Syllabus  MA294
MA283 Linear Algebra
Amongst the topics to be covered are the following

Vector spaces, bases, dimension, linear maps, matrix representation of
linear maps

Matrix algebra, kernels and images, least squares fitting, inner product
spaces, the GramSchmidt process

Fourier series, dual spaces, the rank of a matrix, determinants, eigenvalues
and eigenvectors, the characteristic polynomial, quadratic forms

Diagonalisation of a symmetric or Hermitian linear map

Triangularisation of a linear map

The HamiltonCayley theorem, linear programming
Texts

T.S. Blyth & E.F. Robertson, "Matrices and Vector Spaces and Linear
Algebra" (Chapman & Hall)

S. Lipschutz, "Linear Algebra" (Schaum Outline)
References

H. Anton, "Elementary Linear Algebra" (Wiley)

J.W. Archbold, "Algebra" (Pitman)

G. Birkhoff & S. MacLane, "A Survey of Modern Algebra" (Macmillan)

I.N. Herstein, "Topics in Algebra" (Blaisdell)

S. Lang, "Linear Algebra" (Springer)

T.A. Whitelaw, "An Introduction to Linear Algebra" (Blackie)
MA284 Discrete Maths

Enumeration: product rule, sum rule and sieve principle, selections and
distributions, the pigeonhole principle

Graphs, the fundamentals (including various notions of 'path' and 'tree'),
plus a study of some of the following topics: colouring problems, bipartite
graphs, Hamiltonian graphs, planar graphs and tournaments. Algorithms and
applications are emphasised throughout.
Texts

N.L. Biggs, "Discrete Mathematics", (Oxford)
Back to 2nd Year Syllabus