Number systems, integers, mathematical induction, rational numbers, real numbers, complex numbers, sets, applications of set algebra, introduction to groups.
Functions, limits, differentiation, methods of differentiation, applications of calculus, curve sketching, optimisation problems, anti-differentiation methods, measure of area and volume, logarithm and exponential functions.
Vectors and vector spaces, inner products, matrices, games of strategy, linear equations, linear programming, linear mappings, linear transformations.
Real numbers, limits of sequences and series, real valued functions, continuity, differentiation, applications, Rolle's theorem, Taylor's theorem, applications.
Introduction to computers, data storage and retrieval, development of computers, introduction to computer programming, use of software packages, spreadsheets.
Real vector spaces of dimension n, lines and planes, curves and surfaces. Calculus of several variables, continuity and derivative. Double and line integrals, surface and volume integrals. Introduction to ordinary and partial differential equations.
B.A. students follow the Off Campus Programme for both semesters of the third year. This is comprised of international study placement and / or relevant work placement. Mathematics students, who wish to study abroad, are advised by department staff on the availability of appropriate courses. Guidance is also provided for those who wish to use the opportunity to begin research work for final year projects in Mathematics.
B.Ed. students follow the Education Programme of classroom experience for the Autumn Semester of the third year. They then return to college to join the B.A. class for the taught modules of the Mathematics programme.
Description of sample data, probability theory, random variables, probability distributions, sampling theory, estimation, hypothesis testing, correlation and regression, testing methods.
Groups, subgroups, Lagrange's theorem. Binary codes. Conjugacy, normal subgroups, permutation groups. Rings, subrings. Integral domains, congruences. Fields.
Functions of a complex variable. Cauchy Riemann equations. Complex integration. Taylor and Laurent Series. Theory of residues. Applications.
Computer logic, Boolean algebra, number representation, error analysis, combinatorics, graph theory, non-linear algebraic equations, iteration, numerical integration, polynomial interpolation, systems of linear equations, ordinary differential equations, mathematical software.
An opportunity for personal work / study, with limited supervision, on an approved mathematical topic or computing assignment of special interest to the student; an opportunity to develop research and presentation skills and / or computing expertise.
Description of sample data, probability theory, random variables, probability distributions, sampling theory, estimation, hypothesis testing, correlation and regression, testing methods.
Groups, subgroups, Lagrange's theorem. Binary codes. Conjugacy, normal subgroups, permutation groups. Rings, subrings. Integral domains, congruences. Fields.
An opportunity for personal work / study, with limited supervision, on an approved mathematical topic or computing assignment of special interest to the student; an opportunity to develop research and presentation skills and / or computing expertise.