REQUIED COURSES |
Bachelor of Science (B.Sc.) - Major Physiology and Mathematics (79 Credits)
Program Requirement: 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-
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 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.
- Terms
- Instructors
- Stephanie Weber, Alanna J Watt, Rodrigo Reyes Lamothe, 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
- Gregor F Fussmann, Andrew Hendry, Frederic Guichard, Alexandra Schmidt, Marlene H Oeffinger, Michael Hendricks, Khanh Huy Bui, Stephanie Weber, Arnold L Hayer, Abigail Gerhold
-
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
- Fall 2024
- Winter 2025
- Summer 2025
- Instructors
- Brent Pym, Damien Tageddine
- Hovsep Mazakian
-
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
- Terms
- Instructors
- Shereen Elaidi, Hugues Bellemare
- Jeremy Macdonald
-
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
- Niky Kamran
-
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
- Fall 2024
- Winter 2025
- Summer 2025
- Instructors
- 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
- (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 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
- Terms
- Instructors
- Gil Bub, Frederic Guichard
-
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 frequency-domain descriptions of systems.
Offered by: Biomedical Engineering
- (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 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
- Gabriel Martine
- Jack Anthony Borthwick
-
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
Partial Differential Equations
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, Sturm-Liouville 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.
- Terms
- Instructors
- Tharshanna Nadarajah
- Masoud Asgharian
-
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, Poincare-Bendixson 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, 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, Anne-Marie 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 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.
- 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 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.
- 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: 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.
Offered by: Physiology
- 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
- 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: In-depth 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; 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
- 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, 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
- There are no professors associated with this course for the 2024-2025 academic year
*** Students may take either MATH 248 or MATH 314.
Complementary Courses (9 credits)3 credits from:
-
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
- 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.
- Terms
- Instructors
- David C Becerra
- Kaleem Siddiqi
-
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). 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.
Offered by: Computer Science
- Terms
- Instructors
- Giulia Alberini
- Giulia Alberini
3 credits from:
-
PHGY 311
Channels, Synapses & Hormones
3 Credits
Offered in the: - Fall
- Winter
- Summer
Physiology: In-depth 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; 1-3 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, Jesper Sjöström, Arjun Krishnaswamy, Reza Sharif Naeini
-
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, Pouya Bashivan
3 credits from:
-
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 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 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 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.
- Terms
- Instructors
- Stephanie Weber, Alanna J Watt, Rodrigo Reyes Lamothe, 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
- Terms
- Instructors
- Gil Bub, Frederic Guichard
|
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, 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, Anne-Marie 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 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.
- 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 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.
- 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
- Fall 2024
- Winter 2025
- Summer 2025
- Instructors
- Brent Pym, Damien Tageddine
- Hovsep Mazakian
|
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
ÌýOR |
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
- Terms
- Instructors
- Shereen Elaidi, Hugues Bellemare
- Jeremy Macdonald
|
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.
ÌýOR |
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
- Gabriel Martine
- Jack Anthony Borthwick
|
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
- (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
ÌýOR |
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
- Niky Kamran
|
U2 |
PHGY 311
Channels, Synapses & Hormones
3 Credits
Offered in the: - Fall
- Winter
- Summer
Physiology: In-depth 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; 1-3 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, Jesper Sjöström, Arjun Krishnaswamy, Reza Sharif Naeini
ÌýOR |
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, Pouya Bashivan
|
PHGY 312
Resp.,Renal,&Cardio Physiology
3 Credits
Offered in the: - Fall
- Winter
- Summer
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.
Offered by: Physiology
- 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
- Terms
- Instructors
- John W Hanrahan, James G Martin, Alvin Shrier, Sheldon A Magder
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PHGY 313
Blood,GI,Imm.Syst.Physiol
3 Credits
Offered in the: - Fall
- Winter
- Summer
Physiology: In-depth 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; 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
- Terms
- Instructors
- Judith N Mandl, Volker Manfred Blank, Melissa A Vollrath, Jörg H Fritz, Daniela Quail
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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.
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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
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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
- Fall 2024
- Winter 2025
- Summer 2025
- Instructors
- Alia Sajjad
- Tharshanna Nadarajah
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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, Poincare-Bendixson 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
ORÌý
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
- 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.
- Terms
- Instructors
- David C Becerra
- Kaleem Siddiqi
ÌýOR |
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). 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.
Offered by: Computer Science
- Terms
- Instructors
- Giulia Alberini
- 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
- Gregor F Fussmann, Andrew Hendry, Frederic Guichard, Alexandra Schmidt, Marlene H Oeffinger, Michael Hendricks, Khanh Huy Bui, Stephanie Weber, Arnold L Hayer, Abigail Gerhold
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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
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MATH 319
Partial Differential Equations
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, Sturm-Liouville 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.
- Terms
- Instructors
- Tharshanna Nadarajah
- Masoud Asgharian
|
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, Melissa A Vollrath
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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
- There are no professors associated with this course for the 2024 academic year
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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 frequency-domain descriptions of systems.
Offered by: Biomedical Engineering
- (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
|
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 2024 academic year
- Instructors
- There are no professors associated with this course for the 2024 academic year
ÌýOR |
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
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Total Credits:Ìý 79 |