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to the new course catalogue, the program and course information displayed below may be temporarily unavailable or outdated.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 and Computer Science Major (B.Sc.) (72 credits)
Offered by: Mathematics and Statistics (Faculty of Science)
Degree: Bachelor of Science
Program credit weight: 72
Program Description
The B.Sc.; Major in Mathematics and Computer Science emphasizes fundamental skills in mathematics and computer science, while exploring the interaction between the two fields.
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 Joint Major in Mathematics and Computer Science 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 72 credits of courses in the program specification.
Course List
| 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. See course page for more information |
| 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. See course page for more information |
| 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. See course page for more information |
Required Courses (54 credits)
Course List
| Course |
Title |
Credits |
| COMP 202 | Foundations of Programming. 1 | 3 |
Foundations of Programming. Terms offered: Summer 2025, Fall 2025, Winter 2026 Introduction to computer programming in a high level language: variables, expressions, primitive types, methods, conditionals, loops. Introduction to algorithms, data structures (arrays, strings), modular software design, libraries, file input/output, debugging, exception handling. Selected topics. See course page for more information |
| COMP 206 | Introduction to Software Systems. | 3 |
Introduction to Software Systems. Terms offered: Fall 2025, Winter 2026 Comprehensive overview of programming in C, use of system calls and libraries, debugging and testing of code; use of developmental tools like make, version control systems. See course page for more information |
| COMP 250 | Introduction to Computer Science. | 3 |
Introduction to Computer Science. Terms offered: Fall 2025, Winter 2026 Mathematical tools (binary numbers, induction,recurrence relations, asymptotic complexity,establishing correctness of programs). Datastructures (arrays, stacks, queues, linked lists,trees, binary trees, binary search trees, heaps,hash tables). Recursive and non-recursivealgorithms (searching and sorting, tree andgraph traversal). Abstract data types. Objectoriented programming in Java (classes andobjects, interfaces, inheritance). Selected topics. See course page for more information |
| COMP 251 | Algorithms and Data Structures. | 3 |
Algorithms and Data Structures. Terms offered: Fall 2025, Winter 2026 Data Structures: priority queues, balanced binary search trees, hash tables, graphs. Algorithms: topological sort, connected components, shortest paths, minimum spanning trees, bipartite matching, network flows. Algorithm design: greedy, divide and conquer, dynamic programming, randomization. Mathematicaltools: proofs of asymptotic complexity and program correctness, Master theorem. See course page for more information |
| COMP 273 | Introduction to Computer Systems. | 3 |
Introduction to Computer Systems. Terms offered: Fall 2025, Winter 2026 Number representations, combinational and sequential digital circuits, MIPS instructions and architecture datapath and control, caches, virtual memory, interrupts and exceptions, pipelining. See course page for more information |
| COMP 302 | Programming Languages and Paradigms. | 3 |
Programming Languages and Paradigms. Terms offered: Fall 2025, Winter 2026 Programming language design issues and programming paradigms. Binding and scoping, parameter passing, lambda abstraction, data abstraction, type checking. Functional and logic programming. See course page for more information |
| COMP 310 | Operating Systems. | 3 |
Operating Systems. Terms offered: Fall 2025, Winter 2026 Control and scheduling of large information processing systems. Operating system software - resource allocation, dispatching, processors, access methods, job control languages, main storage management. Batch processing, multiprogramming, multiprocessing, time sharing. See course page for more information |
| COMP 330 | Theory of Computation. | 3 |
Theory of Computation. Terms offered: Fall 2025, Winter 2026 Finite automata, regular languages, context-free languages, push-down automata, models of computation, computability theory, undecidability, reduction techniques. See course page for more information |
| COMP 360 | Algorithm Design. | 3 |
Algorithm Design. Terms offered: Fall 2025, Winter 2026 Advanced algorithm design and analysis. Linear programming, complexity and NP-completeness, advanced algorithmic techniques. See course page for more information |
| MATH 222 | Calculus 3. | 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. See course page for more information |
| 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. See course page for more information |
| 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.
See course page for more information |
| 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. See course page for more information |
| 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. See course page for more information |
| MATH 317 | Numerical Analysis. 2 | 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. See course page for more information |
| 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. See course page for more information |
| 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. See course page for more information |
| 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. See course page for more information |
- 1
Students who have sufficient knowledge in a programming language do not need to take COMP 202 Foundations of Programming. but can replace it with an additional Computer Science complementary course.
- 2
Student cannot replace MATH 317 Numerical Analysis. with COMP 350 Numerical Computing..
Complementary Courses (18 credits)
9 credits from the following.
Other MATH courses, at the undergraduate level, not included in this list may be chosen in consultation with an adviser.
Course List
| 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. See course page for more information |
| 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. See course page for more information |
| 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. See course page for more information |
| 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. See course page for more information |
| 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. See course page for more information |
| 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. See course page for more information |
| 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. See course page for more information |
| MATH 329 | Theory of Interest. | 3 |
|
| 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.
See course page for more information |
| MATH 346 | Number Theory. | 3 |
Number Theory. Terms offered: this course is not currently offered. Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions. See course page for more information |
| 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. See course page for more information |
| 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.
See course page for more information |
| MATH 410 | Majors Project. | 3 |
|
| 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.
See course page for more information |
| 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. See course page for more information |
| MATH 427 | Statistical Quality Control. | 3 |
Statistical Quality Control. Terms offered: Fall 2025 Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes. See course page for more information |
| 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. See course page for more information |
| 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. See course page for more information |
| 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.
See course page for more information |
| MATH 478 | Computational Methods in Applied Mathematics
. | 3 |
Computational Methods in Applied Mathematics
. Terms offered: this course is not currently offered. Solution to initial value problems: Linear, Nonlinear Finite Difference Methods: accuracy and stability, Lax equivalence theorem, CFL and von Neumann conditions,
Fourier analysis: diffusion, dissipation, dispersion, and spectral methods. Solution of large sparse linear systems: iterative methods, preconditioning, incomplete
LU, multigrid, Krylov subspaces, conjugate gradient method. Applications to, e.g., weighted least squares, duality, constrained minimization, calculus of variation,
inverse problems, regularization, level set methods, Navier-Stokes equations
See course page for more information |
9 credits selected from Computer Science courses at the 300 level or above (except COMP 396 Undergraduate Research Project.) and ECSE 508 Multi-Agent Systems..