There will be a minimum of 5 and a maximum of 8 questions all of which must be answered.