Physiology and Mathematics
This program is geared towards students who have a strong interest in both physiology and mathematics, and is well suited to those who wish to pursue careers in the biological or biomedical sciences. This specialized interdisciplinary program lets students explore more than one discipline in some depth, bringing different perspectives to the study of Physiology.
DETAILED PROGRAM OUTLINE(S):
Program Requirement:
Required Courses (70 credits)
BioPhysical Sciences Core

BIOL 219 Intro to Phys Mol & Cell Biol 4 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Fall 2019
 Instructors
 Adam G Hendricks, Jacalyn M Vogel, Gary J Brouhard, Alanna Watt

BIOL 395 Quantitative Biology Seminar 1 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Fall 2019
 Instructors
 Arnold L Hayer

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
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 Fall 2019
 Winter 2020
 Instructors
 Jeremy D Macdonald, Broderick J Causley
 Jérôme Fortier

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
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 Fall 2019
 Winter 2020
 Instructors
 Djivede A Kelome
 Jeremy D Macdonald

MATH 247 Honours Applied Linear Algebra 3 Credits*
 Fall
 Winter
 Summer
Offered in the: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
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 Winter 2020
 Instructors
 Tim Hoheisel

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.
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 Fall 2019
 Winter 2020
 Instructors
 JeanChristophe Nave
 Rosalie BélangerRioux

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 2019
 Winter 2020
 Instructors
 Shomoita Alam, Jose Andres Correa
 David B Wolfson, Djivede A Kelome

MATH 325 Honours ODE's 3 Credits**
 Fall
 Winter
 Summer
Offered in the: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
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 Winter 2020
 Instructors
 JeanPhilippe Lessard
* 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
 Fall
 Winter
 Summer
Offered in the: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
 Fall
 3 hours lecture
 Prerequisite: one year of calculus. An additional course in calculus is recommended
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 Fall 2019
 Instructors
 Gil Bub

BMDE 519 Biomedical Signals & Systems 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
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 Fall 2019
 Instructors
 Robert E Kearney

MATH 242 Analysis 1 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Fall 2019
 Instructors
 Jerome Vetois

MATH 243 Analysis 2 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
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 Winter 2020
 Instructors
 Axel W Hundemer

MATH 248 Honours Vector Calculus 3 Credits***
 Fall
 Winter
 Summer
Offered in the: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.
 Symbols:
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 Fall 2019
 Instructors
 Gantumur Tsogtgerel

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 2019
 Winter 2020
 Instructors
 Charles Roth

MATH 317 Numerical Analysis 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 Fall
 Prerequisites: MATH 315 or MATH 325 or MATH 263, and COMP 202 or permission of instructor.
 Restrictions: Not open to students who have taken COMP 350
 Symbols:
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 Fall 2019
 Instructors
 Peter Bartello

MATH 319 Intro to Partial Diff Equas 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 Winter
 Prerequisites: MATH 223 or MATH 236, MATH 314 or equivalent, MATH 315
 Prerequisites: MATH 223 or MATH 236, MATH 314, MATH 315
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 Winter 2020
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 324 Statistics 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Fall 2019
 Winter 2020
 Instructors
 Masoud AsgharianDastenaei

MATH 326 Nonlinear Dynamics and Chaos 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 Fall
 Prerequisites: MATH 222, MATH 223
 Restriction: Not open to students who have taken or are taking MATH 376
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 Fall 2019
 Instructors
 Antony Raymond Humphries

MATH 437 Mathematical Meth in Biology 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 This course is offered in the winter semester.
 Prerequisite(s): MATH 315 or MATH 325, and MATH 326 or MATH 376, and COMP 202 or COMP 204 or COMP 208 or equivalent.
 Prerequisites: MATH 315 or MATH 325, and MATH 323 or MATH 356, a CEGEP or higher level computer programming course
 Corequisite: MATH 326 or MATH 376
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 Winter 2020
 Instructors
 Anmar Khadra

PHGY 209 Mammalian Physiology 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physiology: Physiology of body fluids, blood, body defense mechanisms, muscle, peripheral, central, and autonomic nervous systems.
Offered by: Physiology
 Fall
 3 hours lectures weekly
 Prerequisites: BIOL 112, CHEM 110, CHEM 120, PHYS 101 or PHYS 131, and PHYS 102 or PHYS 142. Pre/corequisites: BIOL 200, CHEM 212 or equivalent.
 Restriction: Not open to students who have taken PHGY 211 or students who are taking and who have taken NSCI 200.
 Restriction: For students in the Faculty of Science, and other students by permission of the instructor
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 Fall 2019
 Instructors
 Melissa A Vollrath, Phil Gold, Ann Wechsler, David S Ragsdale, Alvin Shrier, Erik Cook

PHGY 210 Mammalian Physiology 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physiology: Physiology of cardiovascular, respiratory, digestive, endocrine and renal systems.
Offered by: Physiology
 Winter
 3 hours lectures weekly
 Prerequisites: BIOL 112, CHEM 110, CHEM 120, PHYS 101 or PHYS 131, and PHYS 102 or PHYS 142. Pre/corequisite: BIOL 200, BIOL 201, BIOC 212, CHEM 212 or equivalent.
 Restriction: For students in the Faculty of Science, and other students by permission of the instructor
 Although PHGY 210 may be taken without the prior passing of PHGY 209, students should note that they may have some initial difficulties because of lack of familiarity with some basic concepts introduced in PHGY 209
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 Winter 2020
 Instructors
 Melissa A Vollrath, Ann Wechsler, Tomoko Takano, Michael R Guevara, AnneMarie Lauzon, John H White

PHGY 212 Introductory Physiology Lab 1 1 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Fall 2019
 Instructors
 Melissa A Vollrath, Mladen I Glavinovic, Judith N Mandl

PHGY 213 Introductory Physiology Lab 2 1 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Winter 2020
 Instructors
 Michael R Guevara, Jacopo Mortola, Sheldon A Magder, John H White, Melissa Vollrath

PHGY 312 Resp.,Renal,&Cardio Physiology 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
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 Winter 2020
 Instructors
 John W Hanrahan, Jacopo Mortola, Alvin Shrier, Sheldon A Magder

PHGY 313 Blood,GI,Imm.Syst.Physiol 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
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 Winter 2020
 Instructors
 Judith N Mandl, Volker Manfred Blank, Russell G Jones, Maia Kokoeva, Jörg Fritz, Anastasia Nijnik

PHGY 461D1 Experimental Physiology 4.5 Credits
 Fall
 Winter
 Summer
Offered in the: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
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 Fall 2019
 Instructors
 Ann Wechsler, Linda H Cooper, John Orlowski, Melissa Vollrath

PHGY 461D2 Experimental Physiology 4.5 Credits
 Fall
 Winter
 Summer
Offered in the: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
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 Winter 2020
 Instructors
 Ann Wechsler, John Orlowski, 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
 Fall
 Winter
 Summer
Offered in the: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
 Prerequisite(s): BIOL 112. CEGEP level mathematics course.
 Restriction(s): Only one of COMP 204, COMP 202 and COMP 208 can be taken for credit.
 COMP 204 cannot be taken for credit with or after COMP 250, COMP 206, COMP 208, or COMP 364.
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 Fall 2019
 Winter 2020
 Instructors
 Mathieu Blanchette
 Yue Li

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.
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 Fall 2019
 Winter 2020
 Instructors
 Michael Langer, Giulia Alberini
 Giulia Alberini
3 credits, one of:

PHGY 311 Channels, Synapses & Hormones 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
 Symbols:
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 Fall 2019
 Instructors
 Ellis Cooper, Per Jesper Sjostrom, Arjun Krishnaswamy, Reza Sharif Naeini

PHGY 314 Integrative Neuroscience 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
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 Fall 2019
 Instructors
 Maurice J Chacron, Reza Sharif Naeini, Erik P Cook, Christopher Pack, Amir Shmuel, Melissa Vollrath, Mark Brandon
3 credits, one of:

PHYS 413 Physical Basis of Physiology 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 Symbols:
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 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

PHYS 519 Advanced Biophysics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: An advanced biophysics course, with a special emphasis on stochastic and out of equilibrium physical processes in living matter.
Offered by: Physics
 Prerequisites: (PHYS 329 or PHYS 333 or PHYS 362 or MATH 437) and (PHYS 340 or PHYS 350), or permission of the instructor.
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 Winter 2020
 Instructors
 Paul Francois