This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues and similarity.

- Problem set 1 (do questions 1,2,3 in week 1, question 4 in week 2) [solutions] (thanks to Gurpreet Singh)
- Problem set 2 (week 2) [solutions] (thanks to Joe Flavin)

Homework 1 due on February 2 - 3 - Problem set 3 (week 3) [solutions]
- Problem set 4 (week 3 and 4) [solutions] (thanks to Patrick Nolan)

Homework 2 due on February 16 - 17 - Problem set 5 (week 4 and 5) [question 1] (by myself), and [other questions] (thanks to Joseph Brennan)
- Problem set 6 (week 5 and 6) selected [solutions] (thanks to Richard Ellard)

Homework 3 due on March 2 - 3 - Problem set 7 (week 7) [solutions] (thanks to Gurpreet Singh) more on [question 3]
- Problem set 8 (week 7 and 8) [solutions] (thanks to Conor Manning)

Homework 4 due on March 30 - 31 - Problem set 9 (week 8 and 9) [solutions] (thanks to joe Flavin)
- Problem set 10 (week 10) [solutions]

Homework 5 due on April 13 - 14 - Problem set 11 (week 11 and 12) [solutions]

- Numbers and polynomials.
- (1.1) What is a field?
- (1.2) Real numbers / digression: a bit of arithmetic / (part 2)

digression: algebraic identities - (1.3) Polynomials with coefficients in a field / (part 2) / (part 3)
- (1.4) Complex numbers / (part 2) / (part 3)
- (1.5) Exponential with complex argument, Euler's formula and trigonometry

- Systems of linear equations.
- (2.1) Introduction: method of elimination / (part 2)
- (2.2) Vectors and matrices
- (2.3) Matrices and linear systems
- (2.4) Vector spaces. Matrix as a map / (part 2)
- (2.5) Inverse matrix / (part 2)
- (2.6) Determinant / (part 2) / (part 3)

digression: composition of permutations and signature - (2.7) Cofactor expansion, inverse matrix and Cramer's rule
- Eigenvalues and eigenvectors.
- (3.1) Eigenvalues and eigenvectors
- (3.2) The Cayley-Hamilton theorem and diagonalization / (part 2)
- (3.3) Trace, determinant and eigenvalues
- Vector spaces and linear maps.
- Vectors and three-dimensional geometry.

- Bernard Kolman, Arnold Shapiro,
*College Algebra and Trigonometry*/ shelf 512.03 (in James Joyce Library, top floor) - Charles C. Carigo,
*College Algebra and Trigonometry*/ 512.13

- Bernard Kolman,
*Introductory Linear Algebra with Applications*/ 512.5 - Gilbert Strang,
*Linear Algebra and Its Applications*/ 512.5

Here are the last year's final [exam paper] and [solutions]. This year's paper layout is different. There will be 8 questions (some of which have parts a,b,c...). Full marks will be given for complete answers to ALL questions. Correctness of the final numerical answer is important for evaluation. Uncollected homeworks can be found in the box located at the ground floor of Sceince North under the staircase. It looks approximately like this -----> Please make sure you leave the box at the same place. Maths Help Centre reports that many students are struggling with determinants. Please note the following: in the final exam there will be no questions like in Problem Set 7. What you really need is to be able to compute determinants, for which the most efficient method is the cofactor expansion. |