Key facts
Details for course being taught in current academic year
Level 1 - 18 credits - spring and summer terms
Resources
Course description
Course outline
1. General theory of linear equations: elementary operations, Gaussian array, row-echelon form, reduced row-echelon form.
2. Real vector spaces Rn: addition, scalar multiplication, properties that are axioms in the general vector spaces, linear dependence and independence, subspaces (defined by closure properties), spanning set, basis, standard basis, dimension scalar product (Euclidean inner product), norm, orthogonal, orthonormal basis.
3. Algebra of matrices: rank, row space, column space, elmentary matrices, inverse.
4. Determinants: permutations, evaluation, product rule, adjoint of a matrix, Cramer’s rule, block matrices, Laplace expansion.
5. Eigenvalues and eigen vectors in Rn: characteristic polynomial, Caylay-Hamilton theorem, minimum polynomial.
Learning outcomes
By the end of the course, a successful student should be able to:
1. Solve a system of linear equations
2. Demonstrate understanding the main theorems on the number of solutions of such a system
3. Manipulate matrices
4. Calculate the determinant of a matrix efficiently
5. Calculate eigenvalues and eigenvectors.
Assessments
| Type | Timing | Weighting |
|---|---|---|
| Coursework | 20.00% | |
| Problem Sets | Spring Week 2 | equal weighting |
| Exercise | Spring Week 8 (1 hour ) | equal weighting |
| Unseen Examination | Summer Term (1 hour 30 minutes) | 80.00% |
Resit mode of assessment
| Type | Timing | Weighting |
|---|---|---|
| Unseen Examination | Summer Vacation (1 hour 30 minutes) | 100.00% |
Timing
Submission deadlines may vary for different types of assignment/groups of students.
Weighting
Coursework components (if listed) total 100% of the overall coursework weighting value.
Teaching methods
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Spring+Summer Terms | LECTURE | 1 hour | 1111111111 |
| Spring+Summer Terms | LECTURE | 2 hours | 1111111111 |
| Spring+Summer Terms | WORKSHOP | 1 hour | 1111111111 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.