Functions of a complex variable, differentiation, analytic and elementary functions, Cauchy's theorem and contour integration, Taylor and Laurent series, residues and poles, and conformal mapping. Emphasis is placed on physical applications.

Introduction to principles of real analysis. Topics include rational numbers, completeness, sequences, limits, continuity, and implications to Calculus.

First-order differential equations, linear differential equations, Laplace transforms, systems of differential equations, non-linear systems, series solutions, applications in the physical, biological, social, and engineering sciences.

The mathematics of inferential statistics. Topics include probability distributions and densities, expectation, moment-generating functions, functions of random variables, limiting distributions, and the theory behind statistical methods such as estimation, hypothesis testing, regression and correlation.

Systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization applications, and linear programming.

Multivariate calculus. Topics include vectors, vector functions and derivatives; curves; partial and directional derivatives; Lagrange multipliers; double and triple integrals; spherical and cylindrical co-ordinates; vector integrals, Green's Theorem, and surface integrals.

An introduction to the theory and application of probability and statistics for students who have experience with calculus. Topics include data collection, descriptive statistics, probability, random variables and standard distributions, central limit theorem, hypothesis tests, interval estimates, and linear regression. Computer software will be used to display, analyze, and simulate data. The focus will be on biostatistics with applications using data from the life sciences.

Mathematical concepts and topics that undergird the elementary school mathematics curriculum. Topics include principles and applications of number systems, sets, equations, linear programming, geometry, and mathematical proof within a historical and societal context. It may not be used to meet a mathematics requirement in any other program. Students are responsible for checking the mathematics requirements of the school at which they intend to take their professional year, as they may be different from those required to obtain a teaching certificate.

An introduction to those branches of pure mathematics which are most commonly used in the study of Computing Science and/or have other practical applications. Topics include logic, proofs, switching circuits, set theory, induction, functions, languages, finite automata, combinatorics, and algebraic structures.

Transcendental functions, integration techniques, polar co-ordinates, sequences, series, and Taylor series.