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.

Examines mathematical techniques for understanding place-based environmental issues, analyzing situations, and taking appropriate action. Students will apply methods for collecting, understanding, and displaying data effectively, including gathering environmental data outdoors, then make conclusions using basic inferential statistics. Students will also examine the use of stock-flow systems and other mathematical tools to model interacting populations, energy, pollution spread, recycling, and financial networks.

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.

Investigates the history of some of the principal mathematical societies, including ancient Egypt, Babylon, and Greece; pre-modern Islamic societies, India, and China; indigenous cultures; and the modern west, providing context for students’ performance of arithmetic, algebra, and geometry. Students shall discover how mathematics is shaped by, and itself shapes, historical movements, philosophical positions, and issues of faith

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.