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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
Credit level (Normal year taken)SCQF Level 8 (Year 1 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryAn 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.
Course description 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)
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Students MUST NOT also be taking Engineering Mathematics 1a (MATH08074) OR Mathematics for the Natural Sciences 1a (MATH08072)
Other requirements Higher Mathematics or A-level at Grade A, or equivalent
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2016/17, Available to all students (SV1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 33, Seminar/Tutorial Hours 17, Supervised Practical/Workshop/Studio Hours 5, Online Activities 5, Summative Assessment Hours 3, Revision Session Hours 4, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 129 )
Additional Information (Learning and Teaching) Students must pass exam and course overall.
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 20%, Examination 80%
Feedback Not entered
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
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.
Reading List
Students will be assumed to have acquired their personal copy of
'Linear Algebra, A Modern Introduction' by David Poole, 4th Revised Edition 2014, Brooks Cole.
Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr Toby Bailey
Tel: (0131 6)50 5068
Course secretaryMs Louise Durie
Tel: (0131 6)50 5050
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