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Major Physiology and Mathematics (79 credits)

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Offered by: Physiology     Degree: Bachelor of Science

Program Requirements

Required Courses (70 credits)

Bio-Physical Sciences Core

  • BIOL 219 Introduction to Physical Molecular and Cell Biology (4 credits)

    Offered by: Biology (Faculty of Science)

    Overview

    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.

    Terms: Fall 2019

    Instructors: Hendricks, Adam; Vogel, Jacalyn; Brouhard, Gary; Watt, Alanna (Fall)

    • 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 Science-Biology, Biology-Mathematics, Biology-Quantitative Biology, Chemistry-Biophysical Chemistry, and Physics-Biological Physics Options.

    • This course is meant to prepare students for related 300-level courses in Biology, Chemistry, Engineering and Physics.

  • BIOL 395 Quantitative Biology Seminar (1 credit)

    Offered by: Biology (Faculty of Science)

    Overview

    Biology (Sci) : Overview of concepts and current research in quantitative biology; theoretical ecology and evolution, computational biology, and physical biology.

    Terms: Fall 2019

    Instructors: Hayer, Arnold; Wiseman, Paul; Guichard, Frederic; Michnick, Stephen W.; Brouhard, Gary; Oeffinger, Marlene; Ehrlicher, Allen; Xia, Yu; Hendricks, Adam; Bui, Khanh Huy (Fall)

    • 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.

  • MATH 222 Calculus 3 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 2019, Winter 2020, Summer 2020

    Instructors: Macdonald, Jeremy; Causley, Broderick (Fall) Fortier, J茅r么me (Winter) Fortier, J茅r么me (Summer)

  • MATH 223 Linear Algebra (3 credits) *

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 2019, Winter 2020

    Instructors: Kelome, Djivede (Fall) Macdonald, Jeremy (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 247 Honours Applied Linear Algebra (3 credits) *

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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.

    Terms: Winter 2020

    Instructors: Hoheisel, Tim (Winter)

    • 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 Equations (3 credits) **

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.

    Terms: Fall 2019, Winter 2020, Summer 2020

    Instructors: Nave, Jean-Christophe (Fall) B茅langer-Rioux, Rosalie (Winter) Roth, Charles (Summer)

    • Prerequisite: MATH 222.

    • Corequisite: MATH 133.

    • Restriction: Not open to students who have taken or are taking MATH 325.

  • MATH 323 Probability (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 2019, Winter 2020, Summer 2020

    Instructors: Correa, Jose Andres; Alam, Shomoita (Fall) Kelome, Djivede; Wolfson, David B (Winter) Kelome, Djivede (Summer)

    • 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

  • MATH 325 Honours Ordinary Differential Equations (3 credits) **

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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.

    Terms: Winter 2020

    Instructors: Lessard, Jean-Philippe (Winter)

    • Fall and Winter

    • (3-0-6)

    • 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 by: Biology (Faculty of Science)

    Overview

    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.

    Terms: Fall 2019

    Instructors: Bub, Gil (Fall)

    • Fall

    • 3 hours lecture

    • Prerequisite: one year of calculus. An additional course in calculus is recommended

  • BMDE 519 Biomedical Signals and Systems (3 credits)

    Offered by: Biomedical Engineering (Faculty of Engineering)

    Overview

    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 frequency-domain descriptions of systems.

    Terms: Fall 2019

    Instructors: Kearney, Robert E (Fall)

    • (3-0-6)

    • Prerequisites: Satisfactory standing in U3 Honours Physiology; or U3 Major in Physics-Physiology; or U3 Major Physiology-Mathematics; or permission of instructor

  • MATH 242 Analysis 1 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.

    Terms: Fall 2019

    Instructors: Vetois, Jerome (Fall)

    • 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 by: Mathematics and Statistics (Faculty of Science)

    Overview

    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.

    Terms: Winter 2020

    Instructors: Hundemer, Axel W (Winter)

  • MATH 248 Honours Vector Calculus (3 credits) ***

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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.

    Terms: Fall 2019

    Instructors: Tsogtgerel, Gantumur (Fall)

    • 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 by: Mathematics and Statistics (Faculty of Science)

    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 2019, Winter 2020

    Instructors: Roth, Charles (Fall) McGregor, Geoffrey; Hurtubise, Jacques Claude (Winter)

  • MATH 317 Numerical Analysis (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.

    Terms: Fall 2019

    Instructors: Bartello, Peter (Fall)

  • MATH 319 Introduction to Partial Differential Equations (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems.

    Terms: Winter 2020

    Instructors: Laborde, Maxime; Hurtubise, Jacques Claude (Winter)

  • MATH 324 Statistics (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.

    Terms: Fall 2019, Winter 2020

    Instructors: Asgharian-Dastenaei, Masoud (Fall) Luo, Yu; Hurtubise, Jacques Claude (Winter)

    • 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 by: Mathematics and Statistics (Faculty of Science)

    Overview

    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, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.

    Terms: Fall 2019

    Instructors: Humphries, Antony Raymond (Fall)

  • MATH 437 Mathematical Methods in Biology (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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.

    Terms: Winter 2020

    Instructors: Khadra, Anmar (Winter)

  • PHGY 209 Mammalian Physiology 1 (3 credits)

    Offered by: Physiology (Faculty of Science)

    Overview

    Physiology : Physiology of body fluids, blood, body defense mechanisms, muscle, peripheral, central, and autonomic nervous systems.

    Terms: Fall 2019

    Instructors: Vollrath, Melissa; Wechsler, Ann; Ragsdale, David S; Shrier, Alvin; Cook, Erik (Fall)

  • PHGY 210 Mammalian Physiology 2 (3 credits)

    Offered by: Physiology (Faculty of Science)

    Overview

    Physiology : Physiology of cardiovascular, respiratory, digestive, endocrine and renal systems.

    Terms: Winter 2020

    Instructors: Vollrath, Melissa; Campeau, Lysanne; Takano, Tomoko; Guevara, Michael R; Hanrahan, John W; Lauzon, Anne-Marie; White, John H (Winter)

  • PHGY 212 Introductory Physiology Laboratory 1 (1 credit)

    Offered by: Physiology (Faculty of Science)

    Overview

    Physiology : Exercises illustrating fundamental principles in physiology: Biological Signals Acquisitions, Blood, Immunology, Neurophysiology, Neuromuscular Physiology.

    Terms: Fall 2019

    Instructors: Vollrath, Melissa; Glavinovic, Mladen I; Mandl, Judith (Fall)

    • (One 3-hour lab and one 1-hour 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.

  • PHGY 213 Introductory Physiology Laboratory 2 (1 credit)

    Offered by: Physiology (Faculty of Science)

    Overview

    Physiology : Exercises illustrating fundamental principles in physiology: Central Nervous System, Cardiovascular, Respiration, Exercise Physiology, Molecular Endocrinology.

    Terms: Winter 2020

    Instructors: Guevara, Michael R; Mortola, Jacopo; Magder, Sheldon A; White, John H; Vollrath, Melissa; Smith, Benjamin (Winter)

    • (One 3-hour lab and one 1-hour 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.

  • PHGY 312 Respiratory, Renal, & Cardiovascular Physiology (3 credits)

    Offered by: Physiology (Faculty of Science)

    Overview

    Physiology : In-depth presentation of experimental results and hypotheses underlying our current understanding of topics in renal, respiratory and cardiovascular functions explored beyond the introductory level.

    Terms: Winter 2020

    Instructors: Hanrahan, John W; Martin, James G; Shrier, Alvin; Magder, Sheldon A (Winter)

    • Winter

    • 3 hours of lectures per week; 1-3 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

  • PHGY 313 Blood, Gastrointestinal, & Immune Systems Physiology (3 credits)

    Offered by: Physiology (Faculty of Science)

    Overview

    Physiology : In-depth presentation of experimental results and hypotheses underlying our current understanding of topics in immunology, blood and fluids, and gastrointestinal physiology.

    Terms: Winter 2020

    Instructors: Mandl, Judith; Mercier, Francois; Blank, Volker Manfred; Orthwein, Alexandre; Kokoeva, Maia; Vollrath, Melissa; Fritz, J枚rg; Quail, Daniela (Winter)

    • Winter

    • 3 hours of lectures per week; 1-3 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

  • PHGY 461D1 Experimental Physiology (4.5 credits)

    Offered by: Physiology (Faculty of Science)

    Overview

    Physiology : Individual project work under the supervision of Departmental Staff members.

    Terms: Fall 2019

    Instructors: Wechsler, Ann; Cooper, Linda H; Orlowski, John; Vollrath, Melissa (Fall)

    • 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

  • PHGY 461D2 Experimental Physiology (4.5 credits)

    Offered by: Physiology (Faculty of Science)

    Overview

    Physiology : See PHGY 461D1 for course description.

    Terms: Winter 2020

    Instructors: Wechsler, Ann; Orlowski, John; Vollrath, Melissa (Winter)

    • 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

*** Students may take either MATH 248 or MATH 314.

Complementary Courses (9 credits)

3 credits, one of:

  • COMP 204 Computer Programming for Life Sciences (3 credits)

    Offered by: Computer Science (Faculty of Science)

    Overview

    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.

    Terms: Fall 2019, Winter 2020, Summer 2020

    Instructors: Blanchette, Mathieu (Fall) Li, Yue (Winter) Blanchette, Mathieu (Summer)

  • COMP 250 Introduction to Computer Science (3 credits)

    Offered by: Computer Science (Faculty of Science)

    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 non-recursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.

    Terms: Fall 2019, Winter 2020

    Instructors: Langer, Michael; Alberini, Giulia (Fall) Alberini, Giulia; Sarrazin Gendron, Roman (Winter)

    • 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.

3 credits, one of:

  • PHGY 311 Channels, Synapses and Hormones (3 credits)

    Offered by: Physiology (Faculty of Science)

    Overview

    Physiology : In-depth presentation of experimental results and hypotheses on cellular communication in the nervous system and the endocrine system.

    Terms: Fall 2019

    Instructors: Cooper, Ellis; Sjostrom, Per Jesper; Krishnaswamy, Arjun; Sharif Naeini, Reza (Fall)

    • Fall

    • 3 hours of lectures per week; 1-3 hours optional lab/demonstration/tutorial arranged for a maximum of 3 afternoons per term

    • Prerequisite: PHGY 209 or permission of the instructor.

  • PHGY 314 Integrative Neuroscience (3 credits)

    Offered by: Physiology (Faculty of Science)

    Overview

    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.

    Terms: Fall 2019

    Instructors: Chacron, Maurice; Sharif Naeini, Reza; Cook, Erik; Pack, Christopher; Shmuel, Amir; Vollrath, Melissa; Brandon, Mark (Fall)

    • Fall

    • 3 hours of lectures per week

    • Prerequisites: PHGY 209

3 credits, one of:

  • PHYS 413 Physical Basis of Physiology (3 credits)

    Offered by: Physics (Faculty of Science)

    Overview

    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.

    Terms: This course is not scheduled for the 2019-2020 academic year.

    Instructors: There are no professors associated with this course for the 2019-2020 academic year.

    • 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

  • PHYS 519 Advanced Biophysics (3 credits)

    Offered by: Physics (Faculty of Science)

    Overview

    Physics : An advanced biophysics course, with a special emphasis on stochastic and out of equilibrium physical processes in living matter.

    Terms: Winter 2020

    Instructors: Francois, Paul (Winter)

Faculty of Science—2019-2020 (last updated Aug. 20, 2019) (disclaimer)
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