Mathematics and Physics Honours (B.Sc.) (81 credits)
Offered by: Physics (Faculty of Science)
Degree: Bachelor of Science
Program credit weight: 81
Program Description
This is a specialized and demanding program intended for students who wish to develop a strong basis in both Mathematics and Physics in preparation for graduate work and a professional or academic career. Although the program is optimized for theoretical physics, it is broad enough and strong enough to prepare students for further study in either experimental physics or mathematics.
The minimum requirement for entry into the program is completion with high standing of the usual CEGEP courses in physics and in mathematics, or the Physics Program Prerequisites as explained below. In addition, a student who has not completed the equivalent of MATH 222 Calculus 3. must take it in the first term without receiving credit toward the 81 credits required in the Honours program.
A student whose average in the required and complementary courses in any year falls below a GPA of 3.00, or whose grade in any individual required or complementary course falls below a C (unless the student improves the grade to a C or higher through a supplemental exam or by retaking the course), may not register in the Honours program the following year, or graduate with the Honours degree, except with the permission of both departments. The student will have two advisers, one from Mathematics and the other from Physics.
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.
Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.
Program Prerequisites
Students entering Physics programs from the Freshman program must have successfully completed the courses below or their equivalents. Quebec students must have completed the DEC with appropriate science and mathematics courses.
| Course | Title | Credits |
|---|---|---|
| CHEM 110 | General Chemistry 1. | 4 |
General Chemistry 1. Terms offered: this course is not currently offered. A study of the fundamental principles of atomic structure, radiation and nuclear chemistry, valence theory, coordination chemistry, and the periodic table. | ||
| CHEM 120 | General Chemistry 2. | 4 |
General Chemistry 2. Terms offered: this course is not currently offered. A study of the fundamental principles of physical chemistry. | ||
| PHYS 131 | Mechanics and Waves. | 4 |
Mechanics and Waves. Terms offered: this course is not currently offered. The basic laws and principles of Newtonian mechanics; oscillations, waves, and wave optics. | ||
| PHYS 142 | Electromagnetism and Optics. | 4 |
Electromagnetism and Optics. Terms offered: this course is not currently offered. The basic laws of electricity and magnetism; geometrical optics. | ||
One of:
| Course | Title | Credits |
|---|---|---|
| BIOL 111 | Principles: Organismal Biology. | 3 |
Principles: Organismal Biology. Terms offered: this course is not currently offered. An introduction to the phylogeny, structure, function and adaptation of unicellular organisms, plants and animals in the biosphere. | ||
| BIOL 112 | Cell and Molecular Biology. | 3 |
Cell and Molecular Biology. Terms offered: this course is not currently offered. The cell: ultrastructure, division, chemical constituents and reactions. Bioenergetics: photosynthesis and respiration. Principles of genetics, the molecular basis of inheritance and biotechnology. | ||
MATH 133 Linear Algebra and Geometry. and either MATH 140 Calculus 1./MATH 141 Calculus 2. or MATH 150 Calculus A./MATH 151 Calculus B..
| Course | Title | Credits |
|---|---|---|
| MATH 133 | Linear Algebra and Geometry. | 3 |
Linear Algebra and Geometry. Terms offered: Summer 2025 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 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 The definite integral. Techniques of integration. Applications. Introduction to sequences and series. | ||
| MATH 150 | Calculus A. | 4 |
Calculus A. Terms offered: this course is not currently offered. Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables. | ||
| MATH 151 | Calculus B. | 4 |
Calculus B. Terms offered: this course is not currently offered. Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration. | ||
U1 Required Courses (27 credits)
| Course | Title | Credits |
|---|---|---|
| MATH 235 | Algebra 1. | 3 |
Algebra 1. Terms offered: this course is not currently offered. 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 248 | Honours Vector Calculus. | 3 |
Honours Vector Calculus. Terms offered: this course is not currently offered. Partial derivatives and differentiation of functions in several variables; Jacobians; maxima and minima; implicit functions. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line and surface integrals; irrotational and solenoidal fields; Green's theorem; the divergence theorem. Stokes' theorem; and applications. | ||
| MATH 249 | Honours Complex Variables. | 3 |
Honours Complex Variables. Terms offered: this course is not currently offered. 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 325 | Honours Ordinary Differential Equations. | 3 |
Honours Ordinary Differential Equations. Terms offered: this course is not currently offered. First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications. | ||
| PHYS 241 | Signal Processing. | 3 |
Signal Processing. Terms offered: this course is not currently offered. Linear circuit elements, resonance, network theorems, diodes, transistors, amplifiers, feedback, integrated circuits. | ||
| PHYS 251 | Honours Classical Mechanics 1. | 3 |
Honours Classical Mechanics 1. Terms offered: this course is not currently offered. Newton's laws, work energy, angular momentum. Harmonic oscillator, forced oscillations. Inertial forces, rotating frames. Central forces, centre of mass, planetary orbits, Kepler's laws. | ||
| PHYS 257 | Experimental Methods 1. | 3 |
Experimental Methods 1. Terms offered: this course is not currently offered. Introductory laboratory work and data analysis as related to mechanics, optics and thermodynamics. Introduction to computers as they are employed for laboratory work, for data analysis and for numerical computation. Previous experience with computers is an asset, but is not required. | ||
| PHYS 258 | Experimental Methods 2. | 3 |
Experimental Methods 2. Terms offered: this course is not currently offered. Advanced laboratory work and data analysis as related to mechanics, optics and thermodynamics. Computers will be employed routinely for data analysis and for numerical computation, and, particularly, to facilitate the use of Fourier methods. | ||
| PHYS 260 | Modern Physics and Relativity. | 3 |
Modern Physics and Relativity. Terms offered: this course is not currently offered. History of special relativity; Lorentz transformations: kinematics and dynamics; transformation of electric and magnetic forces; introduction to topics in modern physics. | ||
U2 Required Courses (24 credits)
| Course | Title | Credits |
|---|---|---|
| MATH 255 | Honours Analysis 2. | 3 |
Honours Analysis 2. Terms offered: this course is not currently offered. Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, Hölder and Minkowski inequalities, sequential compactness, Heine-Borel, Banach Fixed Point theorem. Riemann-(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions. | ||
| MATH 475 | Honours Partial Differential Equations. | 3 |
Honours Partial Differential Equations. Terms offered: this course is not currently offered. First order partial differential equations, geometric theory, classification of second order linear equations, Sturm-Liouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems. | ||
| PHYS 253 | Thermal Physics. | 3 |
Thermal Physics. Terms offered: this course is not currently offered. Energy, work, heat; first law. Temperature, entropy; second law. Absolute zero; third law. Equilibrium, equations of state, gases, liquids, solids, magnets; phase transitions. | ||
| PHYS 350 | Honours Electricity and Magnetism. | 3 |
Honours Electricity and Magnetism. Terms offered: this course is not currently offered. Fundamental laws of electric and magnetic fields in both integral and differential form. | ||
| PHYS 351 | Honours Classical Mechanics 2. | 3 |
Honours Classical Mechanics 2. Terms offered: this course is not currently offered. Rigid bodies, angular momentum, gyroscope, moment of inertia, principal axes, Euler's equations. Coupled oscillations and normal modes. Lagrangian mechanics and applications. Hamiltonian mechanics. Topics in advanced analytical mechanics. | ||
| PHYS 357 | Honours Quantum Physics 1. | 3 |
Honours Quantum Physics 1. Terms offered: this course is not currently offered. Experimental basis for quantum mechanics; wave-packets; uncertainty principle. Hilbert space formalism. Schrodinger equation: eigenvalues and eigenvectors: applications to 1-d problems including the infinite and finite potential wells and the harmonic oscillator. Tunneling. Time independent perturbation theory. | ||
| PHYS 362 | Statistical Mechanics. | 3 |
Statistical Mechanics. Terms offered: this course is not currently offered. Quantum states and ensemble averages. Fermi-Dirac, Bose-Einstein and Boltzmann distribution functions and their applications. | ||
| PHYS 457 | Honours Quantum Physics 2. | 3 |
Honours Quantum Physics 2. Terms offered: this course is not currently offered. Angular momentum and spin operators. Operator methods in quantum mechanics. Coupling of spin and angular momenta. Variational principles and elements of time dependent perturbation theory (the Golden Rule). Solution of the Schrodinger equation in three dimensions. Applications to the hydrogen and helium atoms and to simple problems in atomic and molecular physics. | ||
U3 Required Courses (12 credits)
| Course | Title | Credits |
|---|---|---|
| MATH 454 | Honours Analysis 3. | 3 |
Honours Analysis 3. Terms offered: this course is not currently offered. Measure theory: sigma-algebras, Lebesgue measure in R^n and integration, L^1 functions, Fatou's lemma, monotone and dominated convergence theorem, Egorov’s theorem, Lusin's theorem, Fubini-Tonelli theorem, differentiation of the integral, differentiability of functions of bounded variation, absolutely continuous functions, fundamental theorem of calculus. | ||
| MATH 458 | Honours Differential Geometry. | 3 |
Honours Differential Geometry. Terms offered: this course is not currently offered. In addition to the topics of MATH 320, topics in the global theory of plane and space curves, and in the global theory of surfaces are presented. These include: total curvature and the Fary-Milnor theorem on knotted curves, abstract surfaces as 2-d manifolds, the Euler characteristic, the Gauss-Bonnet theorem for surfaces. | ||
| PHYS 352 | Honours Electromagnetic Waves. | 3 |
Honours Electromagnetic Waves. Terms offered: this course is not currently offered. Vector and scalar potentials; plane waves in homogeneous media; refraction and reflection; guided waves; radiation from simple systems; dipole and quadrupole radiation; introduction to fields of moving charges; synchrotron radiation; Bremsstrahlung. | ||
| PHYS 359 | Advanced Physics Laboratory 1. | 3 |
Advanced Physics Laboratory 1. Terms offered: this course is not currently offered. Advanced level experiments in physics including quantum effects and some properties of condensed matter physics and modern physics. | ||
Complementary Courses (18 credits)
U1 Complementary Course (3 credits)
| Course | Title | Credits |
|---|---|---|
| MATH 247 | Honours Applied Linear Algebra. | 3 |
Honours Applied Linear Algebra. Terms offered: this course is not currently offered. Matrix algebra, determinants, systems of linear equations. Abstract vector spaces, inner product spaces, Fourier series. Linear transformations and their matrix representations. Eigenvalues and eigenvectors, diagonalizable and defective matrices, positive definite and semidefinite matrices. Quadratic and Hermitian forms, generalized eigenvalue problems, simultaneous reduction of quadratic forms. Applications. | ||
| MATH 251 | Honours Algebra 2. | 3 |
Honours Algebra 2. Terms offered: this course is not currently offered. Linear equations over a field. Introduction to vector spaces. Linear maps and their matrix representation. Determinants. Canonical forms. Duality. Bilinear and quadratic forms. Real and complex inner product spaces. Diagonalization of self-adjoint operators. | ||
U2 Complementary Courses (3 credits)
| Course | Title | Credits |
|---|---|---|
| MATH 242 | Analysis 1. | 3 |
Analysis 1. Terms offered: this course is not currently offered. A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line. | ||
| MATH 254 | Honours Analysis 1. 1 | 3 |
Honours Analysis 1. Terms offered: this course is not currently offered. Properties of R. Cauchy and monotone sequences, Bolzano- Weierstrass theorem. Limits, limsup, liminf of functions. Pointwise, uniform continuity: Intermediate Value theorem. Inverse and monotone functions. Differentiation: Mean Value theorem, L'Hospital's rule, Taylor's Theorem. | ||
- 1
It is strongly recommended that students take MATH 254 Honours Analysis 1..
U3 Complementary Courses (12 credits)
12 credits are selected as follows:
3 credits from:
| Course | Title | Credits |
|---|---|---|
| MATH 455 | Honours Analysis 4. | 3 |
Honours Analysis 4. Terms offered: this course is not currently offered. Review of point-set topology: topological spaces, dense sets, completeness, compactness, connectedness and path-connectedness, separability, Baire category theorem, Arzela-Ascoli theorem, Stone-Weierstrass theorem..Functional analysis: L^p spaces, linear functionals and dual spaces, Hilbert spaces, Riesz representation theorems. Fourier series and transform, Riemann-Lebesgue Lemma,Fourier inversion formula, Plancherel theorem, Parseval’s identity, Poisson summation formula. | ||
| MATH 456 | Honours Algebra 3. | 3 |
Honours Algebra 3. Terms offered: this course is not currently offered. Groups, quotient groups and the isomorphism theorems. Group actions. Groups of prime order and the class equation. Sylow's theorems. Simplicity of the alternating group. Semidirect products. Principal ideal domains and unique factorization domains. Modules over a ring. Finitely generated modules over a principal ideal domain with applications to canonical forms. | ||
6 credits selected from:
| Course | Title | Credits |
|---|---|---|
| PHYS 404 | Climate Physics. | 3 |
Climate Physics. Terms offered: this course is not currently offered. This course covers the essentials of climate physics through the lens of one-dimensional, vertical atmospheric models. This includes shortwave and longwave radiative transfer, convection, phase changes, clouds, greenhouse gases, and atmospheric escape. This is an adequate level of detail for understanding Earth's climate, paleoclimate, anthropogenic climate change, or pursing studies of Solar System planets and extrasolar planets. | ||
| PHYS 432 | Physics of Fluids. | 3 |
Physics of Fluids. Terms offered: this course is not currently offered. The physical properties of fluids. The kinematics and dynamics of flow. The effects of viscosity and turbulence. Applications of fluid mechanics in biophysics, geophysics and engineering. | ||
| PHYS 459D1 | Research Thesis. 1 | 3 |
Research Thesis. Terms offered: this course is not currently offered. Supervised research project and thesis. | ||
| PHYS 459D2 | Research Thesis. 1 | 3 |
Research Thesis. Terms offered: this course is not currently offered. See PHYS 459D1 for course description. | ||
| PHYS 479 | Physics Research Project. | 3 |
Physics Research Project. Terms offered: this course is not currently offered. A supervised research project. | ||
| PHYS 512 | Computational Physics with Applications. | 3 |
Computational Physics with Applications. Terms offered: this course is not currently offered. Computational methods in Physics illustrated with realworld applications. | ||
| PHYS 514 | General Relativity. | 3 |
General Relativity. Terms offered: this course is not currently offered. Transition from special to general relativity. Non-Euclidian geometry. The basic laws of Physics in co-variant form, Einstein's equations. Gravitational waves; neutron stars; black holes; cosmology. | ||
| PHYS 519 | Advanced Biophysics. | 3 |
Advanced Biophysics. Terms offered: this course is not currently offered. An advanced biophysics course, with a special emphasis on stochastic and out of equilibrium physical processes in living matter. | ||
| PHYS 521 | Astrophysics. | 3 |
Astrophysics. Terms offered: this course is not currently offered. An advanced course in modern astrophysics, covering topics such as the basic tools of astronomy (statistics, mathematical methods, computational tools, and instrumentation); stellar astrophysics (properties, structure, atmospheres, binaries/exoplanets); the interstellar medium, star formation, stellar evolution and endpoints (white dwarfs, neutron stars, black holes); and the Milky Way, galaxies, and cosmology. | ||
| PHYS 551 | Quantum Theory. | 3 |
Quantum Theory. Terms offered: this course is not currently offered. General formulation, scattering theory, WKBJ approximation, time-dependent perturbation, theory and applications, angular momentum, relativistic wave equations. | ||
| PHYS 557 | Nuclear Physics. | 3 |
Nuclear Physics. Terms offered: this course is not currently offered. General nuclear properties, nucleon-nucleon interaction and scattering theory, radioactivity, nuclear models, nuclear reactions. | ||
| PHYS 558 | Solid State Physics. | 3 |
Solid State Physics. Terms offered: this course is not currently offered. Properties of crystals; free electron model, band structure; metals, insulators and semi-conductors; phonons; magnetism; selected additional topics in solid-state (e.g. ferroelectrics, elementary transport theory). | ||
| PHYS 559 | Advanced Statistical Mechanics. | 3 |
Advanced Statistical Mechanics. Terms offered: this course is not currently offered. Scattering and structure factors. Review of thermodynamics and statistical mechanics; correlation functions (static); mean field theory; critical phenomena; broken symmetry; fluctuations, roughening. | ||
| PHYS 562 | Electromagnetic Theory. | 3 |
Electromagnetic Theory. Terms offered: this course is not currently offered. Electrostatics, dielectrics, magnetostatics, timevarying fields, relativity, radiating systems, fields of moving charges. | ||
| PHYS 567 | Particle Physics. | 3 |
Particle Physics. Terms offered: this course is not currently offered. Survey of elementary particles; hadrons, leptons and hadrons' constituents (quarks). Invariance principles and conservation laws. Detectors and accelerators. Phenomenology of strong, electromagnetic and weak interactions. | ||
- 1
Note: PHYS 459D1 Research Thesis. and PHYS 459D2 Research Thesis. are taken together.
3 credits in Honours Mathematics.