## Teaching

I coordinate the Mathematics & Philosophy B.Sc.(Hons) degree; please do not hesitate to get in touch with me if you have any queries related to this degree. General academic requirements for the B.Sc.(Hons) can be found here.

### Research Supervision

- One Ph.D. student completed in 2014. Thesis:
*Anti-Specker Properties in Constructive Reverse Mathematics*. - Three current Ph.D. students working in: analysis and reverse mathematics in minimal logic; non-classical approaches to naïve set theory; model theory and proof theory for non-standard mathematics.
- Several undergraduate/graduate student short research projects in non-classical mathematics, reverse mathematics, logic, philosophy, and history of mathematics.

### Current teaching

- Hilbert Spaces (MATH 420)
- Foundations of Mathematics (MATH 336 / MATH 432)
- Logic, Automata & Computability (MATH 230 / PHIL 210)

### Previous Courses

- Undergraduate/graduate research projects MATH 395 / MATH 491
- Project topics supervised include studies of: minimal reverse mathematics; semi-decidable proof relations; Gödel's theorems; Frege's
*Grundgesetze der Arithmetik*; and Michael Henle's*Which Numbers are Real?* - Hilbert Spaces MATH 420
- The theory of Hilbert spaces is fundamental in many areas of modern mathematical analysis, having a clear and easy-to-grasp geometric structure, just like Euclidean spaces. However, unlike Euclidean spaces, Hilbert spaces may be infinite dimensional. The course will be self-contained, introducing important vector and function spaces, operators on them, and basic spectral theory.
- Foundations of Mathematics MATH 336 / MATH 432
- Part I: Classical propositional and predicate logic, soundness and completeness, the compactness theorem and its applications.
- Part II: Zermelo-Fraenkel set theory, ordinals, the axiom of choice and the continuum hypothesis, independence of axioms.
- Part III: Gödel's incompleteness theorems.
- Logic, Automata & Computability MATH 230 / PHIL 210
- An introduction to formal logic, equivalence of formalizations of classical logic, links between proof and computation, the theory of automata and formal languages, models of computation, computability, and the theoretical limitations of the computer.
- Mathematics in Perspective MATH 380
- Topics in the history, philosophy, directions and culture of mathematics including significant results from the past and an outline of some major areas of progress in the 20
^{th}century. - Mathematics 1A MATH 102
- An introductory course in calculus and linear algebra that is designed primarily for students who have done well in secondary school mathematics with calculus.
- Topics: linear equations and matrices; limits and continuity; determinants; differentiation; functions of more than one variable; integration, including an introduction to first order differential equations.
- Mathematics 1B MATH 103
- A consolidation of concepts from MATH 102 and introduction to more advanced ideas in calculus and linear algebra.
- Topics: vectors and geometry; eigenvalues and eigenvectors; sequences and mathematical induction; series and approximation; techniques and applications of integration; differential equations; probability.
- Engineering Linear Algebra and Statistics EMTH 211
- A linear/matrix algebra course using MATLAB, with engineering applications and a component of statistics for engineers.
- Topics include: LU factorizations; error estimates; iterative methods; applications of eigenvalues and eigenvectors; projections; QR-factorizations; linear regression; measuring goodness-of-fit.
- Introduction to Logic & Computability MATH 130
- Topics include: Classical propositional and predicate logic; proof trees/tableaux; soundness and completeness; register machines; introductory computability and decidability.
- Logic & Computability MATH 134
- Topics include: introductory formal logic; natural language translation; proof trees; soundness and completeness; introductory computability and decidability.
- Engineering Mathematics 1A EMTH 118
- A first course in the methods and applications of engineering mathematics. Topics include calculus, linear algebra, and modelling techniques. This course is designed for engineering students who have done well in secondary school mathematics with calculus.
- Topics: linear equations and matrices; functions, limits and continuity; vector geometry; differentiation; applications of differentiation; integration; and applications of integration, including an introduction to first order differential equations.
- Engineering Mathematics 1B EMTH 119
- A continuation of EMTH 118. Topics covered include methods and Engineering applications of calculus, differential equations, and linear algebra, along with an introduction to probability.
- Topics: techniques and applications of integration (rational functions, arc length, improper integrals); first-order ordinary differential equations with applications; complex numbers; second-order ordinary differential equations with applications; introduction to convergence of sequences and series; applications of differentiation to approximation; approximation by Taylor polynomials; Landau's notation and order of magnitude; determinants, eigenvalues and eigenvectors; sets and probability; discrete random variables; continuous random variables; expectation, mean, and variance; multivariate differentiation and classification of critical points.
- Engineering Mathematics 2 EMTH 210
- This course covers material in multivariable integral and differential calculus, linear algebra and statistics which is applicable to the engineering professions.
- Topics: partial differentiation, chain rule, gradient, directional derivatives, tangent planes, Jacobian, differentials, line integrals, divergence and curl, extreme values and Lagrange multipliers; second order linear differential equations and their applications; Fourier series; double and triple integrals: elements of area, change of order of integration, polar coordinates, volume elements, cylindrical and spherical coordinates; eigenvalues and eigenvectors and their applications; Laplace transforms; statistics (approximating expectations, characteristic functions, random vectors, linking data to probability models, sample mean and variance, order statistics and the empirical distribution function, convergence of random variables, law of large numbers and point estimation, the central limit theorem, error bounds and confidence intervals, sample size calculations, likelihood).
- Calculus I (Massey University) 160.101
- Functions of one real variable and their graphs. Differentiation, integration and differential equations with applications to mathematical models. Introduction to power series, numerical methods and partial differentiation.