REQUIED COURSES 

Bachelor of Science (B.Sc.)  Major Physiology and Mathematics (79 Credits)
Program Requirement: Required Courses (70 credits)BioPhysical Sciences Core
BIOL 219
Intro to Phys Mol & Cell Biol
4 Credits
Offered in the:  Fall
 Winter
 Summer
Biology (Sci): An introduction to molecular and cell biology from a physical perspective. Techniques and methodologies, both experimental and computational, are included in the presentation of each thematic module.
Offered by: Biology
 Prerequisite(s): BIOL 112; CHEM 110 and CHEM 120; MATH 140, MATH 141 and MATH 133; PHYS 131 and PHYS 142; or the equivalents of these courses.
 Corequisite(s): MATH 222 or equivalent
 Restriction(s): Not open to students who have taken or are taking ANAT 212, BIOC 212, BIOL 200, and BIOL 201, or BIEN 219. Only open to students in Bioengineering, Computer ScienceBiology, BiologyMathematics, BiologyQuantitative Biology, ChemistryBiophysical Chemistry, and PhysicsBiological Physics Options.
 This course is meant to prepare students for related 300level courses in Biology, Chemistry, Engineering and Physics.
 Terms
 Instructors
 Stephanie Weber, Jacalyn M Vogel, Adam G Hendricks

BIOL 395
Quantitative Biology Seminar
1 Credits
Offered in the:  Fall
 Winter
 Summer
Biology (Sci): Overview of concepts and current research in quantitative biology; theoretical ecology and evolution, computational biology, and physical biology.
Offered by: Biology
 Fall
 Prerequisites: BIOL 219; or BIOL 200 plus BIOL 201 or ANAT 212 or BIOC 212; CHEM 212; COMP 202 or COMP 204 or COMP 250; MATH 222; or permission of instructor.
 Restriction: Only open to U2 students in the following programs: B.Sc.; Major and Honours in Biology; Quantitative Biology, B.Sc.; Major and Honours Computer Science and Biology, B.Sc.; Major Biology and Mathematics, B.Sc.; Major Physiology and Mathematics, B.Sc.; Major Physiology and Physics, B.Sc.; Major and Honours Chemistry; Biophysical Chemistry, and B.Sc.; Major and Honours Physics; Biological Physics.
 Terms
 Instructors
 Arnold L Hayer, Paul W Wiseman, Frederic Guichard, Gregor F Fussmann, Paul Francois, Claudia Kleinman, Marlene H Oeffinger, Allen J Ehrlicher, Michael Hendricks, Khanh Huy Bui

MATH 222
Calculus 3
3 Credits
Offered in the:  Fall
 Winter
 Summer
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
 Terms
 Instructors
 Patrick Allen, Allysa Lumley
 Sidney Trudeau

MATH 223
Linear Algebra
3 Credits*
Offered in the:  Fall
 Winter
 Summer
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
 Terms
 Instructors
 Djivede A Kelome
 Henri Darmon

MATH 247
Honours Applied Linear Algebra
3 Credits*
Offered in the:  Fall
 Winter
 Summer
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

MATH 315
Ordinary Differential Eqns
3 Credits**
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Offered by: Mathematics and Statistics
 Terms
 Instructors
 Courtney Paquette
 Rosalie BélangerRioux

MATH 323
Probability
3 Credits
Offered in the:  Fall
 Winter
 Summer
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
 Terms
 Instructors
 David A Stephens, Alia Sajjad
 Alia Sajjad, Tharshanna Nadarajah

MATH 325
Honours ODE's
3 Credits**
Offered in the:  Fall
 Winter
 Summer
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
* Students may take either MATH 223 or MATH 247.
** Students may take either MATH 315 or MATH 325.
Physiology and Mathematics Core
BIOL 309
Mathematical Models in Biology
3 Credits
Offered in the:  Fall
 Winter
 Summer
Biology (Sci): Application of finite difference and differential equations to problems in cell and developmental biology, ecology and physiology. Qualitative, quantitative and graphical techniques are used to analyze mathematical models and to compare theoretical predictions with experimental data.
Offered by: Biology

BMDE 519
Biomedical Signals & Systems
3 Credits
Offered in the:  Fall
 Winter
 Summer
Biomedical Engineering: An introduction to the theoretical framework, experimental techniques and analysis procedures available for the quantitative analysis of physiological systems and signals. Lectures plus laboratory work using the Biomedical Engineering computer system. Topics include: amplitude and frequency structure of signals, filtering, sampling, correlation functions, time and frequencydomain descriptions of systems.
Offered by: Biomedical Engineering
 (306)
 Prerequisites: Satisfactory standing in U3 Honours Physiology; or U3 Major in PhysicsPhysiology; or U3 Major PhysiologyMathematics; or permission of instructor

MATH 242
Analysis 1
3 Credits
Offered in the:  Fall
 Winter
 Summer
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.

MATH 243
Analysis 2
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.
Offered by: Mathematics and Statistics

MATH 248
Honours Vector Calculus
3 Credits***
Offered in the:  Fall
 Winter
 Summer
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.

MATH 314
Advanced Calculus
3 Credits***
Offered in the:  Fall
 Winter
 Summer
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
 Terms
 Instructors
 Charles Roth
 Jeremy Macdonald

MATH 317
Numerical Analysis
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Offered by: Mathematics and Statistics

MATH 319
Intro to Partial Diff Equas
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, SturmLiouville theory, Fourier series, boundary and initial value problems.
Offered by: Mathematics and Statistics

MATH 324
Statistics
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Offered by: Mathematics and Statistics
 Fall and Winter
 Prerequisite: MATH 323 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 357
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.

MATH 326
Nonlinear Dynamics and Chaos
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, PoincareBendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Offered by: Mathematics and Statistics

MATH 437
Mathematical Meth in Biology
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): The formulation and treatment of realistic mathematical models describing biological phenomena through qualitative and quantitative mathematical techniques (e.g. local and global stability theory, bifurcation analysis and phase plane analysis) and numerical simulation. Concrete and detailed examples will be drawn from molecular and cellular biology and mammalian physiology.
Offered by: Mathematics and Statistics

PHGY 209
Mammalian Physiology 1
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Physiology of body fluids, blood, body defense mechanisms, muscle, peripheral, central, and autonomic nervous systems.
Offered by: Physiology
 Terms
 Instructors
 Melissa A Vollrath, Ann Wechsler, David S Ragsdale, Alvin Shrier, Erik P Cook, Céline Aguer

PHGY 210
Mammalian Physiology 2
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Physiology of cardiovascular, respiratory, digestive, endocrine and renal systems.
Offered by: Physiology
 Terms
 Instructors
 Melissa A Vollrath, Tomoko Takano, Michael R Guevara, AnneMarie Lauzon, John H White, Céline Aguer

PHGY 212
Introductory Physiology Lab 1
1 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Exercises illustrating fundamental principles in physiology: Biological Signals Acquisitions, Blood, Immunology, Neurophysiology, Neuromuscular Physiology.
Offered by: Physiology
 (One 3hour lab and one 1hour lecture every second week.)
 Corequisite: PHGY 209.
 Restrictions: Required for Physiology students enrolled in PHGY 209. Open to BA &Sc. students and to others by permission of the instructor. Not open to students who have taken PHGY 212D1/D2.
 Note: For students in a Physiology program, PHGY 212 should be taken concurrently with PHGY 209.
 Terms
 Instructors
 Melissa A Vollrath, Mladen I Glavinovic, Judith N Mandl

PHGY 213
Introductory Physiology Lab 2
1 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Exercises illustrating fundamental principles in physiology: Central Nervous System, Cardiovascular, Respiration, Exercise Physiology, Molecular Endocrinology.
Offered by: Physiology
 (One 3hour lab and one 1hour lecture every second week.)
 Prerequisite: PHGY 212
 Corequisite: PHGY 210.
 Restrictions: Required for Physiology students enrolled in PHGY 210. Open to BA &Sc. students and to others by permission of the instructor. Not open to students who have taken PHGY 212D1/D2.
 Note: For students in a Physiology program, PHGY 213 should be taken concurrently with PHGY 210.
 Terms
 Instructors
 Michael R Guevara, Sheldon A Magder, John H White, Melissa A Vollrath

PHGY 312
Resp.,Renal,&Cardio Physiology
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Indepth presentation of experimental results and hypotheses underlying our current understanding of topics in renal, respiratory and cardiovascular functions explored beyond the introductory level.
Offered by: Physiology
 Winter
 3 hours of lectures per week; 13 hours optional lab/demonstration/tutorial arranged for a maximum of 3 Wednesday afternoons per term
 Prerequisites: PHGY 209 and PHGY 210 or equivalent, PHGY 311 or permission of the instructor
 Terms
 Instructors
 John W Hanrahan, James G Martin, Alvin Shrier, Sheldon A Magder

PHGY 313
Blood,GI,Imm.Syst.Physiol
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Indepth presentation of experimental results and hypotheses underlying our current understanding of topics in immunology, blood and fluids, and gastrointestinal physiology.
Offered by: Physiology
 Winter
 3 hours of lectures per week; 13 hours optional lab/demonstration/tutorial arranged for a maximum of 3 Wednesday afternoons per term
 Prerequisites: PHGY 209 and PHGY 210 or equivalent, PHGY 311 or permission of the instructor
 Terms
 Instructors
 Judith N Mandl, Volker Manfred Blank, Melissa A Vollrath, Jörg H Fritz, Daniela Quail

PHGY 461D1
Experimental Physiology
4.5 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Individual project work under the supervision of Departmental Staff members.
Offered by: Physiology
 Fall
 Restrictions: Departmental approval required. This course is a requirement for U3 students in the Honours Physiology program, the Major Program in Physiology and Mathematics, and the Major program in Physiology and Physics, and is open to a limited number of other U3 Physiology students.
 Students must register for both PHGY 461D1 and PHGY 461D2.
 No credit will be given for this course unless both PHGY 461D1 and PHGY 461D2 are successfully completed in consecutive terms
 Terms
 Instructors
 John Orlowski, Ann Wechsler, Melissa A Vollrath

PHGY 461D2
Experimental Physiology
4.5 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: See PHGY 461D1 for course description.
Offered by: Physiology
 Winter
 Prerequisite: PHGY 461D1
 No credit will be given for this course unless both PHGY 461D1 and PHGY 461D2 are successfully completed in consecutive terms
 Terms
 Instructors
 John Orlowski, Ann Wechsler, Melissa A Vollrath
*** Students may take either MATH 248 or MATH 314.
Complementary Courses (9 credits)3 credits, one of:

COMP 204
Comp. Programming for Life Sci
3 Credits
Offered in the:  Fall
 Winter
 Summer
Computer Science (Sci): Computer Science (Sci): Computer programming in a high level language: variables, expressions, types, functions, conditionals, loops, objects and classes. Introduction to algorithms, modular software design, libraries, file input/output, debugging. Emphasis on applications in the life sciences.
Offered by: Computer Science

COMP 250
Intro to Computer Science
3 Credits
Offered in the:  Fall
 Winter
 Summer
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.
 Terms
 Instructors
 Michael Langer
 Giulia Alberini
3 credits, one of:

PHGY 311
Channels, Synapses & Hormones
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Indepth presentation of experimental results and hypotheses on cellular communication in the nervous system and the endocrine system.
Offered by: Physiology
 Fall
 3 hours of lectures per week; 13 hours optional lab/demonstration/tutorial arranged for a maximum of 3 afternoons per term
 Prerequisite: PHGY 209 or permission of the instructor.
 Terms
 Instructors
 Ellis Cooper, Per Jesper Sjostrom, Arjun Krishnaswamy

PHGY 314
Integrative Neuroscience
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: In depth presentation of experimental results and hypotheses underlying our current understanding of how single neurons and ensembles of neurons encode sensory information, generate movement, and control cognitive functions such as emotion, learning, and memory, during voluntary behaviours.
Offered by: Physiology
 Fall
 3 hours of lectures per week
 Prerequisites: PHGY 209
 Terms
 Instructors
 Maurice J Chacron, Christopher C Pack, Amir Shmuel, Melissa A Vollrath, Stephen Lomber, Mark Brandon, Suresh Krishna
3 credits, one of:

PHYS 413
Physical Basis of Physiology
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physics: Analytic and computer simulation techniques are used to examine the role of nonlinearities and time delays in determining the dynamic behaviour of physiological control systems and their relation to normal and pathophysiological states. Examples drawn from the control of respiration, cellular proliferation and differentiation, biochemical feedback networks, thermoregulatory mechanisms, and neural feedback.
Offered by: Physics
 Fall
 3 hours lectures
 Prerequisite: MATH 315, or MATH 325, and permission of the instructor
 Intended for Major or Honours students in Physics, Physiology, Physiology and Physics, or Mathematics and others with permission
 Terms
 This course is not scheduled for the 20212022 academic year
 Instructors
 There are no professors associated with this course for the 20212022 academic year

PHYS 519
Advanced Biophysics
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physics: An advanced biophysics course, with a special emphasis on stochastic and out of equilibrium physical processes in living matter.
Offered by: Physics

U1 

BIOL 219
Intro to Phys Mol & Cell Biol
4 Credits
Offered in the:  Fall
 Winter
 Summer
Biology (Sci): An introduction to molecular and cell biology from a physical perspective. Techniques and methodologies, both experimental and computational, are included in the presentation of each thematic module.
Offered by: Biology
 Prerequisite(s): BIOL 112; CHEM 110 and CHEM 120; MATH 140, MATH 141 and MATH 133; PHYS 131 and PHYS 142; or the equivalents of these courses.
 Corequisite(s): MATH 222 or equivalent
 Restriction(s): Not open to students who have taken or are taking ANAT 212, BIOC 212, BIOL 200, and BIOL 201, or BIEN 219. Only open to students in Bioengineering, Computer ScienceBiology, BiologyMathematics, BiologyQuantitative Biology, ChemistryBiophysical Chemistry, and PhysicsBiological Physics Options.
 This course is meant to prepare students for related 300level courses in Biology, Chemistry, Engineering and Physics.
 Terms
 Instructors
 Stephanie Weber, Jacalyn M Vogel, Adam G Hendricks

BIOL 309
Mathematical Models in Biology
3 Credits
Offered in the:  Fall
 Winter
 Summer
Biology (Sci): Application of finite difference and differential equations to problems in cell and developmental biology, ecology and physiology. Qualitative, quantitative and graphical techniques are used to analyze mathematical models and to compare theoretical predictions with experimental data.
Offered by: Biology

PHGY 209
Mammalian Physiology 1
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Physiology of body fluids, blood, body defense mechanisms, muscle, peripheral, central, and autonomic nervous systems.
Offered by: Physiology
 Terms
 Instructors
 Melissa A Vollrath, Ann Wechsler, David S Ragsdale, Alvin Shrier, Erik P Cook, Céline Aguer

PHGY 210
Mammalian Physiology 2
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Physiology of cardiovascular, respiratory, digestive, endocrine and renal systems.
Offered by: Physiology
 Terms
 Instructors
 Melissa A Vollrath, Tomoko Takano, Michael R Guevara, AnneMarie Lauzon, John H White, Céline Aguer

PHGY 212
Introductory Physiology Lab 1
1 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Exercises illustrating fundamental principles in physiology: Biological Signals Acquisitions, Blood, Immunology, Neurophysiology, Neuromuscular Physiology.
Offered by: Physiology
 (One 3hour lab and one 1hour lecture every second week.)
 Corequisite: PHGY 209.
 Restrictions: Required for Physiology students enrolled in PHGY 209. Open to BA &Sc. students and to others by permission of the instructor. Not open to students who have taken PHGY 212D1/D2.
 Note: For students in a Physiology program, PHGY 212 should be taken concurrently with PHGY 209.
 Terms
 Instructors
 Melissa A Vollrath, Mladen I Glavinovic, Judith N Mandl

PHGY 213
Introductory Physiology Lab 2
1 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Exercises illustrating fundamental principles in physiology: Central Nervous System, Cardiovascular, Respiration, Exercise Physiology, Molecular Endocrinology.
Offered by: Physiology
 (One 3hour lab and one 1hour lecture every second week.)
 Prerequisite: PHGY 212
 Corequisite: PHGY 210.
 Restrictions: Required for Physiology students enrolled in PHGY 210. Open to BA &Sc. students and to others by permission of the instructor. Not open to students who have taken PHGY 212D1/D2.
 Note: For students in a Physiology program, PHGY 213 should be taken concurrently with PHGY 210.
 Terms
 Instructors
 Michael R Guevara, Sheldon A Magder, John H White, Melissa A Vollrath

MATH 222
Calculus 3
3 Credits
Offered in the:  Fall
 Winter
 Summer
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
 Terms
 Instructors
 Patrick Allen, Allysa Lumley
 Sidney Trudeau

MATH 247
Honours Applied Linear Algebra
3 Credits
Offered in the:  Fall
 Winter
 Summer
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
OR 
MATH 223
Linear Algebra
3 Credits
Offered in the:  Fall
 Winter
 Summer
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
 Terms
 Instructors
 Djivede A Kelome
 Henri Darmon

MATH 248
Honours Vector Calculus
3 Credits
Offered in the:  Fall
 Winter
 Summer
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.
OR 
MATH 314
Advanced Calculus
3 Credits
Offered in the:  Fall
 Winter
 Summer
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
 Terms
 Instructors
 Charles Roth
 Jeremy Macdonald

MATH 325
Honours ODE's
3 Credits
Offered in the:  Fall
 Winter
 Summer
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
OR 
MATH 315
Ordinary Differential Eqns
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Offered by: Mathematics and Statistics
 Terms
 Instructors
 Courtney Paquette
 Rosalie BélangerRioux

U2 

PHGY 311
Channels, Synapses & Hormones
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Indepth presentation of experimental results and hypotheses on cellular communication in the nervous system and the endocrine system.
Offered by: Physiology
 Fall
 3 hours of lectures per week; 13 hours optional lab/demonstration/tutorial arranged for a maximum of 3 afternoons per term
 Prerequisite: PHGY 209 or permission of the instructor.
 Terms
 Instructors
 Ellis Cooper, Per Jesper Sjostrom, Arjun Krishnaswamy
OR 
PHGY 314
Integrative Neuroscience
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: In depth presentation of experimental results and hypotheses underlying our current understanding of how single neurons and ensembles of neurons encode sensory information, generate movement, and control cognitive functions such as emotion, learning, and memory, during voluntary behaviours.
Offered by: Physiology
 Fall
 3 hours of lectures per week
 Prerequisites: PHGY 209
 Terms
 Instructors
 Maurice J Chacron, Christopher C Pack, Amir Shmuel, Melissa A Vollrath, Stephen Lomber, Mark Brandon, Suresh Krishna

PHGY 312
Resp.,Renal,&Cardio Physiology
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Indepth presentation of experimental results and hypotheses underlying our current understanding of topics in renal, respiratory and cardiovascular functions explored beyond the introductory level.
Offered by: Physiology
 Winter
 3 hours of lectures per week; 13 hours optional lab/demonstration/tutorial arranged for a maximum of 3 Wednesday afternoons per term
 Prerequisites: PHGY 209 and PHGY 210 or equivalent, PHGY 311 or permission of the instructor
 Terms
 Instructors
 John W Hanrahan, James G Martin, Alvin Shrier, Sheldon A Magder

PHGY 313
Blood,GI,Imm.Syst.Physiol
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Indepth presentation of experimental results and hypotheses underlying our current understanding of topics in immunology, blood and fluids, and gastrointestinal physiology.
Offered by: Physiology
 Winter
 3 hours of lectures per week; 13 hours optional lab/demonstration/tutorial arranged for a maximum of 3 Wednesday afternoons per term
 Prerequisites: PHGY 209 and PHGY 210 or equivalent, PHGY 311 or permission of the instructor
 Terms
 Instructors
 Judith N Mandl, Volker Manfred Blank, Melissa A Vollrath, Jörg H Fritz, Daniela Quail

MATH 242
Analysis 1
3 Credits
Offered in the:  Fall
 Winter
 Summer
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.

MATH 243
Analysis 2
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.
Offered by: Mathematics and Statistics

MATH 323
Probability
3 Credits
Offered in the:  Fall
 Winter
 Summer
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
 Terms
 Instructors
 David A Stephens, Alia Sajjad
 Alia Sajjad, Tharshanna Nadarajah

MATH 326
Nonlinear Dynamics and Chaos
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, PoincareBendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Offered by: Mathematics and Statistics

MATH 437
Mathematical Meth in Biology
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): The formulation and treatment of realistic mathematical models describing biological phenomena through qualitative and quantitative mathematical techniques (e.g. local and global stability theory, bifurcation analysis and phase plane analysis) and numerical simulation. Concrete and detailed examples will be drawn from molecular and cellular biology and mammalian physiology.
Offered by: Mathematics and Statistics
OR
MATH 537
Honours Math Models in Biology
4 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): The formulation and treatment of realistic mathematical models describing biological phenomena through such qualitative and quantitative mathematical techniques as local and global stability theory, bifurcation analysis, phase plane analysis, and numerical simulation. Concrete and detailed examples will be drawn from molecular, cellular and population biology and mammalian physiology.
Offered by: Mathematics and Statistics
(honours students) 
COMP 204
Comp. Programming for Life Sci
3 Credits
Offered in the:  Fall
 Winter
 Summer
Computer Science (Sci): Computer Science (Sci): Computer programming in a high level language: variables, expressions, types, functions, conditionals, loops, objects and classes. Introduction to algorithms, modular software design, libraries, file input/output, debugging. Emphasis on applications in the life sciences.
Offered by: Computer Science
OR 
COMP 250
Intro to Computer Science
3 Credits
Offered in the:  Fall
 Winter
 Summer
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.
 Terms
 Instructors
 Michael Langer
 Giulia Alberini

BIOL 395
Quantitative Biology Seminar
1 Credits
Offered in the:  Fall
 Winter
 Summer
Biology (Sci): Overview of concepts and current research in quantitative biology; theoretical ecology and evolution, computational biology, and physical biology.
Offered by: Biology
 Fall
 Prerequisites: BIOL 219; or BIOL 200 plus BIOL 201 or ANAT 212 or BIOC 212; CHEM 212; COMP 202 or COMP 204 or COMP 250; MATH 222; or permission of instructor.
 Restriction: Only open to U2 students in the following programs: B.Sc.; Major and Honours in Biology; Quantitative Biology, B.Sc.; Major and Honours Computer Science and Biology, B.Sc.; Major Biology and Mathematics, B.Sc.; Major Physiology and Mathematics, B.Sc.; Major Physiology and Physics, B.Sc.; Major and Honours Chemistry; Biophysical Chemistry, and B.Sc.; Major and Honours Physics; Biological Physics.
 Terms
 Instructors
 Arnold L Hayer, Paul W Wiseman, Frederic Guichard, Gregor F Fussmann, Paul Francois, Claudia Kleinman, Marlene H Oeffinger, Allen J Ehrlicher, Michael Hendricks, Khanh Huy Bui

U3 

MATH 317
Numerical Analysis
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Offered by: Mathematics and Statistics

MATH 319
Intro to Partial Diff Equas
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, SturmLiouville theory, Fourier series, boundary and initial value problems.
Offered by: Mathematics and Statistics

MATH 324
Statistics
3 Credits
Offered in the:  Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Offered by: Mathematics and Statistics
 Fall and Winter
 Prerequisite: MATH 323 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 357
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.

PHGY 461D1
Experimental Physiology
4.5 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: Individual project work under the supervision of Departmental Staff members.
Offered by: Physiology
 Fall
 Restrictions: Departmental approval required. This course is a requirement for U3 students in the Honours Physiology program, the Major Program in Physiology and Mathematics, and the Major program in Physiology and Physics, and is open to a limited number of other U3 Physiology students.
 Students must register for both PHGY 461D1 and PHGY 461D2.
 No credit will be given for this course unless both PHGY 461D1 and PHGY 461D2 are successfully completed in consecutive terms
 Terms
 Instructors
 John Orlowski, Ann Wechsler, Melissa A Vollrath

PHGY 461D2
Experimental Physiology
4.5 Credits
Offered in the:  Fall
 Winter
 Summer
Physiology: See PHGY 461D1 for course description.
Offered by: Physiology
 Winter
 Prerequisite: PHGY 461D1
 No credit will be given for this course unless both PHGY 461D1 and PHGY 461D2 are successfully completed in consecutive terms
 Terms
 Instructors
 John Orlowski, Ann Wechsler, Melissa A Vollrath

BMDE 519
Biomedical Signals & Systems
3 Credits
Offered in the:  Fall
 Winter
 Summer
Biomedical Engineering: An introduction to the theoretical framework, experimental techniques and analysis procedures available for the quantitative analysis of physiological systems and signals. Lectures plus laboratory work using the Biomedical Engineering computer system. Topics include: amplitude and frequency structure of signals, filtering, sampling, correlation functions, time and frequencydomain descriptions of systems.
Offered by: Biomedical Engineering
 (306)
 Prerequisites: Satisfactory standing in U3 Honours Physiology; or U3 Major in PhysicsPhysiology; or U3 Major PhysiologyMathematics; or permission of instructor

PHYS 413
Physical Basis of Physiology
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physics: Analytic and computer simulation techniques are used to examine the role of nonlinearities and time delays in determining the dynamic behaviour of physiological control systems and their relation to normal and pathophysiological states. Examples drawn from the control of respiration, cellular proliferation and differentiation, biochemical feedback networks, thermoregulatory mechanisms, and neural feedback.
Offered by: Physics
 Fall
 3 hours lectures
 Prerequisite: MATH 315, or MATH 325, and permission of the instructor
 Intended for Major or Honours students in Physics, Physiology, Physiology and Physics, or Mathematics and others with permission
 Terms
 This course is not scheduled for the 2021 academic year
 Instructors
 There are no professors associated with this course for the 2021 academic year
OR 
PHYS 519
Advanced Biophysics
3 Credits
Offered in the:  Fall
 Winter
 Summer
Physics: An advanced biophysics course, with a special emphasis on stochastic and out of equilibrium physical processes in living matter.
Offered by: Physics

Total Credits: 79 
