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.
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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 2015
Instructors: Gauthier, Jean-Marc; Sewall, Samuel Lewis; Huot, Mitchell; Barrett, Christopher; Friscic, Tomislav; Pavelka, Laura (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
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CHEM 120 General Chemistry 2 (4 credits)
Overview
Chemistry : A study of the fundamental principles of physical chemistry.
Terms: Winter 2016
Instructors: Pavelka, Laura; Butler, Ian Sydney; Siwick, Bradley; Gauthier, Jean-Marc; 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
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PHYS 131 Mechanics and Waves (4 credits)
Overview
Physics : The basic laws and principles of Newtonian mechanics; oscillations and waves.
Terms: Fall 2015
Instructors: Ragan, Kenneth J (Fall)
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PHYS 142 Electromagnetism and Optics (4 credits)
Overview
Physics : The basic laws of electricity and magnetism; geometrical and physical optics.
Terms: Winter 2016
Instructors: Gervais, Guillaume; Engelberg, Edith M (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 taking or having taken PHYS 102, CEGEP objective 00UR or equivalent
Laboratory sections have limited enrolment
One of:
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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 2015
Instructors: Krahe, Rudiger; Dhindsa, Rajinder S; Gregory-Eaves, Irene (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.
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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 2016
Instructors: Dent, Joseph Alan; Sch枚ck, Frieder (Winter)
MATH 133 and either MATH 140/141 or MATH 150/151.
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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; quadratic loci in two and three dimensions.
Terms: Fall 2015, Winter 2016, Summer 2016
Instructors: Disegni, Daniel; Kelome, Djivede; Baratin, Aristide; Anderson, William J (Fall) Novytska, Yuliya; Kelome, Djivede (Winter) Baratin, Aristide (Summer)
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, MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
Restriction C: Not open to students who are taking or have taken MATH 134.
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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 2015, Winter 2016, Summer 2016
Instructors: Hundemer, Axel W; Hu, Ying; Wallace, Michael (Fall) Vonk, Jan (Winter) Jakobson, Dmitry (Summer)
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 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
Each Tutorial section is enrolment limited
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MATH 141 Calculus 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Terms: Fall 2015, Winter 2016, Summer 2016
Instructors: Pang, Chung Yin Amy (Fall) Shokoohi, Farhad; Hundemer, Axel W; Barsheshat, Yariv (Winter) Al Balushi, Ibrahim; 成人VR视频ivray, Annaliza (Summer)
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 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
Each Tutorial section is enrolment limited
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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 2015
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 or MATH 130 or MATH 131, 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
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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 2016
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 or MATH 130 or MATH 131, 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)
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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 2015
Instructors: Goren, Eyal Z (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent
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MATH 248 Honours Advanced Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Partial derivatives; implicit functions; Jacobians; maxima and minima; Lagrange multipliers. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line integrals; Green's theorem; the divergence theorem. Stokes' theorem; irrotational and solenoidal fields; applications.
Terms: Fall 2015
Instructors: Guan, Pengfei (Fall)
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MATH 249 Honours Complex Variables (3 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Winter 2016
Instructors: Vetois, Jerome (Winter)
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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: Fall 2015, Winter 2016
Instructors: Li, JunFang (Fall) Humphries, Antony Raymond (Winter)
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PHYS 241 Signal Processing (3 credits)
Overview
Physics : Linear circuit elements, resonance, network theorems, diodes, transistors, amplifiers, feedback, integrated circuits.
Terms: Winter 2016
Instructors: Dobbs, Matthew Adam (Winter)
Winter
2 hours lectures; 3 hours laboratory alternate weeks
Prerequisite: CEGEP physics or PHYS 142.
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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 2015
Instructors: Hanna, David (Fall)
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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 2015
Instructors: Warburton, Andreas; Engelberg, Edith M (Fall)
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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 2016
Instructors: Warburton, Andreas; Engelberg, Edith M; Brunner, Thomas (Winter)
Winter
6 hours of laboratory and classroom work
Prerequisite: PHYS 257
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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 2015
Instructors: Childress, Lilian (Fall)
U2 Required Courses (27 credits)
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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 2015
Instructors: Hundemer, Axel W (Fall)
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MATH 255 Honours Analysis 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, H脙露lder 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.
Terms: Winter 2016
Instructors: Jaksic, Vojkan (Winter)
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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, 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.
Terms: Fall 2015
Instructors: Choksi, Rustum (Fall)
Restriction(s): Not open to students who have taken MATH 375.
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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 2015
Instructors: Webb, Tracy (Fall)
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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 2015
Instructors: Reisner, Walter (Fall)
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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 2016
Instructors: Gervais, Guillaume (Winter)
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PHYS 357 Honours Quantum Physics 1 (3 credits)
Overview
Physics : 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.
Terms: Fall 2015
Instructors: Guo, Hong (Fall)
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PHYS 362 Statistical Mechanics (3 credits)
Overview
Physics : Quantum states and ensemble averages. Fermi-Dirac, Bose-Einstein and Boltzmann distribution functions and their applications.
Terms: Winter 2016
Instructors: Sutton, Mark (Winter)
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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 2016
Instructors: Pereg-Barnea, Tamar (Winter)
U3 Required Courses (12 credits)
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MATH 454 Honours Analysis 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of point-set topology: topological space, dense sets, completeness, compactness, connectedness and path-connectedness, separability. Arzela-Ascoli, Stone-Weierstrass, 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. Fubini-Tonelli theorem.
Terms: Fall 2015
Instructors: Drury, Stephen W (Fall)
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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 Fary-Milnor theorem on knotted curves, abstract surfaces as 2-d manifolds, the Euler characteristic, the Gauss-Bonnet theorem for surfaces.
Terms: Winter 2016
Instructors: Przytycki, Piotr (Winter)
Restriction(s): Not open to students who have taken MATH 380.
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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 2015
Instructors: Cooke, David (Fall)
Fall
3 hours lectures
Prerequisite: PHYS 350.
Restriction: Honours students, or permission of the instructor
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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 2016
Instructors: Ryan, Dominic; Lovejoy, Shaun MacDonald (Winter)
Winter
6 hours
Corequisite: PHYS 457. Honours students or permission of instructor
U1 Complementary Course (3 credits)
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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 2016
Instructors: Disegni, Daniel (Winter)
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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 self-adjoint operators.
Terms: Winter 2016
Instructors: Przytycki, Piotr (Winter)
U3 Complementary Courses (12 credits)
12 credits are selected as follows:
3 credits from:
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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, Hahn-Banach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Introduction to Fourier analysis, Fourier transforms.
Terms: Winter 2016
Instructors: Drury, Stephen W (Winter)
Restriction(s): Not open to students who have taken MATH 355.
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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 2015
Instructors: Barrera, Daniel (Fall)
Restriction(s): Not open to students who have taken MATH 370.
6 credits selected from:
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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 2016
Instructors: Cumming, Andrew (Winter)
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PHYS 479 Honours Research Project (3 credits)
Overview
Physics : Honours supervised research project.
Terms: Winter 2016, Summer 2016
Instructors: Sutton, Mark (Winter) Childress, Jack (Summer)
6 hours
Restriction: Honours students or permission of instructor. Only open to students who have completed the U2 year in a Physics program.
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PHYS 514 General Relativity (3 credits)
Overview
Physics : 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.
Terms: Winter 2016
Instructors: Morrison, Ian (Winter)
Winter
3 hours lectures
Restriction: U3 Honours students and graduate students, or permission of the instructor.
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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 2016
Instructors: Francois, Paul (Winter)
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PHYS 521 Astrophysics (3 credits)
Overview
Physics : A quantitative course in galactic and extragalactic astrophysics. Topics include observational techniques, stars and stellar evolution, compact objects, galaxy structure, kinematics, evolution and cosmology.
Terms: Fall 2015
Instructors: Rutledge, Robert (Fall)
Fall
3 hours
Restriction: U3 Honours students and graduate students, or permission of the instructor
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PHYS 551 Quantum Theory (3 credits)
Overview
Physics : General formulation, scattering theory, WKBJ approximation, time-dependent perturbation, theory and applications, angular momentum, relativistic wave equations.
Terms: Fall 2015
Instructors: Dasgupta, Keshav (Fall)
Fall
3 hours lectures
Restriction: U3 Honours students and graduate students, or permission of the instructor
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PHYS 557 Nuclear Physics (3 credits)
Overview
Physics : General nuclear properties, nucleon-nucleon interaction and scattering theory, radioactivity, nuclear models, nuclear reactions.
Terms: Fall 2015
Instructors: Gale, Charles (Fall)
Fall
3 hours lectures
Restriction: U3 Honours students, graduate students, or permission of the instructor
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PHYS 558 Solid State Physics (3 credits)
Overview
Physics : 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).
Terms: Fall 2015
Instructors: Coish, William (Fall)
Fall
3 hours lectures
Restriction: U3 Honours students, graduate students, or permission of the instructor
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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 2015
Instructors: Reisner, Walter (Fall)
Fall
3 hours lectures
Restriction: U3 Honours students, graduate students, or permission of the instructor
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PHYS 562 Electromagnetic Theory (3 credits)
Overview
Physics : Electrostatics, dielectrics, magnetostatics, timevarying fields, relativity, radiating systems, fields of moving charges.
Terms: Winter 2016
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
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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 2016
Instructors: Dobbs, Matthew Adam (Winter)
Winter
3 hours lectures
Restriction: U3 Honours students, graduate students, or permission of the instructor
3 credits in Honours Mathematics.