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REQUIED COURSES
Bachelor of Science (B.Sc.) - Major Physiology and Mathematics (79 Credits) Offered by:Physiology Degree:Bachelor of Science 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 Fall 2024 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 Fall 2024 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 Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133 Restriction: Not open to students who have taken MATH 150, MATH 151 or MATH 262. Terms Fall 2024 Winter 2025 Instructors Brent Pym, Damien Tageddine MATH 223 Linear Algebra 3 Credits* Offered in the: Fall Winter Summer Mathematics & Statistics (Sci): Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications. Offered by: Mathematics and Statistics Fall and Winter Prerequisite: MATH 133 or equivalent Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 206, MATH 236, MATH 247, or MATH 251. Symbols: * Terms Fall 2024 Winter 2025 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 Symbols: * Terms Winter 2025 Instructors Tim Hoheisel 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 Prerequisite: MATH 222. Corequisite: MATH 133. Restriction: Not open to students who have taken or are taking MATH 325. Symbols: Terms Fall 2024 Winter 2025 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 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 Symbols: Terms Winter 2025 Instructors Jean-Philippe 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 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 Fall 3 hours lecture Prerequisites:BIOL 200, BIOL 201 (or ANAT 212/BIOC 212); or BIOL 219 Terms Fall 2024 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 Terms Fall 2024 Instructors Robert E Kearney 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. Terms Fall 2024 Instructors Dmitry Jakobson 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 Winter Prerequisite: MATH 242 or MATH 254. Terms Winter 2025 Instructors Axel W Hundemer 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. Symbols: * Terms Fall 2024 Instructors Jean Pierre Mutanguha 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 Prerequisites: MATH 133, MATH 222 Restriction: Not open to students who have taken or are taking MATH 248 or MATH 358. Symbols: *** Terms Fall 2024 Winter 2025 Instructors Gabriel Martine 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 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 Terms Fall 2024 Instructors Gabriel William Duchesne 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 Winter Prerequisites: MATH 223 or MATH 236, MATH 314 or equivalent, MATH 315 Not open to students who have taken or are taking MATH 475. Terms Winter 2025 Instructors Jessica Lin 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 Fall 2024 Winter 2025 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 Fall Prerequisites: MATH 222, MATH 223 Restriction: Not open to students who have taken or are taking MATH 376 Terms Fall 2024 Instructors Tony Humphries 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 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. Terms Winter 2025 Instructors Anmar Khadra 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 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 Terms Fall 2024 Instructors Melissa A Vollrath, David S Ragsdale, Alvin Shrier, Erik P Cook, C茅line 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 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 Terms Winter 2025 Instructors Melissa A Vollrath, Tomoko Takano, Anne-Marie Lauzon, John H White, C茅line 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 Fall 2024 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 Winter 2025 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 Winter 2025 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 Winter 2025 Instructors Judith N Mandl, Volker Manfred Blank, Melissa A Vollrath, J枚rg 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 Fall 2024 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 Winter 2025 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 Fall 2024 Winter 2025 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 3 hours Prerequisite(s): MATH 140 or equivalent. COMP 202 or COMP 204 or COMP 208 (or equivalent). Corequisite(s): MATH 133 Restriction(s): Not open to students who have taken or are taking ECSE 250. Terms Fall 2024 Winter 2025 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 Fall 2024 Instructors Ellis Cooper, Per Jesper Sjostrom, 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 Fall 2024 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 Prerequisites: (PHYS 329 or PHYS 333 or PHYS 362 or MATH 437) and (PHYS 340 or PHYS 350), or permission of the instructor. Terms Winter 2025 Instructors Paul W Wiseman For more information, see Programs, Courses and University Regulations.
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 Fall 2024 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 Fall 3 hours lecture Prerequisites:BIOL 200, BIOL 201 (or ANAT 212/BIOC 212); or BIOL 219 Terms Fall 2024 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 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 Terms Fall 2024 Instructors Melissa A Vollrath, David S Ragsdale, Alvin Shrier, Erik P Cook, C茅line 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 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 Terms Winter 2025 Instructors Melissa A Vollrath, Tomoko Takano, Anne-Marie Lauzon, John H White, C茅line 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 Fall 2024 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 Winter 2025 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 Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133 Restriction: Not open to students who have taken MATH 150, MATH 151 or MATH 262. Terms Fall 2024 Winter 2025 Instructors Brent Pym, Damien Tageddine
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 Terms Winter 2025 Instructors Tim Hoheisel 听OR
MATH 223 Linear Algebra 3 Credits Offered in the: Fall Winter Summer Mathematics & Statistics (Sci): Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications. Offered by: Mathematics and Statistics Fall and Winter Prerequisite: MATH 133 or equivalent Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 206, MATH 236, MATH 247, or MATH 251. Terms Fall 2024 Winter 2025 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. Terms Fall 2024 Instructors Jean Pierre Mutanguha 听OR
MATH 314 Advanced Calculus 3 Credits Offered in the: Fall Winter Summer Mathematics & Statistics (Sci): Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications. Offered by: Mathematics and Statistics Prerequisites: MATH 133, MATH 222 Restriction: Not open to students who have taken or are taking MATH 248 or MATH 358. Terms Fall 2024 Winter 2025 Instructors Gabriel Martine
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 Terms Winter 2025 Instructors Jean-Philippe Lessard 听OR
MATH 315 Ordinary Differential Eqns 3 Credits Offered in the: Fall Winter Summer Mathematics & Statistics (Sci): First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions. Offered by: Mathematics and Statistics Prerequisite: MATH 222. Corequisite: MATH 133. Restriction: Not open to students who have taken or are taking MATH 325. Terms Fall 2024 Winter 2025 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 Fall 2024 Instructors Ellis Cooper, Per Jesper Sjostrom, Arjun Krishnaswamy, Reza Sharif Naeini 听OR
PHGY 314 Integrative Neuroscience 3 Credits Offered in the: Fall Winter Summer Physiology: In depth presentation of experimental results and hypotheses underlying our current understanding of how single neurons and ensembles of neurons encode sensory information, generate movement, and control cognitive functions such as emotion, learning, and memory, during voluntary behaviours. Offered by: Physiology Fall 3 hours of lectures per week Prerequisites: PHGY 209 Terms Fall 2024 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 Winter 2025 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 Winter 2025 Instructors Judith N Mandl, Volker Manfred Blank, Melissa A Vollrath, J枚rg H Fritz, Daniela Quail
MATH 242 Analysis 1 3 Credits Offered in the: Fall Winter Summer Mathematics & Statistics (Sci): A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line. Offered by: Mathematics and Statistics Fall Prerequisite: MATH 141 Restriction(s): Not open to students who are taking or who have taken MATH 254. Terms Fall 2024 Instructors Dmitry Jakobson
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 Winter Prerequisite: MATH 242 or MATH 254. Terms Winter 2025 Instructors Axel W Hundemer
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 Instructors Alia Sajjad Tharshanna Nadarajah
MATH 326 Nonlinear Dynamics and Chaos 3 Credits Offered in the: Fall Winter Summer Mathematics & Statistics (Sci): Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, Poincare-Bendixson 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 Terms Fall 2024 Instructors Tony Humphries
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 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. Terms Winter 2025 Instructors Anmar Khadra OR听 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 Prerequisite(s): MATH 325, MATH 376, and COMP 202 or COMP 204 or COMP 208 or equivalent. Restriction(s): Not open to students who have taken MATH 437. This course is offered in the winter semester. Terms Winter 2025 Instructors Anmar Khadra (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 Fall 2024 Winter 2025 Instructors David C Becerra Kaleem Siddiqi 听OR
COMP 250 Intro to Computer Science 3 Credits Offered in the: Fall Winter Summer Computer Science (Sci): Mathematical tools (binary numbers, induction,recurrence relations, asymptotic complexity,establishing correctness of programs). 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 3 hours Prerequisite(s): MATH 140 or equivalent. COMP 202 or COMP 204 or COMP 208 (or equivalent). Corequisite(s): MATH 133 Restriction(s): Not open to students who have taken or are taking ECSE 250. Terms Fall 2024 Winter 2025 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 Fall 2024 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
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 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 Terms Fall 2024 Instructors Gabriel William Duchesne
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 Winter Prerequisites: MATH 223 or MATH 236, MATH 314 or equivalent, MATH 315 Not open to students who have taken or are taking MATH 475. Terms Winter 2025 Instructors Jessica Lin
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 Fall 2024 Winter 2025 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 Fall 2024 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 Winter 2025 Instructors There are no professors associated with this course for the 2024 academic year
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 Terms Fall 2024 Instructors Robert E Kearney
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 听OR
PHYS 519 Advanced Biophysics 3 Credits Offered in the: Fall Winter Summer Physics: An advanced biophysics course, with a special emphasis on stochastic and out of equilibrium physical processes in living matter. Offered by: Physics Prerequisites: (PHYS 329 or PHYS 333 or PHYS 362 or MATH 437) and (PHYS 340 or PHYS 350), or permission of the instructor. Terms Winter 2025 Instructors Paul W Wiseman
Total Credits:听 79

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