We seek applicants with a strong quantitative undergraduate training, e.g., those graduating with degrees in Statistics, Actuarial Science, Mathematics, Economics, and Engineering.

Below you will find a collection of suggested courses (using the University of Toronto course codes), as well as brief course descriptions, that we recommend students complete before applying to the program:

### MAT 137Y (Calculus)

A conceptual approach for students with a serious interest in mathematics. Attention is given to computational aspects as well as theoretical foundations and problem solving techniques. Review of Trigonometry. Limits and continuity, mean value theorem, inverse function theorem, differentiation, integration, fundamental theorem of calculus, elementary transcendental functions, Taylor’s theorem, sequence and series, power series.

### MAT 237Y (Multivariable Calculus)

Sequences and series. Uniform convergence. Convergence of integrals. Elements of topology in R^2 and R^3. Differential and integral calculus of vector valued functions of a vector variable, with emphasis on vectors in two and three dimensional euclidean space. Extremal problems, Lagrange multipliers, line and surface integrals, vector analysis, Stokes’ theorem, Fourier series, calculus of variations.

### MAT 223H (Linear Algebra I)

Systems of linear equations, matrix algebra, real vector spaces, subspaces, span, linear dependence and independence, bases, rank, inner products, orthogonality, orthogonal complements, Gram-Schmidt, linear transformations, determinants, Cramer’s rule, eigenvalues, eigenvectors, eigenspaces, diagonalization.

### STA 257H (Introductory Probability and Statistics I)

Abstract probability and expectation, discrete and continuous random variables and vectors, with the special mathematics of distribution and density functions, all realized in the special examples of ordinary statistical practice: the binomial, poisson and geometric group, and the gaussian (normal), gamma, chi-squared complex.

### STA 261H (Introductory Probability and Statistics II)

Statistical models, parameters, samples and estimates; the general concept of statistical confidence with applications to the discrete case and the construction of confidence intervals and more general regions in both the univariate and vector-valued cases; hypothesis testing; the likelihood function and its applications; time permitting: the basics of data analysis, unbiasedness, sufficiency, line+D5ar models and regression.

### ACT 240H (Mathematics of Investment & Credit)

Interest, discount and present values, as applied to determine prices and values of annuities, mortgages, bonds, equities; loan repayment schedules and consumer finance payments in general; yield rates on investments given the costs on investments.

### ACT 245H (Financial Principles for Actuarial Science I)

Term structure of interest rates, cashflow duration, convexity and immunization, forward and futures contracts, interest rate swaps, introduction to investment derivatives and hedging strategies

### STA 302H (Applied Regression Analysis)

Introduction to data analysis with a focus on regression. Initial Examination of data. Correlation. Simple and multiple regression models using least squares. Inference for regression parameters, confidence and prediction intervals. Diagnostics and remedial measures. Interactions and dummy variables. Variable selection. Least squares estimation and inference for non-linear regression.

### STA 347H (Probability Theory)

Probability from a non-measure theoretic point of view. Random variables/vectors; independence, conditional expectation/probability and consequences. Various types of convergence leading to proofs of the major theorems in basic probability. An introduction to simple stochastic processes such as Poisson and branching processes

### ACT 370H (Financial Principles for Actuarial Science II)

Mathematical theory of financial derivatives, discrete and continuous option pricing models, hedging strategies and exotic option valuation.

### STA 437H (Applied Multivariate Analysis)

Practical techniques for the analysis of multivariate data; fundamental methods of data reduction with an introduction to underlying distribution theory; basic estimation and hypothesis testing for multivariate means and variances; regression coefficients; principal components and partial, multiple and canonical correlations; multivariate analysis of variance; profile analysis and curve fitting for repeated measurements; classification and the linear discriminant function

### ACT 460H (Stochastic methods for Actuarial Science)

Applications of the lognormal distribution, Brownian motion, geometric Brownian motion, martingales, Ito’s lemma, stochastic differential equations, interest rate models, the Black-Scholes model, volatility, value at risk, conditional tail expectation.

It is not necessary to have all of the above courses, rather we seek students with a solid breadth and depth in their training to be successful in the program.