Program Requirements
The physiology and mathematics major program is an interdisciplinary program that integrates the world of physiology with mathematics. It explores the relationship between Physiological systems and the quantitative principles underpinning them. Physiology covers topics from cellular function to organ systems and behaviour. Mathematics delves into the basis of pure and applied mathematics with a focus on developing analytical, computational and problem-solving skills with an emphasis on nonlinear dynamics.
Required Courses (70 credits)
Bio-Physical Sciences Core
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BIOL 219 Introduction to Physical
Molecular and Cell Biology (4 credits)
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 2024
Instructors: Weber, Stephanie; Watt, Alanna; Reyes Lamothe, Rodrigo; Hendricks, Adam (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.
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BIOL 395 Quantitative Biology Seminar (1 credit)
Overview
Biology (Sci) : Overview of concepts and current research in quantitative biology; theoretical ecology and evolution, computational biology, and physical biology.
Terms: Fall 2024
Instructors: Fussmann, Gregor; Hendry, Andrew; Guichard, Frederic; Schmidt, Alexandra; Oeffinger, Marlene; Hendricks, Michael; Bui, Khanh Huy; Weber, Stephanie; Hayer, Arnold; Gerhold, Abigail (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.
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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 2024, Winter 2025, Summer 2025
Instructors: Pym, Brent; Tageddine, Damien (Fall) Mazakian, Hovsep (Winter)
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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 2024, Winter 2025
Instructors: Elaidi, Shereen; Bellemare, Hugues (Fall) Macdonald, Jeremy (Winter)
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MATH 247 Honours Applied Linear Algebra (3 credits) *
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 2025
Instructors: Hoheisel, Tim (Winter)
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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 2024, Winter 2025
Instructors: Paquette, Courtney (Fall) Kamran, Niky (Winter)
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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 2024, Winter 2025, Summer 2025
Instructors: Sajjad, Alia (Fall) Nadarajah, Tharshanna (Winter)
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MATH 325 Honours Ordinary Differential Equations (3 credits) **
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 2025
Instructors: Lessard, Jean-Philippe (Winter)
* Students may take either MATH 223 or MATH 247.
** Students may take either MATH 315 or MATH 325.
Physiology and Mathematics Core
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BIOL 309 Mathematical Models in Biology (3 credits)
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 2024
Instructors: Bub, Gil; Guichard, Frederic (Fall)
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BMDE 519 Biomedical Signals and Systems (3 credits)
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 2024
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
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MATH 242 Analysis 1 (3 credits)
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 2024
Instructors: Jakobson, Dmitry (Fall)
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MATH 243 Analysis 2 (3 credits)
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 2025
Instructors: Hundemer, Axel (Winter)
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MATH 248 Honours Vector Calculus (3 credits) ***
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 2024
Instructors: Mutanguha, Jean Pierre (Fall)
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MATH 314 Advanced Calculus (3 credits) ***
Overview
Mathematics & Statistics (Sci) : Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.
Terms: Fall 2024, Winter 2025
Instructors: Martine, Gabriel (Fall) Borthwick, Jack Anthony (Winter)
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MATH 317 Numerical Analysis (3 credits)
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 2024
Instructors: Duchesne, Gabriel William (Fall)
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MATH 319 Partial Differential
Equations
(3 credits)
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 2025
Instructors: Lin, Jessica (Winter)
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MATH 324 Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Terms: Fall 2024, Winter 2025
Instructors: Nadarajah, Tharshanna (Fall) Asgharian, Masoud (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.
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MATH 326 Nonlinear Dynamics and Chaos (3 credits)
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 2024
Instructors: Humphries, Tony (Fall)
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MATH 437 Mathematical Methods in Biology (3 credits)
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 2025
Instructors: Khadra, Anmar (Winter)
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PHGY 209 Mammalian Physiology 1 (3 credits)
Overview
Physiology : Physiology of body fluids, blood, body defense mechanisms, muscle, peripheral, central, and autonomic nervous systems.
Terms: Fall 2024
Instructors: Vollrath, Melissa; Ragsdale, David S; Shrier, Alvin; Cook, Erik; Aguer, C茅line (Fall)
Fall
3 hours lectures weekly
Prerequisites: BIOL 112, CHEM 110, CHEM 120, PHYS 101 or PHYS 131, and PHYS 102 or PHYS 142. Pre-/co-requisites: 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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PHGY 210 Mammalian Physiology 2 (3 credits)
Overview
Physiology : Physiology of cardiovascular, respiratory, digestive, endocrine and renal systems.
Terms: Winter 2025
Instructors: Vollrath, Melissa; Takano, Tomoko; Lauzon, Anne-Marie; White, John H; Aguer, C茅line (Winter)
Winter
3 hours lectures weekly
Prerequisites: BIOL 112, CHEM 110, CHEM 120, PHYS 101 or PHYS 131, and PHYS 102 or PHYS 142. Pre-/co-requisite: 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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PHGY 212 Introductory Physiology Laboratory 1 (1 credit)
Overview
Physiology : Exercises illustrating fundamental principles in physiology: Biological Signals Acquisitions, Blood, Immunology, Neurophysiology, Neuromuscular Physiology.
Terms: Fall 2024
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.
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PHGY 213 Introductory Physiology Laboratory 2 (1 credit)
Overview
Physiology : Exercises illustrating fundamental principles in physiology: Central Nervous System, Cardiovascular, Respiration, Exercise Physiology, Molecular Endocrinology.
Terms: Winter 2025
Instructors: Guevara, Michael R; Magder, Sheldon A; White, John H; Vollrath, Melissa (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.
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PHGY 312 Respiratory, Renal, and Cardiovascular Physiology (3 credits)
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 2025
Instructors: Hanrahan, John W; Martin, James G; Shrier, Alvin; Magder, Sheldon A (Winter)
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PHGY 313 Blood, Gastrointestinal, and Immune Systems Physiology (3 credits)
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 2025
Instructors: Mandl, Judith; Blank, Volker Manfred; Vollrath, Melissa; Fritz, J枚rg; Quail, Daniela (Winter)
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PHGY 461D1 Experimental Physiology (4.5 credits)
Overview
Physiology : Individual project work under the supervision of Departmental Staff members.
Terms: Fall 2024
Instructors: 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
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PHGY 461D2 Experimental Physiology (4.5 credits)
Overview
Physiology : See PHGY 461D1 for course description.
Terms: Winter 2025
Instructors: There are no professors associated with this course for the 2024-2025 academic year.
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 from:
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COMP 204 Computer Programming for Life Sciences (3 credits)
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 2024, Winter 2025
Instructors: Becerra, David (Fall) Siddiqi, Kaleem (Winter)
Co-requisite: BIOL 112
Restrictions: Not open to students who have taken or are taking COMP 202, COMP 208, or GEOG 333; not open to students who have taken or are taking COMP 206 or COMP 250.
To take COMP 204, students should have a solid understanding of pre-calculus fundamentals such as polynomial, trigonometric, exponential, and logarithmic functions.
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COMP 250 Introduction to Computer Science (3 credits)
Overview
Computer Science (Sci) : Mathematical tools (binary numbers, induction,recurrence relations, asymptotic complexity,establishing correctness of programs). Datastructures (arrays, stacks, queues, linked lists,trees, binary trees, binary search trees, heaps,hash tables). Recursive and non-recursivealgorithms (searching and sorting, tree andgraph traversal). Abstract data types. Objectoriented programming in Java (classes andobjects, interfaces, inheritance). Selected topics.
Terms: Fall 2024, Winter 2025
Instructors: Alberini, Giulia (Fall) Alberini, Giulia (Winter)
3 credits from:
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PHGY 311 Channels, Synapses and Hormones (3 credits)
Overview
Physiology : In-depth presentation of experimental results and hypotheses on cellular communication in the nervous system and the endocrine system.
Terms: Fall 2024
Instructors: Cooper, Ellis; Sj枚str枚m, 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.
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PHGY 314 Integrative Neuroscience (3 credits)
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 2024
Instructors: Chacron, Maurice; Pack, Christopher; Shmuel, Amir; Vollrath, Melissa; Lomber, Stephen; Brandon, Mark; Bashivan, Pouya (Fall)
Fall
3 hours of lectures per week
Prerequisites: PHGY 209
3 credits from:
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PHYS 413 Physical Basis of Physiology (3 credits)
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 2024-2025 academic year.
Instructors: There are no professors associated with this course for the 2024-2025 academic year.
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PHYS 519 Advanced Biophysics (3 credits)
Overview
Physics : An advanced biophysics course, with a special emphasis on stochastic and out of equilibrium physical processes in living matter.
Terms: Winter 2025
Instructors: Wiseman, Paul (Winter)
