For current modules go to the modules page for more details.
Convergence of sequences and series. The structure of the reals. Introduction to proofs using epsilon and delta, for second year JH students.
Syllabus: Combinatorics and counting, probability, and graph theory.
Syllabus: Polynomials over rings and fields, ideals, quotients, field of fractions.
Syllabus: The completeness, compactness and soundness theorems for first-order logic.
Convergence of sequences and series. The structure of the reals. Introduction to proofs using epsilon and delta.
Computability via Turing machines. The halting problem. Measures of time and space complexity. The P=NP problem.
The secong half of this module, and my contributions started in January 2001.
Functions of several variables, PDEs, multiple integrals, etc., for second year students in the School of Civil Engineering, which I taught in the second semester of the academic years 1996-7, 1997-8, 1998-9 and 1999-2000.
Part-module givenin the academic years 1997-8, 1998-9 and 1999-2000. It ran in the second semester of the first-year programme, as backup for the double module MSM1G2. Worksheets include numerical and symbolic integration and solutions of ODEs, and vector spaces.
Autumn of 1998, and 1999. The course introduced the ideas of axioms, proofs and rigour to first year students, and also introduces them to some of the main number systems in mathematics.
(Autumn terms of 1995, 1996, and 1997). Eigenvectors, eigenvalues and diagonalization of matrices, and bilinear and sesquilinear forms.