Download 6301 (Discrete Mathematics for Computer Scientists)

6301 (Discrete Mathematics for Computer Scientists)
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2016–2017
MATH6301
First
Half unit (= 7.5 ECTS credits)
2
3 hour lectures and 1 hour problem class per week.
Weekly assessed coursework.
90% examination, 10% coursework
A-level Mathematics or equivalent
Prof Y Kurylev
Prof A Sokal
Course Description and Objectives
This is a first year course for Computer Scientists, introducing students to material they will
need in future computer science courses and providing basic tools for problem solving. Topics covered include: set theory, equivalence relations, functions, symmetry groups, counting
arguments, modular arithmetic and linear algebra.
Recommended Texts
A relevant book is Kenneth H Rosen, Discrete Mathematics and its Applications, Third Edition,
McGraw-Hill, 1995.
Detailed Syllabus
Foundations. Sets theoretic notation. Relations, in particular equivalence relations. Injections, surjections, bijections and their inverses. Cardinality of sets. The symmetry group,
disjoint cycle notation; the sign of a permutation. Abstract groups and Lagrange’s Theorem. Euclid’s algorithm, solving linear congruences, Fermat’s little theorem, the Euler totient
function, application to public key cryptography.
Linear Algebra. The correspondence between linear maps and matrices. Associativity and
non-commutativity of matrix manipulation, Gaussian elimination. LU decomposition. Inverting
matrices. Determinants. Eigenvalues and eigenvectors. Diagonalizing matrices and calculating
polynomials in diagonalizing matrices. Singular value decomposition.
Counting. Combinations, permutations, binomial theorem.
July 2016 MATH6301