Physics and Computer Science (Joint Major)
The Joint Major in Physics and Computer Science is designed to give motivated students the opportunity to combine the two fields in a way that will distinguish them from the graduates of either field by itself. The two disciplines complement each other, with physics providing an analytic problemsolving outlook and basic understanding of nature, while computer science enhances the ability to make practical and marketable applications, in addition to having its own theoretical interest. Graduates of this program may be able to present themselves as being more immediately useful than a pure physics major, but with more breadth than just a programmer.
DETAILED PROGRAM OUTLINE:
Program Requirement:
The Major Physics and Computer Science is designed to give motivated students the opportunity to combine the two fields in a way that will distinguish them from the graduates of either field by itself. The two disciplines complement each other, with physics providing an analytic problemsolving outlook and basic understanding of nature, while computer science enhances the ability to make practical and marketable applications, in addition to having its own theoretical interest. Graduates of this program may be able to present themselves as being more immediately useful than a pure physics major, but with more breadth than just a programmer. They will be able to demonstrate their combined expertise in the Special Project course which is the centrepiece of the final year of the program.
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:
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 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:
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 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:
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 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:
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 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:
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 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:
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 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:
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 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:
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 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:
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 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:
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 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:
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 Winter 2021
 Instructors
 Charles Roth
U1 Required Courses (21 credits)

COMP 250 Intro to Computer Science 3 Credits
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Mathematical tools (binary numbers, induction, recurrence relations, asymptotic complexity, establishing correctness of programs), Data structures (arrays, stacks, queues, linked lists, trees, binary trees, binary search trees, heaps, hash tables), Recursive and nonrecursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.
Offered by: Computer Science
 3 hours
 Prerequisites: Familiarity with a high level programming language and CEGEP level Math.
 Students with limited programming experience should take COMP 202 or equivalent before COMP 250. See COMP 202 Course Description for a list of topics.
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Giulia Alberini
 Giulia Alberini

MATH 222 Calculus 3 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
 Restriction: Not open to students who have taken CEGEP course 201303 or MATH 150, MATH 151 or MATH 227
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Djivede A Kelome, Jérôme Fortier
 Jerome Vetois

MATH 223 Linear Algebra 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications.
Offered by: Mathematics and Statistics
 Fall and Winter
 Prerequisite: MATH 133 or equivalent
 Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 236, MATH 247 or MATH 251. It is open to students in Faculty Programs
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Michael Y Pichot

MATH 240 Discrete Structures 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Introduction to discrete mathematics and applications. Logical reasoning and methods of proof. Elementary number theory and cryptography: prime numbers, modular equations, RSA encryption. Combinatorics: basic enumeration, combinatorial methods, recurrence equations. Graph theory: trees, cycles, planar graphs.
Offered by: Mathematics and Statistics
 Fall and Winter
 Corequisite: MATH 133.
 Restriction: For students in any Computer Science, Computer Engineering, or Software Engineering programs. Others only with the instructor's permission. Not open to students who have taken or are taking MATH 235.
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 Fall 2020
 Winter 2021
 Instructors
 Dana Louis AddarioBerry, Elliot Paquette
 Adrian Roshan Vetta, Jérôme Fortier

PHYS 230 Dynamics of Simple Systems 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: Translational motion under Newton's laws; forces, momentum, work/energy theorem. Special relativity; Lorentz transforms, relativistic mechanics, mass/energy equivalence. Topics in rotational dynamics. Noninertial frames.
Offered by: Physics
 Fall
 3 hours lectures
 Prerequisite: CEGEP Physics or PHYS 131.
 Corequisite: MATH 222
 Restriction: Not open to students taking or having passed PHYS 251
 Symbols:
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 Fall 2020
 Instructors
 Hong Guo

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:
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 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
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 Winter 2021
 Instructors
 Thomas Brunner
U2 Required Courses (24 credits)

COMP 206 Intro to Software Systems 3 Credits
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Comprehensive overview of programming in C, use of system calls and libraries, debugging and testing of code; use of developmental tools like make, version control systems.
Offered by: Computer Science
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Joseph V D'silva
 Joseph V D'silva

COMP 251 Algorithms and Data Structures 3 Credits
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Introduction to algorithm design and analysis. Graph algorithms, greedy algorithms, data structures, dynamic programming, maximum flows.
Offered by: Computer Science
 3 hours
 Prerequisite: COMP 250
 Corequisite(s): MATH 235 or MATH 240.
 COMP 251 uses mathematical proof techniques that are taught in the corequisite course(s). If possible, students should take the corequisite course prior to COMP 251.
 COMP 251 uses basic counting techniques (permutations and combinations) that are covered in MATH 240 but not in MATH 235. These techniques will be reviewed for the benefit of MATH 235 students.
 Restrictions: Not open to students who have taken or are taking COMP 252.
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Jérôme Waldispuhl, David C Becerra
 David C Becerra

COMP 302 Programming Lang & Paradigms 3 Credits
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Programming language design issues and programming paradigms. Binding and scoping, parameter passing, lambda abstraction, data abstraction, type checking. Functional and logic programming.
Offered by: Computer Science
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Brigitte Pientka

COMP 350 Numerical Computing 3 Credits
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Computer representation of numbers, IEEE Standard for Floating Point Representation, computer arithmetic and rounding errors. Numerical stability. Matrix computations and software systems. Polynomial interpolation. Leastsquares approximation. Iterative methods for solving a nonlinear equation. Discretization methods for integration and differential equations.
Offered by: Computer Science
 3 hours
 Prerequisites: MATH 222 and MATH 223 and one of: COMP 202, COMP 208, COMP 250; or equivalents.
 Restrictions: Students cannot receive credit for both COMP 350 and MATH 317.
 Symbols:
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 Fall 2020
 Instructors
 XiaoWen Chang

MATH 314 Advanced Calculus 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 133, MATH 222
 Restriction: Not open to students who have taken or are taking MATH 248 or MATH 358.
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Charles Roth
 John A Toth

MATH 315 Ordinary Differential Eqns 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 222.
 Corequisite: MATH 133.
 Restriction: Not open to students who have taken or are taking MATH 325.
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Courtney Paquette

PHYS 232 Heat and Waves 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: The laws of thermodynamics and their consequences. Thermodynamics of PVT systems and simple heat engines. Free, driven, and damped harmonic oscillators. Coupled systems and normal modes. Fourier methods. Wave motion and dispersion. The wave equation.
Offered by: Physics
 Winter
 3 hours lectures
 Prerequisites: CEGEP Physics or PHYS 142, and CEGEP chemistry or CHEM 120, and PHYS 230.
 Restriction: Not open to students taking or having passed PHYS 253
 Symbols:
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 Winter 2021
 Instructors
 Simon P CaronHuot

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:
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 Winter 2021
 Instructors
 Walter Reisner
U3 Required Courses (21 credits)

COMP 360 Algorithm Design 3 Credits
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Advanced algorithm design and analysis. Linear programming, complexity and NPcompleteness, advanced algorithmic techniques.
Offered by: Computer Science
 3 hours
 Prerequisite: Either COMP 251 or COMP 252, and either MATH 240 or MATH 235 or MATH 363.
 Restriction: Not open to students who have taken or are taking COMP 362.
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Bruce Alan Reed

MATH 323 Probability 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 141 or equivalent.
 Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
 Restriction: Not open to students who have taken or are taking MATH 356
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 David B Wolfson, Alia Sajjad
 David B Wolfson, Alia Sajjad

PHYS 331 Topics in Classical Mechanics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: Forced and damped oscillators, Newtonian mechanics in three dimensions, rotational motion, Lagrangian and Hamiltonian mechanics, small vibrations, normal modes. Nonlinear dynamics and chaos.
Offered by: Physics
 Winter
 3 hours lectures
 Prerequisite: PHYS 230
 Corequisite: MATH 315
 Restriction: Not open to students having passed PHYS 451 or PHYS 351
 Symbols:
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 Winter 2021
 Instructors
 Guillaume Gervais

PHYS 339 Measurements Lab in Gen Phys 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: Introduction to modern techniques of measurement. The use of computers in performing and analysing experiments. Data reduction, statistical methods, report writing. Extensive use of computers is made in this laboratory; therefore some familiarity with computers and computing is an advantage.
Offered by: Physics
 Winter
 6 hours
 Prerequisite: PHYS 241 or permission of instructor
 Symbols:
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 Winter 2021
 Instructors
 Walter Reisner

PHYS 340 Majors Electricity & Magnetism 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: The electrostatic field and scalar potential. Dielectric properties of matter. Energy in the electrostatic field. Methods for solving problems in electrostatics. The magnetic field. Induction and inductance. Energy in the magnetic field. Magnetic properties of matter. Maxwell's equations. The dipole approximation.
Offered by: Physics
 Fall
 3 hours lectures
 Prerequisites: CEGEP physics or PHYS 142, MATH 222
 Corequisite: MATH 314
 Restriction: Not open to students who have passed PHYS 242 or PHYS 350
 Symbols:
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 Fall 2020
 Instructors
 Hong Guo

PHYS 346 Majors Quantum Physics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: De Broglie waves, Bohr atom. Schroedinger equation, wave functions, observables. One dimensional potentials. Schroedinger equation in three dimensions. Angular momentum, hydrogen atom. Spin, experimental consequences.
Offered by: Physics
 Fall
 Prerequisite: PHYS 230 and PHYS 232, or PHYS 251
 Restriction: Not open to students who have taken PHYS 357, PHYS 446, or PHYS 457.
 3 hours lectures
 Symbols:
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 Fall 2020
 Instructors
 Brigitte Vachon

PHYS 489 Special Project 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: A project incorporating aspects of both physics and computer science, under the joint supervision of the two departments. The Physics aspect may be either laboratorybased or theoretical in nature. The Computational aspect will involve the development and implementation of algorithms arising from the investigation.
Offered by: Physics
 Winter
 6 hours
 Restriction: Only open to students in their final year of the Joint Major in Physics and Computer Science after consultation with the adviser(s) for the program
 Symbols:
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 Winter 2021
 Instructors
 Lilian Childress