Program Requirements
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)
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 2018
Instructors: Mitchell Huot, JeanMarc Gauthier, Ian Sydney Butler, Pallavi Sirjoosingh (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 2019
Instructors: Laura Pavelka, Samuel Lewis Sewall, Pallavi Sirjoosingh, Mitchell Huot, JeanMarc Gauthier (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 2018
Instructors: Kenneth J Ragan (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 2019
Instructors: Michael Hilke (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 2018
Instructors: Andrew Hendry, Elena Cristescu, Anna Hargreaves (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 2019
Instructors: Joseph Alan Dent, Frieder Schöck (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; quadratic loci in two and three dimensions.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Jerome Fortier, Liangming Shen, Yann Batiste Pequignot, Damian Osajda (Fall) Jerome Fortier (Winter) Rebecca Patrias (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.

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 2018, Winter 2019, Summer 2019
Instructors: Sidney Trudeau, Jerome Fortier, Rebecca Patrias (Fall) Alexander Garver (Winter) Peter Zenz (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

MATH 141 Calculus 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Corentin PerretGentilditMaillard, Jonah Gaster (Fall) Sidney Trudeau, Jerome Fortier, Thomas F Fox (Winter) Bogdan Nica (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

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 2018
Instructors: Charles Roth (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

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 2019
Instructors: Charles Roth (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 (21 credits)

COMP 250 Introduction to Computer Science (3 credits)
Overview
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.
Terms: Fall 2018, Winter 2019
Instructors: Michael Langer, Giulia Alberini (Fall) Martin Robillard, Giulia Alberini (Winter)

MATH 222 Calculus 3 (3 credits)
Overview
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.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Jeremy Macdonald, Dmitry Faifman (Fall) Lars Sektnan (Winter) Yann Batiste Pequignot (Summer)

MATH 223 Linear Algebra (3 credits)
Overview
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.
Terms: Fall 2018, Winter 2019
Instructors: Djivede Kelome (Fall) Jeremy Macdonald (Winter)

MATH 240 Discrete Structures 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : Mathematical foundations of logical thinking and reasoning. Mathematical language and proof techniques. Quantifiers. Induction. Elementary number theory. Modular arithmetic. Recurrence relations and asymptotics. Combinatorial enumeration. Functions and relations. Partially ordered sets and lattices. Introduction to graphs, digraphs and rooted trees.
Terms: Fall 2018, Winter 2019
Instructors: Jeremy Macdonald, Bogdan Nica (Fall) Jeremy Macdonald, Yann Batiste Pequignot (Winter)

PHYS 230 Dynamics of Simple Systems (3 credits)
Overview
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.
Terms: Fall 2018
Instructors: Keshav Dasgupta (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 2018
Instructors: Bradley Siwick (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 2019
Instructors: Thomas Brunner (Winter)
Winter
6 hours of laboratory and classroom work
Prerequisite: PHYS 257
U2 Required Courses (24 credits)

COMP 206 Introduction to Software Systems (3 credits)
Overview
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.
Terms: Fall 2018, Winter 2019
Instructors: David Meger (Fall) Chad Zammar, Joseph P Vybihal (Winter)

COMP 251 Algorithms and Data Structures (3 credits)
Overview
Computer Science (Sci) : Introduction to algorithm design and analysis. Graph algorithms, greedy algorithms, data structures, dynamic programming, maximum flows.
Terms: Fall 2018, Winter 2019
Instructors: Jérôme Waldispuhl (Fall) Luc P Devroye, Erin Leigh McLeish (Winter)
3 hours
Prerequisite: COMP 250
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 and 363, 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.

COMP 302 Programming Languages and Paradigms (3 credits)
Overview
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.
Terms: Fall 2018, Winter 2019
Instructors: Brigitte Pientka (Fall) Prakash Panangaden (Winter)
3 hours
Prerequisite: COMP 250

COMP 350 Numerical Computing (3 credits)
Overview
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.
Terms: Fall 2018
Instructors: XiaoWen Chang (Fall)

MATH 314 Advanced Calculus (3 credits)
Overview
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.
Terms: Fall 2018, Winter 2019
Instructors: Charles Roth (Fall) Stephen W Drury (Winter)

MATH 315 Ordinary Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: JeanChristophe Nave (Fall) Antony Raymond Humphries (Winter) Charles Roth (Summer)

PHYS 232 Heat and Waves (3 credits)
Overview
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.
Terms: Winter 2019
Instructors: Robert Rutledge (Winter)

PHYS 241 Signal Processing (3 credits)
Overview
Physics : Linear circuit elements, resonance, network theorems, diodes, transistors, amplifiers, feedback, integrated circuits.
Terms: Winter 2019
Instructors: Matthew Adam Dobbs (Winter)
Winter
2 hours lectures; 3 hours laboratory alternate weeks
Prerequisite: CEGEP physics or PHYS 142.
U3 Required Courses (21 credits)

COMP 360 Algorithm Design (3 credits)
Overview
Computer Science (Sci) : Advanced algorithm design and analysis. Linear programming, complexity and NPcompleteness, advanced algorithmic techniques.
Terms: Fall 2018, Winter 2019
Instructors: Bruce Alan Reed (Fall) Bruce Alan Reed (Winter)

MATH 323 Probability (3 credits)
Overview
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.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: David Stephens (Fall) David B Wolfson (Winter) Djivede Kelome (Summer)

PHYS 331 Topics in Classical Mechanics (3 credits)
Overview
Physics : Forced and damped oscillators, Newtonian mechanics in three dimensions, rotational motion, Lagrangian mechanics, small vibrations, normal modes. Introduction to Hamiltonian mechanics.
Terms: Winter 2019
Instructors: Simon CaronHuot (Winter)

PHYS 339 Measurements Laboratory in General Physics (3 credits)
Overview
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.
Terms: Winter 2019
Instructors: Walter Reisner (Winter)
Winter
6 hours
Prerequisite: PHYS 241 or permission of instructor

PHYS 340 Majors Electricity and Magnetism (3 credits)
Overview
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.
Terms: Fall 2018
Instructors: Robert Rutledge (Fall)

PHYS 446 Majors Quantum Physics (3 credits)
Overview
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.
Terms: Fall 2018
Instructors: Jack Childress (Fall)

PHYS 489 Special Project (3 credits)
Overview
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.
Terms: Winter 2019
Instructors: Guillaume Gervais (Winter)
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