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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Introduction to Linear Algebra (MATH08057)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 8 (Year 1 Undergraduate) Credits20
Home subject areaMathematics Other subject areaNone
Course website None Taught in Gaelic?No
Course descriptionAn introduction to linear algebra, mainly in R^n but concluding with an introduction to abstract vector spaces.

The principal topics are vectors, systems of linear equations, matrices, eigenvalues and eigenvectors and orthogonality. The important notions of linear independence, span and bases are introduced.

This course is preparation for the practical using of ideas around vectors, matrices and linearity and also lays the groundwork for a more abstract, pure-mathematical treatment of vector spaces.

Students will also learn how to use Maple for some simple matrix operations.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Students MUST NOT also be taking Mathematics for Science and Engineering 1a (MATH08060) OR Solving Equations (MATH08002) OR Applicable Mathematics 1 (MATH08027) OR Mathematics for Informatics 1a (MATH08046) OR Mathematics for Informatics 1b (MINF08001)
Other requirements Higher Mathematics or A-level at Grade A, or equivalent
Additional Costs None
Information for Visiting Students
Displayed in Visiting Students Prospectus?Yes
Course Delivery Information
Delivery period: 2013/14 Semester 1, Available to all students (SV1) Learn enabled:  Yes Quota:  None
Web Timetable Web Timetable
Course Start Date 16/09/2013
Breakdown of Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 40, Seminar/Tutorial Hours 10, Supervised Practical/Workshop/Studio Hours 10, Summative Assessment Hours 3, Revision Session Hours 4, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 129 )
Additional Notes Students must pass exam and course overall.
Breakdown of Assessment Methods (Further Info) Written Exam 85 %, Coursework 15 %, Practical Exam 0 %
Exam Information
Exam Diet Paper Name Hours:Minutes
Main Exam Diet S1 (December)(MATH08057) Introduction to Linear Algebra3:00
Resit Exam Diet (August)(MATH08057) Introduction to Linear Algebra3:00
Summary of Intended Learning Outcomes
- Facility in practical calculation with vectors and matrices in arbitrary dimensions
- Geometrical understanding of vectors and vector operations in 2 and 3 dimensions
- Thorough understanding of systems of linear equations and solution methods.
- Understanding of and facility in calculation with eigenvalues and eigenvectors.
- Understanding of orthogonality and projection in arbitrary dimensions.
- Acquaintance with the idea of abstract vector spaces.
- Ability to do matrix calculations with Maple.
Assessment Information
See 'Breakdown of Assessment Methods' and 'Additional Notes' above.
Special Arrangements
Additional Information
Academic description Not entered
Syllabus This syllabus is for guidance purposes only :

Essentially the contents of Poole Chapters 1 to Chapter 6.2, with a selection (not all) of the applications covered and selected topics omitted.

The course will have four lecture-theatre-hours per week, with the understanding that one of those or equivalent pro rata is for Example Classes and other reinforcement activities. The figures in parentheses below are indicative only and refer to numbers of lecture-theatre hours.

- Complex Numbers (Appendix C) (3)
- Vectors and geometry (4)
- Systems of linear equations, echelon form, Gaussian elimination, intro to span and linear independence. (6)
- Matrices, multiplication, transpose, inverses, linear maps. Intro to subspaces and bases. Rank. (8)
- Eigenvalues and eigenvectors. Determinants (6)
- Orthogonality, Gram-Schmidt, orthogonal diagonalisation. (5)
- Introduction to abstract vector spaces and subspaces. (4)
- Selected applications (taught in sequence where appropriate) (4)
Transferable skills Not entered
Reading list Students will be assumed to have acquired their personal copy of
'Linear Algebra, A Modern Introduction' by David Poole, 3rd Int. Ed. 2011, Brooks Cole.
Study Abroad Not entered
Study Pattern Not entered
Course organiserDr Susan Sierra
Tel: (0131 6)50 5070
Course secretaryMs Louise Durie
Tel: (0131 6)50 5050
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