2011/12 Undergraduate Module Catalogue

MATH1060 Introductory Linear Algebra

10 Credits Class Size: 180

Module manager: Dr Charles Harris
Email: charlie@maths.leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2011/12

Pre-requisite qualifications

A good A-level Mathematics grade or equivalent.

Mutually Exclusive

MATH1010 Mathematics 1
MATH1012 Mathematics 2
MATH1015 Linear Algebra 1
MATH1331 Linear Algebra with Applications

This module is approved as an Elective

Module summary

Linear Algebra is the formal, detailed theory which covers the ideas involved in solving simultaneous equations, and using matrices and determinants. This course starts by treating simultaneous equations in full generality, and introduces the notions involved in matrices and vector spaces. These basic ideas will be used and expanded in a wide variety of further mathematics modules, and are essential for understanding much of numerical computing. Hence this (or an equivalent) is an essential module for all students of mathematics and many others.

Objectives

A first introduction to Linear Algebra, and in particular to the use of matrices.

On completion of this module, students should be able to:
(a) solve systems of linear equations
(b) perform elementary matrix algebra
(c) solve simple eigenvalue problems.

Syllabus

1. General systems of linear equations: Reduction by elementary row operations to echelon form; solution from echelon form by back substitution.
2. Matrices and matrix algebra: Elementary matrices and inverse of a matrix.
3. Determinants: Definition by expansion, effect of elementary operations, evaluation.
4. Concrete vector spaces and subspaces: Definitions of span and linear combination; linear dependence. Basis and dimensions of a vector space. Rank. Linear maps.
4. Eigenvalues and eigenvectors: Characteristic polynomial for eigenvalues. Eigenvalues adn eigenvectors of symmetric matrices. Classification of critical points of multivariate maps.

Teaching Methods

Delivery type Number Length hours Student hours
Lecture 22 1 22
Tutorial 10 1 10
Private study hours 68
Total Contact hours 32
Total hours (100hr per 10 credits) 100

Opportunities for Formative Feedback

Regular example sheets and in-class quizzes.

Methods of Assessment

Coursework
Assessment type Notes % of formal assessment
In-course Assessment . 20
Total percentage (Assessment Coursework) 20

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
Exam type Exam duration % of formal assessment
Standard exam (closed essays, MCQs etc) 2.0 Hrs 0 Mins 80
Total percentage (Assessment Exams) 80

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading List

The reading list is available from the Library website

Last updated: 2/27/2012

Errors, omissions, failed links etc should be notified to the Catalogue Team