This is an archived handbook for a previous year. The current undergraduate and postgraduate handbooks can be viewed using the links above.

Undergraduate Handbook 2006-2007 (archived)

Module MATH2021: LINEAR ALGEBRA II

Department: Mathematical Sciences

MATH2021: LINEAR ALGEBRA II

Type	Level	Credits	Availability	Module Cap	Location
Open	2	20	Available in 2006/2007	None.	Durham

Pre-requisites

Core A Mathematics (MATH1012)

Corequisites

None.

Excluded Combinations

Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571), Foundation Mathematics (MATH1641)

Aims

To develop Linear Algebra (vector spaces, inner product spaces) providing a foundation for study in a number of other areas.

Content

Vector spaces: Axioms, subspaces, linear independence, spanning sets, bases, dimension, coordinates.
Linear Mappings: Definition.
Image, isomorphism, epimorphism, automorphism, endomorphism.
Rank + nullity = dimension, matrix representation, change of basis, canonical form, determinant.
Vector space of linear maps, dual space, dual basis.
Eigenvalues and Eigenspaces: Characteristic polynomial, similar matrices, diagonalisation, Cayley Hamilton theorem, symmetric, skew-symmetric matrices, sesquilinear forms, Hermitian and unitary matrices.
Sturm-Liouville theory: Special functions as solutions of S-L equation, eigenvalues and eigenfunctions and applications.
Normal Forms: Endomorphisms.
Invariant subspaces, minimum polynomial, rational normal form.
Jordan normal form.

Learning Outcomes

Subject-specific Knowledge

By the end of the module students will: be able to solve a range of predictable and unpredictable problems in Linear Algebra.
have a knowledge and understanding of fundamentals of Linear Algebra.
have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas: Vector Spaces.
Linear Mappings.
Eigenvalues and Eigenspaces.
Inner Product Spaces.
Sturm-Liouville Theory.
Normal Forms.

Subject-specific Skills

In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Abstract reasoning and spatial awareness

Key Skills

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
Tutorials provide active engagement and feedback to the learning process.
The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total Hours
Lectures	38	2 per week	1 Hour	38
Tutorials	10	Fortnightly for 20 weeks	1 Hour	10
Problems Classes	10	Fortnightly for 20 weeks	1 Hour	10
Preparation and Reading				142
Total				200

Summative Assessment

Component	Component Weighting	Element	Length/Duration	Element Weighting	Resit Opportunity
Examination	100%	end of year examination three-hours		100%

Formative Assessment

Weekly homework problems.

Students who do not attend monitored activities shown under Teaching Methods and Learning Hours, or who fail to complete the summative or formative assessment(s) specified above, may be subject to the Academic Progress procedures defined in the University's General Regulation V, and may be required to leave the University.