Undergraduate Course: Introduction to Linear Algebra (MATH08057)
|School||School of Mathematics
||College||College of Science and Engineering
||Availability||Available to all students
|Credit level (Normal year taken)||SCQF Level 8 (Year 1 Undergraduate)
|Home subject area||Mathematics
||Other subject area||None
||Taught in Gaelic?||No
|Course description||An 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.
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
|Course Start Date
|Breakdown of Learning and Teaching activities (Further Info)
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
Students must pass exam and course overall.
|Breakdown of Assessment Methods (Further Info)
||Hours & Minutes
|Main Exam Diet S1 (December)||(MATH08057) Introduction to Linear Algebra||3:00|
|Resit Exam Diet (August)||(MATH08057) Introduction to Linear Algebra||3:00|
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.
|See 'Breakdown of Assessment Methods' and 'Additional Notes' above.|
||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)
||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.
|Course organiser||Dr Susan Sierra
Tel: (0131 6)50 5070
|Course secretary||Ms Louise Durie
Tel: (0131 6)50 5050
© Copyright 2013 The University of Edinburgh - 13 January 2014 4:39 am