School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2023/24 Last Updated: 13 February 2024

MAT-10038 - Algebra I

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This module is intended to help students with the transition from the methods based approach of A level mathematics to the higher levels of understanding and rigour expected at degree level. It begins by discussing mathematical statements and the meaning and basic strategies of proof. This is followed by a short exposition of naive set theory and by a careful treatment of the notion of a function. The remainder of the module covers the algebraic development of number systems and their properties. The module ends with a brief discussion of the properties of polynomials, including the Fundamental Theorem of Algebra.

The aim of the module is to provide students with an introduction to pure mathematics, through the study of techniques of proof, sets and functions, real and complex numbers, factorisation of the integers, modular arithmetic and polynomials.

state clearly the key definitions and theorems of algebra, including those related to sets and functions, real and complex numbers, factorisation and divisiblity, modular arithmetic and polynomials: 1,2,3

use the basic concepts and theory to develop mathematical and logical arguments: 1,2

use the basic concepts and theory to make judgements and to evaluate different approaches to solving problems: 2

derive and apply the key theorems of algebra, including those related to sets and functions, real and complex numbers, factorisation and divisibility, modular arithmetic and polynomials: 3

use the basic concepts and theory to develop mathematical and logical arguments: 1,2

use the basic concepts and theory to make judgements and to evaluate different approaches to solving problems: 2

derive and apply the key theorems of algebra, including those related to sets and functions, real and complex numbers, factorisation and divisibility, modular arithmetic and polynomials: 3

36 hours lectures

12 hours Examples Classes

20 hours coursework preparation

82 hours private study

12 hours Examples Classes

20 hours coursework preparation

82 hours private study

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A take-home, written assignment.

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

A take-home, written assignment.

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

Unseen, two hour examination

A closed book examination based on material covered over the semester.