Program Requirements
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 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.
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.

CHEM 110 General Chemistry 1 (4 credits)
Overview
Chemistry : A study of the fundamental principles of atomic structure, radiation and nuclear chemistry, valence theory, coordination chemistry, and the periodic table.
Terms: Fall 2020
Instructors: Sirjoosingh, Pallavi; McKeague, Maureen; Huot, Mitchell (Fall)
Fall
Prerequisites/corequisites: College level mathematics and physics or permission of instructor; CHEM 120 is not a prerequisite
Each lab section is limited enrolment

CHEM 120 General Chemistry 2 (4 credits)
Overview
Chemistry : A study of the fundamental principles of physical chemistry.
Terms: Winter 2021
Instructors: Sewall, Samuel Lewis; Wiseman, Paul; Sirjoosingh, Pallavi; Huot, Mitchell (Winter)
Winter
Prerequisites/corequisites: College level mathematics and physics, or permission of instructor: CHEM 110 is not a prerequisite
Each lab section is limited enrolment

PHYS 131 Mechanics and Waves (4 credits)
Overview
Physics : The basic laws and principles of Newtonian mechanics; oscillations, waves, and wave optics.
Terms: Fall 2020
Instructors: Ragan, Kenneth J (Fall)
Fall
3 hours lectures; 1 hour tutorial, 3 hours laboratory in alternate weeks; tutorial sessions
Corequisite: MATH 139 or higher level calculus course.
Restriction(s): Not open to students who have taken or are taking PHYS 101, or who have taken CEGEP objective 00UR or equivalent.
Laboratory sections have limited enrolment

PHYS 142 Electromagnetism and Optics (4 credits)
Overview
Physics : The basic laws of electricity and magnetism; geometrical optics.
Terms: Winter 2021
Instructors: Webb, Tracy (Winter)
Winter
3 hours lectures, 3 hours laboratory in alternate weeks; tutorial sessions
Prerequisite: PHYS 131.
Corequisite: MATH 141 or higher level calculus course.
Restriction: Not open to students who have taken or are taking PHYS 102, or who have taken CEGEP objective 00US or equivalent.
Laboratory sections have limited enrolment
One of:

BIOL 111 Principles: Organismal Biology (3 credits)
Overview
Biology (Sci) : An introduction to the phylogeny, structure, function and adaptation of unicellular organisms, plants and animals in the biosphere.
Terms: Fall 2020
Instructors: Hendry, Andrew; Bell, Graham; Cristescu, Elena; Hargreaves, Anna (Fall)
Fall
2 hours lecture and 3 hours laboratory
Restriction: Not open to students who have taken CEGEP objective 00UK or equivalent; or BIOL 115.
This course serves as an alternative to CEGEP objective code 00UK
May require departmental approval.
Open to all students wishing introductory biology.
Attendance at first lab is mandatory to confirm registration in the course.
This class will use a Student Response System (clicker) which can be obtained from the Bookstore.

BIOL 112 Cell and Molecular Biology (3 credits)
Overview
Biology (Sci) : The cell: ultrastructure, division, chemical constituents and reactions. Bioenergetics: photosynthesis and respiration. Principles of genetics, the molecular basis of inheritance and biotechnology.
Terms: Winter 2021
Instructors: Dent, Joseph Alan; Schöck, Frieder (Winter)
MATH 133 and either MATH 140/141 or MATH 150/151.

MATH 133 Linear Algebra and Geometry (3 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Fall 2020, Winter 2021, Summer 2021
Instructors: BélangerRioux, Rosalie; Ball, Gavin; Aigner, Florian; Przytycki, Piotr (Fall) Kelome, Djivede (Winter)
3 hours lecture, 1 hour tutorial
Prerequisite: a course in functions
Restriction A: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent.
Restriction B: Not open to students who have taken or are taking MATH 123, except by permission of the Department of Mathematics and Statistics.
Restriction C: Not open to students who are taking or have taken MATH 134.

MATH 140 Calculus 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Terms: Fall 2020, Winter 2021, Summer 2021
Instructors: Trudeau, Sidney; Ghaswala, Tyrone; Albanese, Michael (Fall) Fortier, Jérôme (Winter)
3 hours lecture, 1 hour tutorial
Prerequisite: High School Calculus
Restriction: Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN or equivalent
Restriction: Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics
Each Tutorial section is enrolment limited

MATH 141 Calculus 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Terms: Fall 2020, Winter 2021, Summer 2021
Instructors: Fortier, Jérôme; Sabok, Marcin (Fall) Trudeau, Sidney; Albanese, Michael; Ghaswala, Tyrone (Winter)

MATH 150 Calculus A (4 credits)
Overview
Mathematics & Statistics (Sci) : Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.
Terms: Fall 2020
Instructors: Roth, Charles (Fall)
Fall
3 hours lecture, 2 hours tutorial
Students with no prior exposure to vector geometry are advised to take MATH 133 concurrently. Intended for students with high school calculus who have not received six advanced placement credits
Restriction: Not open to students who have taken CEGEP objective 00UN or equivalent
Restriction Note B: Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics
MATH 150 and MATH 151 cover the material of MATH 139, MATH 140, MATH 141, MATH 222

MATH 151 Calculus B (4 credits)
Overview
Mathematics & Statistics (Sci) : Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.
Terms: Winter 2021
Instructors: Roth, Charles (Winter)
Winter
3 hours lecture; 2 hours tutorial
Each Tutorial section is enrolment limited
Prerequisite: MATH 150
Restriction: Not open to students who have taken CEGEP objective 00UP or equivalent
Restriction: Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics
Restriction: Not open to students who have taken MATH 152
U1 Required Courses (27 credits)

MATH 235 Algebra 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : 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; group actions on sets.
Terms: Fall 2020
Instructors: Wise, Daniel (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent

MATH 248 Honours Vector Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Fall 2020
Instructors: Guan, Pengfei (Fall)

MATH 249 Honours Complex Variables (3 credits)
Overview
Mathematics & Statistics (Sci) : Functions of a complex variable; CauchyRiemann 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; SchwarzChristoffel transformation; Poisson's integral formulas; applications.
Terms: Winter 2021
Instructors: Harrison, Sarah (Winter)

MATH 325 Honours Ordinary Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.
Terms: Winter 2021
Instructors: Humphries, Antony Raymond (Winter)

PHYS 241 Signal Processing (3 credits)
Overview
Physics : Linear circuit elements, resonance, network theorems, diodes, transistors, amplifiers, feedback, integrated circuits.
Terms: Winter 2021
Instructors: Reisner, Walter (Winter)
Winter
2 hours lectures; 3 hours laboratory alternate weeks
Prerequisite: CEGEP physics or PHYS 142.

PHYS 251 Honours Classical Mechanics 1 (3 credits)
Overview
Physics : 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.
Terms: Fall 2020
Instructors: Cline, James M (Fall)

PHYS 257 Experimental Methods 1 (3 credits)
Overview
Physics : 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.
Terms: Fall 2020
Instructors: Siwick, Bradley (Fall)

PHYS 258 Experimental Methods 2 (3 credits)
Overview
Physics : 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.
Terms: Winter 2021
Instructors: Brunner, Thomas (Winter)
Winter
6 hours of laboratory and classroom work
Prerequisite: PHYS 257

PHYS 260 Modern Physics and Relativity (3 credits)
Overview
Physics : History of special relativity; Lorentz transformations: kinematics and dynamics; transformation of electric and magnetic forces; introduction to topics in modern physics.
Terms: Fall 2020
Instructors: Liu, Adrian (Fall)
U2 Required Courses (24 credits)

MATH 255 Honours Analysis 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Basic pointset topology, metric spaces: open and closed sets, normed and Banach spaces, HÃ¶lder and Minkowski inequalities, sequential compactness, HeineBorel, Banach Fixed Point theorem. Riemann(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions.
Terms: Winter 2021
Instructors: Jaksic, Vojkan (Winter)

MATH 475 Honours Partial Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order partial differential equations, geometric theory, classification of second order linear equations, SturmLiouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems.
Terms: Fall 2020
Instructors: Lin, Jessica (Fall)

PHYS 253 Thermal Physics (3 credits)
Overview
Physics : Energy, work, heat; first law. Temperature, entropy; second law. Absolute zero; third law. Equilibrium, equations of state, gases, liquids, solids, magnets; phase transitions.
Terms: Fall 2020
Instructors: CaronHuot, Simon (Fall)

PHYS 350 Honours Electricity and Magnetism (3 credits)
Overview
Physics : Fundamental laws of electric and magnetic fields in both integral and differential form.
Terms: Fall 2020
Instructors: Sievers, Jonathan Le Roy (Fall)

PHYS 351 Honours Classical Mechanics 2 (3 credits)
Overview
Physics : 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.
Terms: Winter 2021
Instructors: Dasgupta, Keshav (Winter)

PHYS 357 Honours Quantum Physics 1 (3 credits)
Overview
Physics : Experimental basis for quantum mechanics; wavepackets; uncertainty principle. Hilbert space formalism. Schrodinger equation: eigenvalues and eigenvectors: applications to 1d problems including the infinite and finite potential wells and the harmonic oscillator. Tunneling. Time independent perturbation theory.
Terms: Fall 2020
Instructors: PeregBarnea, Tamar (Fall)

PHYS 362 Statistical Mechanics (3 credits)
Overview
Physics : Quantum states and ensemble averages. FermiDirac, BoseEinstein and Boltzmann distribution functions and their applications.
Terms: Winter 2021
Instructors: Grant, Martin (Winter)

PHYS 457 Honours Quantum Physics 2 (3 credits)
Overview
Physics : 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.
Terms: Winter 2021
Instructors: Agarwal, Kartiek (Winter)
U3 Required Courses (12 credits)

MATH 454 Honours Analysis 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of pointset topology: topological space, dense sets, completeness, compactness, connectedness and pathconnectedness, separability. ArzelaAscoli, StoneWeierstrass, Baire category theorems. Measure theory: sigma algebras, Lebesgue measure and integration, L^1 functions. Fatou's lemma, monotone and dominated convergence theorem. Egorov, Lusin's theorems. FubiniTonelli theorem.
Terms: Fall 2020
Instructors: Vetois, Jerome (Fall)

MATH 458 Honours Differential Geometry (3 credits)
Overview
Mathematics & Statistics (Sci) : 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 FaryMilnor theorem on knotted curves, abstract surfaces as 2d manifolds, the Euler characteristic, the GaussBonnet theorem for surfaces.
Terms: Winter 2021
Instructors: Kamran, Niky (Winter)

PHYS 352 Honours Electromagnetic Waves (3 credits)
Overview
Physics : 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.
Terms: Fall 2020
Instructors: Rutledge, Robert (Fall)
Fall
3 hours lectures
Prerequisite: PHYS 350.
Restriction: Honours students, or permission of the instructor

PHYS 359 Honours Laboratory in Modern Physics 1 (3 credits)
Overview
Physics : Advanced level experiments in modern physics stressing quantum effects and some properties of condensed matter.
Terms: Winter 2021
Instructors: Brunner, Thomas; Ryan, Dominic (Winter)
Complementary Courses (18 credits)
U1 Complementary Course (3 credits)

MATH 247 Honours Applied Linear Algebra (3 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Winter 2021
Instructors: Hoheisel, Tim (Winter)

MATH 251 Honours Algebra 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : 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 selfadjoint operators.
Terms: Winter 2021
Instructors: Lipnowski, Michael (Winter)
U2 Complementary Courses (3 credits)

MATH 242 Analysis 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Terms: Fall 2020
Instructors: Hundemer, Axel W (Fall)

MATH 254 Honours Analysis 1 (3 credits) **
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Fall 2020
Instructors: Jaksic, Vojkan; Hundemer, Axel W; Hurtubise, Jacques Claude (Fall)
** It is strongly recommended that students take MATH 254.
U3 Complementary Courses (12 credits)
12 credits are selected as follows:
3 credits from:

MATH 455 Honours Analysis 4 (3 credits)
Overview
Mathematics & Statistics (Sci) : Continuation of measure theory. Functional analysis: L^p spaces, linear functionals and dual spaces, HahnBanach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Introduction to Fourier analysis, Fourier transforms.
Terms: Winter 2021
Instructors: Jakobson, Dmitry (Winter)

MATH 456 Honours Algebra 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to monoids, groups, permutation groups; the isomorphism theorems for groups; the theorems of Cayley, Lagrange and Sylow; structure of groups of low order. Introduction to ring theory; integral domains, fields, quotient field of an integral domain; polynomial rings; unique factorization domains.
Terms: Fall 2020
Instructors: Goren, Eyal Z (Fall)
6 credits selected from:

PHYS 432 Physics of Fluids (3 credits)
Overview
Physics : 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.
Terms: Winter 2021
Instructors: Lee, Eve J (Winter)

PHYS 479 Physics Research Project (3 credits)
Overview
Physics : A supervised research project.
Terms: Fall 2020, Winter 2021
Instructors: Leslie, Sabrina (Fall) Childress, Lilian (Winter)
6 hours
Restriction: U2 or U3 students in a Physics program, or permission of the instructor.

PHYS 512 Computational Physics with Applications (3 credits)
Overview
Physics : Computational methods in Physics illustrated with realworld applications.
Terms: Fall 2020
Instructors: Sievers, Jonathan Le Roy (Fall)
U3 or graduate students in Physics, Chemistry, or Engineering, or permission of the instructor. Basic familiarity with computer programming highly recommended.

PHYS 514 General Relativity (3 credits)
Overview
Physics : Transition from special to general relativity. NonEuclidian geometry. The basic laws of Physics in covariant form, Einstein's equations. Gravitational waves; neutron stars; black holes; cosmology.
Terms: Winter 2021
Instructors: Maloney, Alexander (Winter)
Winter
3 hours lectures
Restriction: U3 Honours students and graduate students, or permission of the instructor.

PHYS 519 Advanced Biophysics (3 credits)
Overview
Physics : An advanced biophysics course, with a special emphasis on stochastic and out of equilibrium physical processes in living matter.
Terms: Winter 2021
Instructors: Francois, Paul (Winter)

PHYS 521 Astrophysics (3 credits)
Overview
Physics : 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.
Terms: Fall 2020
Instructors: Rutledge, Robert (Fall)
Fall
3 hours
Restriction: U3 students and graduate students, or permission of the instructor

PHYS 551 Quantum Theory (3 credits)
Overview
Physics : General formulation, scattering theory, WKBJ approximation, timedependent perturbation, theory and applications, angular momentum, relativistic wave equations.
Terms: Fall 2020
Instructors: Cumming, Andrew (Fall)
Fall
3 hours lectures
Restriction: U3 Honours students and graduate students, or permission of the instructor

PHYS 557 Nuclear Physics (3 credits)
Overview
Physics : General nuclear properties, nucleonnucleon interaction and scattering theory, radioactivity, nuclear models, nuclear reactions.
Terms: Fall 2020
Instructors: Jeon, Sang Yong (Fall)
Fall
3 hours lectures
Restriction: U3 Honours students, graduate students, or permission of the instructor

PHYS 558 Solid State Physics (3 credits)
Overview
Physics : Properties of crystals; free electron model, band structure; metals, insulators and semiconductors; phonons; magnetism; selected additional topics in solidstate (e.g. ferroelectrics, elementary transport theory).
Terms: Fall 2020
Instructors: Childress, Lilian (Fall)
Fall
3 hours lectures
Restriction: U3 Honours students, graduate students, or permission of the instructor

PHYS 559 Advanced Statistical Mechanics (3 credits)
Overview
Physics : Scattering and structure factors. Review of thermodynamics and statistical mechanics; correlation functions (static); mean field theory; critical phenomena; broken symmetry; fluctuations, roughening.
Terms: Fall 2020
Instructors: Coish, William (Fall)
Fall
3 hours lectures
Restriction: U3 Honours students, graduate students, or permission of the instructor

PHYS 562 Electromagnetic Theory (3 credits)
Overview
Physics : Electrostatics, dielectrics, magnetostatics, timevarying fields, relativity, radiating systems, fields of moving charges.
Terms: Winter 2021
Instructors: Hilke, Michael (Winter)
Winter
3 hours lectures
Prerequisites (Graduate): U1 or U2 Honours Physics or permission of instructor.
Restriction: U3 Honours students, graduate students, or permission of the instructor

PHYS 567 Particle Physics (3 credits)
Overview
Physics : 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.
Terms: Winter 2021
Instructors: Cline, James M (Winter)
Winter
3 hours lectures
Restriction: U3 Honours students, graduate students, or permission of the instructor
3 credits in Honours Mathematics.