Undergraduate Course: Introduction to Linear Algebra (MATH08057)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 8 (Year 1 Undergraduate)
||Availability||Available to all students
|Summary||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.
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)
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2017/18, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
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
|Additional Information (Learning and Teaching)
Students must pass exam and course overall.
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 20%, Examination 80%
||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|
| - 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.
|Students will require a copy of the course textbook. This is currently "Linear Algebra, A Modern Introduction" by David Poole. Students are advised not to commit to a purchase until this is confirmed by the Course Team and advice on Editions, etc is given.|
|Graduate Attributes and Skills
|Course organiser||Dr Toby Bailey
Tel: (0131 6)50 5068
|Course secretary||Ms Louise Durie
Tel: (0131 6)50 5050