Mathematics and Physics
This is a specialized and demanding Honours 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.
If you are interested in the Mathematics and Physics Honours, you can select either “Mathematics” or “Physics” on your application to the B.Sc. and consult with an advisor once admitted.
DETAILED PROGRAM OUTLINE:
Program Requirement:
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
 Fall
 Winter
 Summer
Offered in the:Chemistry: A study of the fundamental principles of atomic structure, radiation and nuclear chemistry, valence theory, coordination chemistry, and the periodic table.
Offered by: Chemistry
 Fall
 Prerequisites/corequisites: College level mathematics and physics or permission of instructor; CHEM 120 is not a prerequisite
 Each lab section is limited enrolment
 Symbols:
 Terms
 Fall 2020
 Instructors
 Mitchell J Huot, Pallavi Sirjoosingh, Maureen H McKeague

CHEM 120 General Chemistry 2 4 Credits
 Fall
 Winter
 Summer
Offered in the:Chemistry: A study of the fundamental principles of physical chemistry.
Offered by: Chemistry
 Winter
 Prerequisites/corequisites: College level mathematics and physics, or permission of instructor: CHEM 110 is not a prerequisite
 Each lab section is limited enrolment
 Symbols:
 Terms
 Winter 2021
 Instructors
 Samuel Lewis Sewall, Paul W Wiseman, Pallavi Sirjoosingh, Mitchell J Huot

PHYS 131 Mechanics and Waves 4 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: The basic laws and principles of Newtonian mechanics; oscillations, waves, and wave optics.
Offered by: Physics
 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
 Symbols:
 Terms
 Fall 2020
 Instructors
 Kenneth J Ragan

PHYS 142 Electromagnetism & Optics 4 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: The basic laws of electricity and magnetism; geometrical optics.
Offered by: Physics
 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
 Symbols:
 Terms
 Winter 2021
 Instructors
 Tracy Webb
One of:

BIOL 111 Principles:Organismal Biology 3 Credits
 Fall
 Winter
 Summer
Offered in the:Biology (Sci): An introduction to the phylogeny, structure, function and adaptation of unicellular organisms, plants and animals in the biosphere.
Offered by: Biology
 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.
 Symbols:
 Terms
 Fall 2020
 Instructors
 Andrew Hendry, Graham Bell, Elena M Cristescu, Anna L Hargreaves

BIOL 112 Cell and Molecular Biology 3 Credits
 Fall
 Winter
 Summer
Offered in the:Biology (Sci): The cell: ultrastructure, division, chemical constituents and reactions. Bioenergetics: photosynthesis and respiration. Principles of genetics, the molecular basis of inheritance and biotechnology.
Offered by: Biology
 Winter
 2 hours lecture and 3.5 hours laboratory/seminar
 Restriction: Not open to students who have taken or are taking CEGEP objective 00XU or equivalent; or BIOL 115; or AEBI 122
 Attendance at first lab is mandatory to confirm registration in the course. Lab start the 2nd week of term.
 Symbols:
 Terms
 Winter 2021
 Instructors
 Joseph Alan Dent, Frieder B Schöck
MATH 133 and either MATH 140/141 or MATH 150/151.

MATH 133 Linear Algebra and Geometry 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 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.
 Symbols:
 Terms
 Fall 2020
 Winter 2021
 Instructors
 Rosalie BélangerRioux, Piotr Przytycki
 Djivede A Kelome

MATH 140 Calculus 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Offered by: Mathematics and Statistics
 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
 Symbols:
 Terms
 Fall 2020
 Winter 2021
 Instructors
 Jérôme Fortier

MATH 141 Calculus 2 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 139 or MATH 140 or MATH 150.
 Restriction: Not open to students who have taken MATH 121 or CEGEP objective 00UP 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.
 Each Tutorial section is enrolment limited
 Symbols:
 Terms
 Fall 2020
 Winter 2021
 Instructors
 Jérôme Fortier, Marcin Sabok
 Sidney Trudeau

MATH 150 Calculus A 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.
Offered by: Mathematics and Statistics
 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
 Symbols:
 Terms
 Fall 2020
 Instructors
 Charles Roth

MATH 151 Calculus B 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.
Offered by: Mathematics and Statistics
 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
 Symbols:
 Terms
 Winter 2021
 Instructors
 Charles Roth
U1 Required Courses (27 credits)

MATH 235 Algebra 1 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Fall
 3 hours lecture; 1 hour tutorial
 Prerequisite: MATH 133 or equivalent
 Symbols:
 Terms
 Fall 2020
 Instructors
 Daniel T Wise

MATH 248 Honours Vector Calculus 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Fall and Winter and Summer
 Prerequisites: MATH 133 and MATH 222 or consent of Department.
 Restriction: Intended for Honours Physics, Computer Science, Physiology and Engineering students.
 Restriction: Not open to students who have taken or are taking MATH 314 or MATH 358.
 Symbols:
 Terms
 Fall 2020
 Instructors
 Pengfei Guan

MATH 249 Honours Complex Variables 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite(s): MATH 248 or MATH 358 or equivalent.
 Restriction: Intended for Honours Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 316
 Symbols:
 Terms
 Winter 2021
 Instructors
 Sarah Harrison

MATH 325 Honours ODE's 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Fall and Winter
 (306)
 Prerequisite: MATH 222.
 Restriction: Intended for Honours Mathematics, Physics and Engineering programs.
 Restriction: Not open to students who have taken MATH 263 (formerly MATH 261), MATH 315
 Symbols:
 Terms
 Winter 2021
 Instructors
 Antony Raymond Humphries

PHYS 241 Signal Processing 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: Linear circuit elements, resonance, network theorems, diodes, transistors, amplifiers, feedback, integrated circuits.
Offered by: Physics
 Winter
 2 hours lectures; 3 hours laboratory alternate weeks
 Prerequisite: CEGEP physics or PHYS 142.
 Symbols:
 Terms
 Winter 2021
 Instructors
 Walter Reisner

PHYS 251 Honours Classical Mechanics 1 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Physics
 Fall
 3 hours lectures
 Prerequisite: CEGEP physics or PHYS 131.
 Corequisite: MATH 222
 Restriction: Not open to students taking or having taken PHYS 230.
 Symbols:
 Terms
 Fall 2020
 Instructors
 James M Cline

PHYS 257 Experimental Methods 1 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Physics
 Symbols:
 Terms
 Fall 2020
 Instructors
 Bradley J Siwick

PHYS 258 Experimental Methods 2 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Physics
 Winter
 6 hours of laboratory and classroom work
 Prerequisite: PHYS 257
 Symbols:
 Terms
 Winter 2021
 Instructors
 Thomas Brunner

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

MATH 255 Honours Analysis 2 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2021
 Instructors
 Vojkan Jaksic

MATH 475 Honours PDE's 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 247 or MATH 251 or equivalent, and MATH 248 or MATH 358 or equivalent, MATH 325.
 Restriction: Not open to students who have taken MATH 375.
 Symbols:
 Terms
 Fall 2020
 Instructors
 Jessica Lin

PHYS 253 Thermal Physics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: Energy, work, heat; first law. Temperature, entropy; second law. Absolute zero; third law. Equilibrium, equations of state, gases, liquids, solids, magnets; phase transitions.
Offered by: Physics
 Fall
 3 hours lectures
 Prerequisites: CEGEP physics or PHYS 131, and CEGEP chemistry or CHEM 120.
 Corequisite: MATH 222
 Restriction: Not open to students taking or having taken PHYS 232.
 Symbols:
 Terms
 Fall 2020
 Instructors
 Simon P CaronHuot

PHYS 350 Hons Electricity & Magnetism 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: Fundamental laws of electric and magnetic fields in both integral and differential form.
Offered by: Physics
 Fall
 3 hours lectures
 Prerequisites: MATH 248, MATH 325.
 Restriction: Honours students or permission of the instructor
 Restriction: Not open to students having taken PHYS 340
 Symbols:
 Terms
 Fall 2020
 Instructors
 Jonathan Le Roy Sievers

PHYS 351 Honours Classical Mechanics 2 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Physics
 Winter
 3 hours lectures
 Prerequisite: PHYS 251.
 Restriction: Not open to students who have taken PHYS 451.
 Symbols:
 Terms
 Winter 2021
 Instructors
 Keshav Dasgupta

PHYS 357 Honours Quantum Physics 1 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Physics
 Fall
 3 hours lectures
 Prerequisites: MATH 223 or equivalent, and one of PHYS 230, PHYS 251, or CIVE 281
 Restriction: Honours students or permission of the instructor
 Restriction: Not open to students taking or having passed PHYS 346
 Symbols:
 Terms
 Fall 2020
 Instructors
 Tamar PeregBarnea

PHYS 362 Statistical Mechanics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: Quantum states and ensemble averages. FermiDirac, BoseEinstein and Boltzmann distribution functions and their applications.
Offered by: Physics
 Winter
 3 hours lectures
 Prerequisites: MATH 248 or equivalents, PHYS 253.
 Restriction: Honours students, or permission of the instructor
 Restriction: Not open to students taking or having passed PHYS 333
 Symbols:
 Terms
 Winter 2021
 Instructors
 Martin Grant

PHYS 457 Honours Quantum Physics 2 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Physics
 Winter
 3 hours lectures
 Prerequisite: PHYS 357
 Restriction: Honours students or permission of instructor
 Restriction: Not open to students who have taken PHYS 346
 Symbols:
 Terms
 Winter 2021
 Instructors
 Kartiek Agarwal
U3 Required Courses (12 credits)

MATH 454 Honours Analysis 3 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Fall 2020
 Instructors
 Jerome Vetois

MATH 458 Honours Differential Geometry 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 251 or MATH 247, and MATH 248 or MATH 314 or MATH 358
 Restriction: Not open to students who have taken MATH 380.
 Symbols:
 Terms
 Winter 2021
 Instructors
 Niky Kamran

PHYS 352 Honours Electromagnetic Waves 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Physics
 Fall
 3 hours lectures
 Prerequisite: PHYS 350.
 Restriction: Honours students, or permission of the instructor
 Symbols:
 Terms
 Fall 2020
 Instructors
 Robert E Rutledge

PHYS 359 Hons Lab in Modern Physics 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: Advanced level experiments in modern physics stressing quantum effects and some properties of condensed matter.
Offered by: Physics
 Winter
 6 hours
 Corequisite: PHYS 457. Honours students or permission of instructor
 Symbols:
 Terms
 Winter 2021
 Instructors
 Thomas Brunner, Dominic Ryan
U1 Complementary Course (3 credits)

MATH 247 Honours Applied Linear Algebra 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 133 or equivalent.
 Restriction: Intended for Honours Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 236, MATH 223 or MATH 251
 Symbols:
 Terms
 Winter 2021
 Instructors
 Tim Hoheisel

MATH 251 Honours Algebra 2 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Winter
 Prerequisites: MATH 235 or permission of the Department
 Restriction: Not open to students who are taking or have taken MATH 247
 Symbols:
 Terms
 Winter 2021
 Instructors
 Michael Lipnowski
U2 Complementary Courses (3 credits)

MATH 242 Analysis 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite: MATH 141
 Restriction(s): Not open to students who are taking or who have taken MATH 254.
 Symbols:
 Terms
 Fall 2020
 Instructors
 Axel W Hundemer

MATH 254 Honours Analysis 1 3 Credits**
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Prerequisite(s): MATH 141
 Restriction(s): Not open to students who are taking or who have taken MATH 242.
 Symbols:
 **
 Terms
 Fall 2020
 Instructors
 Vojkan Jaksic
** 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
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2021
 Instructors
 Dmitry Jakobson

MATH 456 Honours Algebra 3 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 235 and either (MATH 247 or MATH 251).
 Restriction: Not open to students who have taken MATH 370.
 Symbols:
 Terms
 Fall 2020
 Instructors
 Eyal Z Goren
6 credits selected from:

PHYS 432 Physics of Fluids 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Physics
 Winter
 3 hours lectures
 Prerequisites: PHYS 230, MATH 223, MATH 314, MATH 315
 Restriction: Not open to students who have taken PHYS 332.
 Symbols:
 Terms
 Winter 2021
 Instructors
 Eve J Lee

PHYS 479 Physics Research Project 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: A supervised research project.
Offered by: Physics
 6 hours
 Restriction: U2 or U3 students in a Physics program, or permission of the instructor.
 Symbols:
 Terms
 Winter 2021
 Instructors
 Sabrina Leslie

PHYS 512 Comp. Phys. with Applications 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: Computational methods in Physics illustrated with realworld applications.
Offered by: Physics
 U3 or graduate students in Physics, Chemistry, or Engineering, or permission of the instructor. Basic familiarity with computer programming highly recommended.
 Symbols:
 Terms
 Fall 2020
 Instructors
 Jonathan Le Roy Sievers

PHYS 514 General Relativity 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Physics
 Winter
 3 hours lectures
 Restriction: U3 Honours students and graduate students, or permission of the instructor.
 Symbols:
 Terms
 Winter 2021
 Instructors
 Alexander Maloney

PHYS 519 Advanced Biophysics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: An advanced biophysics course, with a special emphasis on stochastic and out of equilibrium physical processes in living matter.
Offered by: Physics
 Prerequisites: (PHYS 329 or PHYS 333 or PHYS 362 or MATH 437) and (PHYS 340 or PHYS 350), or permission of the instructor.
 Symbols:
 Terms
 Winter 2021
 Instructors
 Paul Francois

PHYS 521 Astrophysics 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Physics
 Fall
 3 hours
 Restriction: U3 students and graduate students, or permission of the instructor
 Symbols:
 Terms
 Fall 2020
 Instructors
 Robert E Rutledge

PHYS 551 Quantum Theory 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: General formulation, scattering theory, WKBJ approximation, timedependent perturbation, theory and applications, angular momentum, relativistic wave equations.
Offered by: Physics
 Fall
 3 hours lectures
 Restriction: U3 Honours students and graduate students, or permission of the instructor
 Symbols:
 Terms
 Fall 2020
 Instructors
 Andrew Cumming

PHYS 557 Nuclear Physics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: General nuclear properties, nucleonnucleon interaction and scattering theory, radioactivity, nuclear models, nuclear reactions.
Offered by: Physics
 Fall
 3 hours lectures
 Restriction: U3 Honours students, graduate students, or permission of the instructor
 Symbols:
 Terms
 Fall 2020
 Instructors
 Sang Yong Jeon

PHYS 558 Solid State Physics 3 Credits
 Fall
 Winter
 Summer
Offered in the: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).
Offered by: Physics
 Fall
 3 hours lectures
 Restriction: U3 Honours students, graduate students, or permission of the instructor
 Symbols:
 Terms
 Fall 2020
 Instructors
 Lilian Childress

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

PHYS 562 Electromagnetic Theory 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: Electrostatics, dielectrics, magnetostatics, timevarying fields, relativity, radiating systems, fields of moving charges.
Offered by: Physics
 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
 Symbols:
 Terms
 Winter 2021
 Instructors
 Michael Hilke

PHYS 567 Particle Physics 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Physics
 Winter
 3 hours lectures
 Restriction: U3 Honours students, graduate students, or permission of the instructor
 Symbols:
 Terms
 Winter 2021
 Instructors
 James M Cline