Please note: Due to the ongoing transition to the new course catalogue, the program and course information displayed below may be temporarily unavailable or outdated. In particular, details about whether a course will be offered in an upcoming term may be inaccurate. Official course scheduling information for Fall 2025 will be available on Minerva during the first week of May. We appreciate your patience and understanding during this transition.
Mathematics Liberal Program - Core Science Component (B.Sc.) (45 credits)
Offered by: Mathematics and Statistics (Faculty of Science)
Degree: Bachelor of Science
Program credit weight: 45
Program Description
The B.Sc.; Liberal Program – Core Science Component in Mathematics provides a general overview of Mathematics, including a rigorous foundation and exploration of the different branches of Mathematics,
Degree Requirements — B.Sc.
This program is offered as part of a Bachelor of Science (B.Sc.) degree.
To graduate, students must satisfy both their program requirements and their degree requirements.
- The program requirements (i.e., the specific courses that make up this program) are listed under the Course Tab (above).
- The degree requirements—including the mandatory Foundation program, appropriate degree structure, and any additional components—are outlined on the Degree Requirements page.
Students are responsible for ensuring that this program fits within the overall structure of their degree and that all degree requirements are met. Consult the Degree Planning Guide on the SOUSA website for additional guidance.
Program Prerequisites
Students entering the Core Science Component in Mathematics are normally expected to have completed the courses below or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the 45 credits required for the program.
| Course | Title | Credits |
|---|---|---|
| MATH 133 | Linear Algebra and Geometry. | 3 |
Linear Algebra and Geometry. Terms offered: Summer 2025, Fall 2025, Winter 2026 Systems of linear equations, matrices, inverses, determinants; geometric vectors in three dimensions, dot product, cross product, lines and planes; introduction to vector spaces, linear dependence and independence, bases. Linear transformations. Eigenvalues and diagonalization. | ||
| MATH 140 | Calculus 1. | 3 |
Calculus 1. Terms offered: Summer 2025, Fall 2025, Winter 2026 Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications. | ||
| MATH 141 | Calculus 2. | 4 |
Calculus 2. Terms offered: Summer 2025, Fall 2025, Winter 2026 The definite integral. Techniques of integration. Applications. Introduction to sequences and series. | ||
Guidelines for Selection of Courses
The following informal guidelines should be discussed with the student's adviser. Where appropriate, Honours courses may be substituted for equivalent Major courses. Students planning to pursue graduate studies are encouraged to make such substitutions.
Students interested in computer science are advised to choose courses from the following and to complete the Computer Science Minor:
| Course | Title | Credits |
|---|---|---|
| MATH 317 | Numerical Analysis. | 3 |
Numerical Analysis. Terms offered: Fall 2025 Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations. | ||
| MATH 318 | Mathematical Logic. | 3 |
Mathematical Logic. Terms offered: Fall 2025 Propositional logic: truth-tables, formal proof systems, completeness and compactness theorems, Boolean algebras; first-order logic: formal proofs, Gödel's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; Gödel's incompleteness theorem. | ||
| MATH 327 | Matrix Numerical Analysis. | 3 |
Matrix Numerical Analysis. Terms offered: this course is not currently offered. An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems. | ||
| MATH 335 | Groups, Tilings and Algorithms. | 3 |
Groups, Tilings and Algorithms. Terms offered: Winter 2026 Transformation groups of the plane. Inversions and Moebius transformations. The hyperbolic plane. Tilings in dimension 2 and 3. Group presentations and Cayley graphs. Free groups and Schreier's theorem. Coxeter groups. Dehn's Word and Conjugacy Problems. Undecidability of the Word Problem for semigroups. Regular languages and automatic groups. Automaticity of Coxeter groups. | ||
| MATH 340 | Discrete Mathematics. | 3 |
Discrete Mathematics. Terms offered: Winter 2026 Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs. | ||
| MATH 417 | Linear Optimization. | 3 |
Linear Optimization. Terms offered: this course is not currently offered. An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interior-point methods, quadratic optimization, applications in game theory. | ||
Students interested in probability and statistics are advised to take
| Course | Title | Credits |
|---|---|---|
| MATH 204 | Principles of Statistics 2. | 3 |
Principles of Statistics 2. Terms offered: Winter 2026 The concept of degrees of freedom and the analysis of variability. Planning of experiments. Experimental designs. Polynomial and multiple regressions. Statistical computer packages (no previous computing experience is needed). General statistical procedures requiring few assumptions about the probability model. | ||
| MATH 324 | Statistics. | 3 |
Statistics. Terms offered: Fall 2025, Winter 2026 Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference. | ||
| MATH 423 | Applied Regression. | 3 |
Applied Regression. Terms offered: Fall 2025 Multiple regression estimators and their properties. Hypothesis tests and confidence intervals. Analysis of variance. Prediction and prediction intervals. Model diagnostics. Model selection. Introduction to weighted least squares. Basic contingency table analysis. Introduction to logistic and Poisson regression. Applications to experimental and observational data. | ||
| MATH 447 | Introduction to Stochastic Processes. | 3 |
Introduction to Stochastic Processes. Terms offered: Winter 2026 Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory. | ||
| MATH 523 | Generalized Linear Models. | 4 |
Generalized Linear Models. Terms offered: Winter 2026 Exponential families, link functions. Inference and parameter estimation for generalized linear models; model selection using analysis of deviance. Residuals. Contingency table analysis, logistic regression, multinomial regression, Poisson regression, log-linear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data. | ||
| MATH 525 | Sampling Theory and Applications. | 4 |
Sampling Theory and Applications. Terms offered: Winter 2026 Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse. | ||
Students interested in applied mathematics should take
| Course | Title | Credits |
|---|---|---|
| MATH 317 | Numerical Analysis. | 3 |
Numerical Analysis. Terms offered: Fall 2025 Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations. | ||
| MATH 319 | Partial Differential Equations . | 3 |
Partial Differential Equations . Terms offered: Winter 2026 First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems. | ||
| MATH 324 | Statistics. | 3 |
Statistics. Terms offered: Fall 2025, Winter 2026 Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference. | ||
| MATH 326 | Nonlinear Dynamics and Chaos. | 3 |
Nonlinear Dynamics and Chaos. Terms offered: Fall 2025 Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos. | ||
| MATH 327 | Matrix Numerical Analysis. | 3 |
Matrix Numerical Analysis. Terms offered: this course is not currently offered. An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems. | ||
| MATH 417 | Linear Optimization. | 3 |
Linear Optimization. Terms offered: this course is not currently offered. An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interior-point methods, quadratic optimization, applications in game theory. | ||
Students considering a career in secondary school teaching are advised to take
| Course | Title | Credits |
|---|---|---|
| MATH 318 | Mathematical Logic. | 3 |
Mathematical Logic. Terms offered: Fall 2025 Propositional logic: truth-tables, formal proof systems, completeness and compactness theorems, Boolean algebras; first-order logic: formal proofs, Gödel's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; Gödel's incompleteness theorem. | ||
| MATH 338 | History and Philosophy of Mathematics. | 3 |
History and Philosophy of Mathematics. Terms offered: Fall 2025 Egyptian, Babylonian, Greek, Indian and Arab contributions to mathematics are studied together with some modern developments they give rise to, for example, the problem of trisecting the angle. European mathematics from the Renaissance to the 18th century is discussed, culminating in the discovery of the infinitesimal and integral calculus by Newton and Leibnitz. Demonstration of how mathematics was done in past centuries, and involves the practice of mathematics, including detailed calculations, arguments based on geometric reasoning, and proofs. | ||
| MATH 346 | Number Theory. | 3 |
Number Theory. Terms offered: this course is not currently offered. Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions. | ||
| MATH 348 | Euclidean Geometry. | 3 |
Euclidean Geometry. Terms offered: Fall 2025 Points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area. Power of a point with respect to a circle. Ceva’s theorem. Isometries. Homothety. Inversion. | ||
Students interested in careers in business, industry or government are advised to select courses from the following list:
| Course | Title | Credits |
|---|---|---|
| MATH 317 | Numerical Analysis. | 3 |
Numerical Analysis. Terms offered: Fall 2025 Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations. | ||
| MATH 319 | Partial Differential Equations . | 3 |
Partial Differential Equations . Terms offered: Winter 2026 First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems. | ||
| MATH 327 | Matrix Numerical Analysis. | 3 |
Matrix Numerical Analysis. Terms offered: this course is not currently offered. An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems. | ||
| MATH 329 | Theory of Interest. | 3 |
Theory of Interest. Terms offered: Winter 2026 Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation. | ||
| MATH 417 | Linear Optimization. | 3 |
Linear Optimization. Terms offered: this course is not currently offered. An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interior-point methods, quadratic optimization, applications in game theory. | ||
| MATH 423 | Applied Regression. | 3 |
Applied Regression. Terms offered: Fall 2025 Multiple regression estimators and their properties. Hypothesis tests and confidence intervals. Analysis of variance. Prediction and prediction intervals. Model diagnostics. Model selection. Introduction to weighted least squares. Basic contingency table analysis. Introduction to logistic and Poisson regression. Applications to experimental and observational data. | ||
| MATH 430 | Mathematical Finance. | 3 |
Mathematical Finance. Terms offered: this course is not currently offered. Introduction to concepts of price and hedge derivative securities. The following concepts will be studied in both concrete and continuous time: filtrations, martingales, the change of measure technique, hedging, pricing, absence of arbitrage opportunities and the Fundamental Theorem of Asset Pricing. | ||
| MATH 447 | Introduction to Stochastic Processes. | 3 |
Introduction to Stochastic Processes. Terms offered: Winter 2026 Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory. | ||
| MATH 523 | Generalized Linear Models. | 4 |
Generalized Linear Models. Terms offered: Winter 2026 Exponential families, link functions. Inference and parameter estimation for generalized linear models; model selection using analysis of deviance. Residuals. Contingency table analysis, logistic regression, multinomial regression, Poisson regression, log-linear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data. | ||
| MATH 525 | Sampling Theory and Applications. | 4 |
Sampling Theory and Applications. Terms offered: Winter 2026 Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse. | ||
Required Courses (27 credits)
| Course | Title | Credits |
|---|---|---|
| MATH 222 | Calculus 3. 1 | 3 |
Calculus 3. Terms offered: Summer 2025, Fall 2025, Winter 2026 Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals. | ||
| MATH 235 | Algebra 1. | 3 |
Algebra 1. Terms offered: Fall 2025 Sets, functions and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. Rings, ideals and quotient rings. Fields and construction of fields from polynomial rings. Groups, subgroups and cosets; homomorphisms and quotient groups. | ||
| MATH 236 | Algebra 2. | 3 |
Algebra 2. Terms offered: Winter 2026 Linear equations over a field. Introduction to vector spaces. Linear mappings. Matrix representation of linear mappings. Determinants. Eigenvectors and eigenvalues. Diagonalizable operators. Cayley-Hamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms. | ||
| MATH 242 | Analysis 1. | 3 |
Analysis 1. Terms offered: Fall 2025 A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line. | ||
| MATH 243 | Analysis 2. | 3 |
Analysis 2. Terms offered: Winter 2026 Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces. | ||
| MATH 249 | Honours Complex Variables. 2 | 3 |
Honours Complex Variables. Terms offered: Winter 2026 Functions of a complex variable; Cauchy-Riemann equations; Cauchy's theorem and consequences. Taylor and Laurent expansions. Residue calculus; evaluation of real integrals; integral representation of special functions; the complex inversion integral. Conformal mapping; Schwarz-Christoffel transformation; Poisson's integral formulas; applications. Additional topics if time permits: homotopy of paths and simple connectivity, Riemann sphere, rudiments of analytic continuation. | ||
| MATH 314 | Advanced Calculus. | 3 |
Advanced Calculus. Terms offered: Fall 2025, Winter 2026 Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications. | ||
| MATH 315 | Ordinary Differential Equations. | 3 |
Ordinary Differential Equations. Terms offered: Fall 2025, Winter 2026 First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions. | ||
| MATH 316 | Complex Variables. 2 | 3 |
Complex Variables. Terms offered: Fall 2025 Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications. | ||
| MATH 323 | Probability. | 3 |
Probability. Terms offered: Summer 2025, Fall 2025, Winter 2026 Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem. | ||
- 1
Students who have successfully completed a course equivalent to MATH 222 Calculus 3. with a grade of C or better may omit MATH 222 Calculus 3., but must replace it with 3 credits of complementary courses.
- 2
Students may select either MATH 249 Honours Complex Variables. or MATH 316 Complex Variables. but not both.
Complementary Courses (18 credits)
6 credits selected from:
| Course | Title | Credits |
|---|---|---|
| MATH 317 | Numerical Analysis. | 3 |
Numerical Analysis. Terms offered: Fall 2025 Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations. | ||
| MATH 324 | Statistics. | 3 |
Statistics. Terms offered: Fall 2025, Winter 2026 Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference. | ||
| MATH 335 | Groups, Tilings and Algorithms. | 3 |
Groups, Tilings and Algorithms. Terms offered: Winter 2026 Transformation groups of the plane. Inversions and Moebius transformations. The hyperbolic plane. Tilings in dimension 2 and 3. Group presentations and Cayley graphs. Free groups and Schreier's theorem. Coxeter groups. Dehn's Word and Conjugacy Problems. Undecidability of the Word Problem for semigroups. Regular languages and automatic groups. Automaticity of Coxeter groups. | ||
| MATH 340 | Discrete Mathematics. | 3 |
Discrete Mathematics. Terms offered: Winter 2026 Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs. | ||
12 credits selected from:
| Course | Title | Credits |
|---|---|---|
| MATH 204 | Principles of Statistics 2. | 3 |
Principles of Statistics 2. Terms offered: Winter 2026 The concept of degrees of freedom and the analysis of variability. Planning of experiments. Experimental designs. Polynomial and multiple regressions. Statistical computer packages (no previous computing experience is needed). General statistical procedures requiring few assumptions about the probability model. | ||
| MATH 208 | Introduction to Statistical Computing. | 3 |
Introduction to Statistical Computing. Terms offered: Fall 2025 Basic data management. Data visualization. Exploratory data analysis and descriptive statistics. Writing functions. Simulation and parallel computing. Communication data and documenting code for reproducible research. | ||
| MATH 308 | Fundamentals of Statistical Learning. | 3 |
Fundamentals of Statistical Learning. Terms offered: Winter 2026 Theory and application of various techniques for the exploration and analysis of multivariate data: principal component analysis, correspondence analysis, and other visualization and dimensionality reduction techniques; supervised and unsupervised learning; linear discriminant analysis, and clustering techniques. Data applications using appropriate software. | ||
| MATH 318 | Mathematical Logic. | 3 |
Mathematical Logic. Terms offered: Fall 2025 Propositional logic: truth-tables, formal proof systems, completeness and compactness theorems, Boolean algebras; first-order logic: formal proofs, Gödel's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; Gödel's incompleteness theorem. | ||
| MATH 319 | Partial Differential Equations . | 3 |
Partial Differential Equations . Terms offered: Winter 2026 First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems. | ||
| MATH 326 | Nonlinear Dynamics and Chaos. | 3 |
Nonlinear Dynamics and Chaos. Terms offered: Fall 2025 Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos. | ||
| MATH 327 | Matrix Numerical Analysis. | 3 |
Matrix Numerical Analysis. Terms offered: this course is not currently offered. An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems. | ||
| MATH 329 | Theory of Interest. | 3 |
Theory of Interest. Terms offered: Winter 2026 Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation. | ||
| MATH 338 | History and Philosophy of Mathematics. | 3 |
History and Philosophy of Mathematics. Terms offered: Fall 2025 Egyptian, Babylonian, Greek, Indian and Arab contributions to mathematics are studied together with some modern developments they give rise to, for example, the problem of trisecting the angle. European mathematics from the Renaissance to the 18th century is discussed, culminating in the discovery of the infinitesimal and integral calculus by Newton and Leibnitz. Demonstration of how mathematics was done in past centuries, and involves the practice of mathematics, including detailed calculations, arguments based on geometric reasoning, and proofs. | ||
| MATH 346 | Number Theory. | 3 |
Number Theory. Terms offered: this course is not currently offered. Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions. | ||
| MATH 348 | Euclidean Geometry. | 3 |
Euclidean Geometry. Terms offered: Fall 2025 Points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area. Power of a point with respect to a circle. Ceva’s theorem. Isometries. Homothety. Inversion. | ||
| MATH 352 | Problem Seminar. | 1 |
Problem Seminar. Terms offered: this course is not currently offered. Seminar in Mathematical Problem Solving. The problems considered will be of the type that occur in the Putnam competition and in other similar mathematical competitions. | ||
| MATH 378 | Nonlinear Optimization . | 3 |
Nonlinear Optimization . Terms offered: Fall 2025 Optimization terminology. Convexity. First- and second-order optimality conditions for unconstrained problems. Numerical methods for unconstrained optimization: Gradient methods, Newton-type methods, conjugate gradient methods, trust-region methods. Least squares problems (linear + nonlinear). Optimality conditions for smooth constrained optimization problems (KKT theory). Lagrangian duality. Augmented Lagrangian methods. Active-set method for quadratic programming. SQP methods. | ||
| MATH 410 | Majors Project. | 3 |
Majors Project. Terms offered: Summer 2025, Fall 2025, Winter 2026 A supervised project. | ||
| MATH 417 | Linear Optimization. | 3 |
Linear Optimization. Terms offered: this course is not currently offered. An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interior-point methods, quadratic optimization, applications in game theory. | ||
| MATH 423 | Applied Regression. | 3 |
Applied Regression. Terms offered: Fall 2025 Multiple regression estimators and their properties. Hypothesis tests and confidence intervals. Analysis of variance. Prediction and prediction intervals. Model diagnostics. Model selection. Introduction to weighted least squares. Basic contingency table analysis. Introduction to logistic and Poisson regression. Applications to experimental and observational data. | ||
| MATH 430 | Mathematical Finance. | 3 |
Mathematical Finance. Terms offered: this course is not currently offered. Introduction to concepts of price and hedge derivative securities. The following concepts will be studied in both concrete and continuous time: filtrations, martingales, the change of measure technique, hedging, pricing, absence of arbitrage opportunities and the Fundamental Theorem of Asset Pricing. | ||
| MATH 447 | Introduction to Stochastic Processes. | 3 |
Introduction to Stochastic Processes. Terms offered: Winter 2026 Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory. | ||
| MATH 451 | Introduction to General Topology. | 3 |
Introduction to General Topology. Terms offered: Winter 2026 This course is an introduction to point set topology. Topics include basic set theory and logic, topological spaces, separation axioms, continuity, connectedness, compactness, Tychonoff Theorem, metric spaces, and Baire spaces. | ||
| MATH 462 | Machine Learning . | 3 |
Machine Learning . Terms offered: this course is not currently offered. Introduction to supervised learning: decision trees, nearest neighbors, linear models, neural networks. Probabilistic learning: logistic regression, Bayesian methods, naive Bayes. Classification with linear models and convex losses. Unsupervised learning: PCA, k-means, encoders, and decoders. Statistical learning theory: PAC learning and VC dimension. Training models with gradient descent and stochastic gradient descent. Deep neural networks. Selected topics chosen from: generative models, feature representation learning, computer vision. | ||
| MATH 463 | Convex Optimization. | 3 |
Convex Optimization. Terms offered: Winter 2026 Introduction to convex analysis and convex optimization: Convex sets and functions, subdifferential calculus, conjugate functions, Fenchel duality, proximal calculus. Subgradient methods, proximal-based methods. Conditional gradient method, ADMM. Applications including data classification, network-flow problems, image processing, convex feasibility problems, DC optimization, sparse optimization, and compressed sensing. | ||
| MATH 510 | Quantitative Risk Management. | 4 |
Quantitative Risk Management. Terms offered: Winter 2026 Basics concepts in quantitative risk management: types of financial risk, loss distribution, risk measures, regulatory framework. Empirical properties of financial data, models for stochastic volatility. Extreme-value theory models for maxima and threshold exceedances. Multivariate models, copulas, and dependence measures. Risk aggregation. | ||
| MATH 523 | Generalized Linear Models. | 4 |
Generalized Linear Models. Terms offered: Winter 2026 Exponential families, link functions. Inference and parameter estimation for generalized linear models; model selection using analysis of deviance. Residuals. Contingency table analysis, logistic regression, multinomial regression, Poisson regression, log-linear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data. | ||
| MATH 524 | Nonparametric Statistics. | 4 |
Nonparametric Statistics. Terms offered: Fall 2025 Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used. | ||
| MATH 525 | Sampling Theory and Applications. | 4 |
Sampling Theory and Applications. Terms offered: Winter 2026 Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse. | ||
| MATH 545 | Introduction to Time Series Analysis. | 4 |
Introduction to Time Series Analysis. Terms offered: this course is not currently offered. Stationary processes; estimation and forecasting of ARMA models; non-stationary and seasonal models; state-space models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models. | ||