The course introduces mathematical techniques commonly used in mathematical modeling, and demonstrates their application to problems in physics and engineering. The course requires students to actively apply these techniques in similar problems.

This is a Level II compulsory course for majors and minors in Mathematics, which is suitable for all science students. This course introduces methods for solving first- and second-order ordinary differential equations, systems of differential equations, and power series solutions. The purpose of this course is to introduce students to the theory and application of differential equations. Specifically, the course prepares students to apply differential equations to scientific, engineering and economic problems.

In this course we take an axiomatic approach in defining a vector space. Functions on vector spaces are then defined. Various other spaces are defined such as innerproducts and eigenspaces. The course will be take a formal approach, containing definitions, theorems, lemmas and proofs. Examples will be interspersed throughout.

The course introduces several of the main classes of stochastic process. Their properties are studied, and various case study examples are used to show how they may be used in the construction of real-world models. The course also provides students with practical experience of simulation, and, as part of a group project, requires them to construct and analyse a stochastic model using modern mathematical software.

This is a classical course in the theory of probability - the branch of mathematics that quantifies uncertainty. The course provides an initial review of concepts in elementary probability, before moving to a detailed exploration of the notions of density, distribution and moment for discrete and continuous random variables. Various case study examples are used to show how these ideas can be used in solving real-world problems.

Multivariable Calculus applies the techniques and theory of differentiation and integration to vector-valued functions and functions of more than one variable. The course presents a thorough study of vectors in two and three dimensions, vector-valued functions, curves and surfaces, motion in two and three dimensions, and an introduction to vector fields. Students will be exposed to modern mathematical software to visually represent these 2D and 3D objects.

This is a classical course in analysis, providing a foundation for many other mathematical courses. The course exposes students to rigorous mathematical definitions of limits of sequences of numbers and functions, classical results about continuity and differentiability, series of numbers and functions, and their proofs. A particular focus of the course is in providing students with practical expertise working with rigorous definitions and creating proofs. The following topics will be covered: sequences, continuity, differentiability, series of numbers, series of functions.

Ordinary differential equations; Laplace transform; Fourier series; Partial differential equations; Vector calculus; Line integrals; surface integral Stroke theorem and divergence theorem.

Sampling distributions including X^2, t, and F; order statistics; estimation of parameters, likelihood, sufficiency, significance test, simple linear regression and correlation; analysis of variance; non-parametric  procedures, elementary principles of experimental design.

Basic probability theory: laws of probability, conditional probability,  independence, Bayes formula, random variables, discrete and continuous distributions, expectations, moments, moment generating functions,  functions of random variables.

 Special distributions: binomial, geometric, negative binomial, Poisson,  hypergeometric, uniform, exponential, gamma, normal, laws of large  numbers, the Central Limit Theorem.