Undergraduate Course: Introduction to Linear Algebra (MATH08057)
Course Outline
| School |
School of Mathematics |
College |
College of Science and Engineering |
| Course type |
Standard |
Availability |
Available to all students |
| Credit level (Normal year taken) |
SCQF Level 8 (Year 1 Undergraduate) |
Credits |
20 |
| Home subject area |
Mathematics |
Other subject area |
None |
| Course website |
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. |
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)
|
Other requirements |
Higher Mathematics or A-level at Grade A, or equivalent
|
| Additional Costs |
None |
Information for Visiting Students
| Pre-requisites |
None |
| Displayed in Visiting Students Prospectus? |
Yes |
Course Delivery Information
|
| Delivery period: 2011/12 Semester 1, Available to all students (SV1)
|
WebCT enabled: Yes |
Quota: None |
| Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| Central | Lecture | Appleton Th 5 | 1-11 | 12:10 - 13:00 | | | | | | Central | Lecture | Appleton Th 5 | 1-11 | | | 12:10 - 13:00 | | | | Central | Lecture | Appleton Th 5 | 1-11 | | | | 12:10 - 13:00 | | | Central | Lecture | Appleton Th 5 | 1-11 | | | | | 12:10 - 13:00 |
| First Class |
Week 1, Monday, 12:10 - 13:00, Zone: Central. Appleton Tower Lecture Theatre 5 |
| Additional information |
Tutorials are held on a Tuesday (9:00, 10:00, 11:10, 12:10 or 13:05) in Appleton Tower Teaching Studio |
| Exam Information |
| Exam Diet |
Paper Name |
Hours:Minutes |
|
|
| Main Exam Diet S1 (December) | MATH08057 Introduction to Linear Algebra | 2:00 | | |
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
| Up to 15% Continuous Assessment, the remainder examination. |
Special Arrangements
| None |
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 |
| Keywords |
ILA |
Contacts
| Course organiser |
Dr Toby Bailey
Tel: (0131 6)50 5068
Email: t.n.bailey@ed.ac.uk |
Course secretary |
Ms Louise Durie
Tel: (0131 6)50 5050
Email: L.Durie@ed.ac.uk |
|
copyright 2011 The University of Edinburgh -
1 September 2011 6:25 am
|
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