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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 2010
Instructors: Ian Sydney Butler, Ariel Fenster, Ashok K Kakkar, JeanMarc Gauthier (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 2011
Instructors: JeanMarc Gauthier, Ariel Fenster, Anthony Mittermaier, Bradley Siwick (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 and waves.
Terms: Fall 2010
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: Not open to students taking or having taken PHYS 101, 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 and physical optics.
Terms: Winter 2011
Instructors: Yoichi Miyahara (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:

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 2010
Instructors: Irene GregoryEaves, Rajinder S Dhindsa, Claire Seizilles de Mazancourt (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 2011
Instructors: Joseph Alan Dent, Jacalyn Vogel (Winter)
 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.
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 2010, Winter 2011, Summer 2011
Instructors: Djivede Kelome, William J Anderson, James G Loveys, Shahab Shahabi, Adam Clay (Fall) Djivede Kelome, William J Anderson (Winter) Karol Palka (Summer)
 Prerequisite: a course in functions
 Restriction: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent.
 Restriction Note 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.

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 2010, Winter 2011, Summer 2011
Instructors: Stephen W Drury, Sidney Trudeau, Shahab Shahabi (Fall) Axel W Hundemer (Winter)
 3 hours lecture, 1 hour tutorial
 Prerequisite: High School Calculus
 Restriction: Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN or equivalent
 Restriction: Not open to students who have taken or are taking MATH 122 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 2010, Winter 2011, Summer 2011
Instructors: Sidney Trudeau (Fall) Neville G F Sancho, Stephen W Drury, Sidney Trudeau (Winter)
 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 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 2010
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 2011
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) : An introduction to the design of computer algorithms, including basic data structures, analysis of algorithms, and establishing correctness of programs. Overview of topics in computer science.
Terms: Fall 2010, Winter 2011
Instructors: Doina Precup (Fall) Michael Langer (Winter)
 3 hours
 Prerequisites: Familiarity with a high level programming language and CEGEP level Math.
 Restrictions: COMP 203 and COMP 250 are considered to be equivalent from a prerequisite point of view, and cannot both be taken for credit.

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 2010, Winter 2011, Summer 2011
Instructors: Wilbur Jonsson, Neville G F Sancho (Fall) Wilbur Jonsson (Winter)
 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

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 2010, Winter 2011
Instructors: James G Loveys, Hongnian Huang (Fall) James G Loveys (Winter)
 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

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 2010
Instructors: Frederick Shepherd (Fall)
 Fall
 Corequisite: MATH 133.
 Restriction: For students in any Computer Science program. Others only with the instructor's permission. Not open to students who have taken or are taking MATH 235.

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 2010
Instructors: Hong Guo (Fall)
 Fall
 3 hours lectures
 Prerequisite: CEGEP Physics or PHYS 131.
 Corequisite: MATH 222
 Restriction: Not open to students taking or having passed PHYS 251

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 2010
Instructors: Bradley Siwick (Fall)
 Fall
 6 hours of laboratory and classroom work
 Corequisite: PHYS 230 or PHYS 251

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 2011
Instructors: Dominic Ryan, Edith M Engelberg (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 2010, Winter 2011
Instructors: Joseph P Vybihal (Fall) Joseph P Vybihal, Gregory L Dudek (Winter)
 3 hours
 Prerequisite: COMP 202 or COMP 250

COMP 251 Data Structures and Algorithms (3 credits)
Overview
Computer Science (Sci) : Design and analysis of algorithms. Complexity of algorithms. Data structures. Introduction to graph algorithms and their analysis.
Terms: Fall 2010, Winter 2011
Instructors: Clark Verbrugge (Fall) Claude Crepeau (Winter)
 3 hours
 Prerequisite: COMP 250 or COMP 203.
 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 2010, Winter 2011
Instructors: Brigitte Pientka (Fall) Jesse Doherty (Winter)
 3 hours
 Prerequisite: COMP 250 or COMP 203

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 2010
Instructors: XiaoWen Chang (Fall)
 3 hours
 Prerequisites: MATH 222 and MATH 223 and one of: COMP 202, COMP 208, COMP 250; or equivalents.

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.
Terms: Fall 2010, Winter 2011, Summer 2011
Instructors: Wilbur Jonsson (Fall) Wilbur Jonsson (Winter) Charles Roth (Summer)
 Prerequisites: MATH 133, MATH 222
 Restriction: Not open to students who have taken or are taking MATH 248

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 2010, Winter 2011, Summer 2011
Instructors: Neville G F Sancho (Fall) JianJun Xu (Winter)
 Prerequisite: MATH 222.
 Corequisite: MATH 133.
 Restriction: Not open to students who have taken or are taking MATH 325.

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 2011
Instructors: Dominic Ryan (Winter)
 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

PHYS 241 Signal Processing (3 credits)
Overview
Physics : Linear circuit elements, resonance, network theorems, diodes, transistors, amplifiers, feedback, integrated circuits.
Terms: Winter 2011
Instructors: Jean Barrette (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 Techniques (3 credits)
Overview
Computer Science (Sci) : A study of techniques for the design and analysis of algorithms.
Terms: Fall 2010, Winter 2011
Instructors: Adrian Roshan Vetta (Fall) The Phuong Nguyen (Winter)
 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.

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 2010, Winter 2011, Summer 2011
Instructors: William J Anderson (Fall) Vahid Partovi Nia (Winter)
 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

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 2011
Instructors: Guillaume Gervais (Winter)
 Winter
 3 hours lectures
 Prerequisite: PHYS 230
 Corequisite: MATH 315
 Restriction: Not open to students having passed PHYS 451 or PHYS 351

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 2011
Instructors: Michael Hilke (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 2010
Instructors: Robert Rutledge (Fall)
 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

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 2010
Instructors: Walter Reisner (Fall)
 Fall
 3 hours lectures
 Prerequisite: PHYS 230 and PHYS 232, or PHYS 251
 Restriction: Not open to students taking or having taken PHYS 357 or PHYS 457

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 2011
Instructors: Jean Barrette, Fritz Buchinger (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