# ALGEBRA - 2017/8

Module code: MAT1031

Module provider

Mathematics

Module Leader

FISHER D Dr (Maths)

Number of Credits

15

ECT Credits

7.5

Framework

FHEQ Level 4

JACs code

G100

Module cap (Maximum number of students)

N/A

Module Availability

Semester 1

Overall student workload

Independent Study Hours: 101

Lecture Hours: 47

Seminar Hours: 5

Tutorial Hours: 1

Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

Examination | EXAMINATION | 75% |

School-timetabled exam/test | IN-SEMESTER TEST | 25% |

Alternative Assessment

N/A

Prerequisites / Co-requisites

None

Module overview

This module combines an introduction to methods of proof with an overview of the basic mathematical entities and structures that will be encountered throughout the degree programme: integers, polynomials, complex numbers, vectors, matrices, groups. These concepts are fundamental to subsequent modules including MAT1034 Linear Algebra and MAT2048 Groups and Rings

Module aims

introduce the standard techniques of mathematical proof

develop the theory and methods of a number of key algebraic systems

develop confidence in algebraic manipulation and the selection of suitable techniques to solve problems

Learning outcomes

Attributes Developed | |
---|---|

Understand and be able to formulate simple algebraic proofs, selecting an appropriate method. | CT |

Know properties of the integers and the integers modulo n. | KC |

Understand polynomials, complex numbers and vectors, and be able to solve problems involving properties. them. | KC |

Understand matrices and determinants, and apply them in various contexts. | KCT |

Know and apply the concepts and notation associated with permutations, groups and fields. | KC |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

Module content

Indicative content includes:

Proof by deduction, induction, contraposition and contradiction.

Prime numbers. Prime factorisation of integers.

The Euclidean algorithm. Greatest common divisor, lowest common multiple.

Equivalence relations, congruences and modular arithmetic.

Polynomials: definitions and basic properties.

Complex numbers. Modulus, argument, exponential form, De Moivre's theorem.

Vectors in two and three dimensions. Scalar and vector products.

Matrix algebra. Properties of the transpose and the trace of a matrix.

Permutations: definitions and basic properties.

Determinants andrties of the transpose and the trace of a matrix. inverse matrices. Solution of simultaneous linear equations.

Linear maps. Eigenvalues and eigenvectors of 2 x 2 matrices.

Introduction to groups and fields.

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

A detailed introduction to logical reasoning and methods of proof

Experience of the methods used to interpret, understand and solve problems in elementary number theory and algebra

The learning and teaching methods include:

Four 50-minute lectures per week for eleven weeks, some being used as tutorials and problem classes.

Online notes supplemented by additional examples in lectures.

A 50-minute seminar in alternate weeks, with preparatory problem sheets which students are expected to attempt in advance.

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

· Ability to interpret and construct formal mathematical proofs.

· Subject knowledge through the recall of key definitions and results.

· Ability to apply the techniques learnt to unseen problems in the test and exam.

Thus, the summative assessment for this module consists of:

· One two-hour examination at the end of Semester 1, worth 75% of the module mark.

· One 45-minute in-semester test; worth 25% of the module mark.

Formative assessment and feedback

Students receive written comments on their marked coursework assignments. Maple TA is used for part of the assignments and provides immediate is used for part of the assignments and provides instant grading and feedback.s to solve problemsials, complex numbers,grading and feedback. Verbal feedback is provided in lectures, seminars and office hours.

Reading list

Reading list for ALGEBRA : http://aspire.surrey.ac.uk/modules/mat1031

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.