Major Physiology and Mathematics (77 credits)

Program Requirements

U1 Required Courses (14 credits)

• BIOL 200 Molecular Biology (3 credits)

  Offered by: Biology (Faculty of Science)

  Overview

  Biology (Sci) : The physical and chemical properties of the cell and its components in relation to their structure and function. Topics include: protein structure, enzymes and enzyme kinetics; nucleic acid replication, transcription and translation; the genetic code, mutation, recombination, and regulation of gene expression.

  Terms: Fall 2013

  Instructors: Thomas E Bureau, Richard D W Roy, Francesco Fagotto, Monique Zetka (Fall)

  • Fall
  • 3 hours lecture, 1 hour optional tutorial
  • Prerequisite: BIOL 112 or equivalent
  • Corequisite: CHEM 212 or equivalent
• BIOL 309 Mathematical Models in Biology (3 credits)

  Offered by: Biology (Faculty of Science)

  Overview

  Biology (Sci) : Application of finite difference and differential equations to problems in cell and developmental biology, ecology and physiology. Qualitative, quantitative and graphical techniques are used to analyze mathematical models and to compare theoretical predictions with experimental data.

  Terms: Fall 2013

  Instructors: Leon Glass (Fall)

  • Fall
  • 3 hours lecture
  • Prerequisite: one year of calculus. An additional course in calculus is recommended
• MATH 222 Calculus 3 (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.

  Terms: Fall 2013, Winter 2014

  Instructors: There are no professors associated with this course for the 2013-2014 academic year.

  • Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
  • Restriction: Not open to students who have taken CEGEP course 201-303 or MATH 150, MATH 151 or MATH 227
• PHGY 212 Introductory Physiology Laboratory 1 (1 credit)

  Offered by: Physiology (Faculty of Science)

  Overview

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

  Terms: Fall 2013

  Instructors: Julio Martinez Trujillo, Mladen I Glavinovic, Kresimir Krnjevic (Fall)

  • (One 3-hour lab and one 1-hour lecture every second week.)
  • Corequisite: PHGY 209.
  • Restrictions: Required for Physiology students enrolled in PHGY 209. Open to BA &Sc. students and to others by permission of the instructor. Not open to students who have taken PHGY 212D1/D2.
  • Note: For students in a Physiology program, PHGY 212 should be taken concurrently with PHGY 209.
• PHGY 213 Introductory Physiology Laboratory 2 (1 credit)

  Offered by: Physiology (Faculty of Science)

  Overview

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

  Terms: Winter 2014

  Instructors: Michael R Guevara, Douglas Watt, Jacopo Mortola (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.

One of:

• MATH 223 Linear Algebra (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications.

  Terms: Fall 2013, Winter 2014

  Instructors: There are no professors associated with this course for the 2013-2014 academic year.

  • Fall and Winter
  • Prerequisite: MATH 133 or equivalent
  • Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 236, MATH 247 or MATH 251. It is open to students in Faculty Programs
• MATH 247 Honours Applied Linear Algebra (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Matrix algebra, determinants, systems of linear equations. Abstract vector spaces, inner product spaces, Fourier series. Linear transformations and their matrix representations. Eigenvalues and eigenvectors, diagonalizable and defective matrices, positive definite and semidefinite matrices. Quadratic and Hermitian forms, generalized eigenvalue problems, simultaneous reduction of quadratic forms. Applications.

  Terms: Winter 2014

  Instructors: Axel W Hundemer (Winter)

  • Winter
  • Prerequisite: MATH 133 or equivalent.
  • Restriction: Intended for Honours Physics and Engineering students
  • Restriction: Not open to students who have taken or are taking MATH 236, MATH 223 or MATH 251

U1 Complementary Courses (15 credits)

3 credits, one of:

• BIOC 212 Molecular Mechanisms of Cell Function (3 credits)

  Offered by: Biochemistry (Faculty of Science)

  Overview

  Biochemistry : An introductory course describing the biochemistry and molecular biology of selected key functions of animal cells, including: gene expression; mitochondrial production of metabolic energy; cellular communication with the extra-cellular environment; and regulation of cell division.

  Terms: Winter 2014

  Instructors: Thomas Duchaine, Arnim Pause, Maxime Bouchard (Winter)

  • Winter
  • Prerequisite: BIOL 200
  • Restrictions: A non-terminal course intended to be followed by BIOC 311; BIOC 312 in the U2 year. Not open to students who have taken or are taking BIOL 201 or ANAT 212.
• BIOL 201 Cell Biology and Metabolism (3 credits)

  Offered by: Biology (Faculty of Science)

  Overview

  Biology (Sci) : This course introduces the student to our modern understanding of cells and how they work. Major topics to be covered include: photosynthesis, energy metabolism and metabolic integration; plasma membrane including secretion, endocytosis and contact mediated interactions between cells; cytoskeleton including cell and organelle movement; the nervous system; hormone signaling; the cell cycle.

  Terms: Winter 2014

  Instructors: Gary Brouhard, Gregory G Brown (Winter)

  • Winter
  • 3 hours lecture, 1 hour optional tutorial
  • Prerequisite: BIOL 200.
  • Restriction: Not open to students who have taken or are taking ANAT 212 or BIOC 212

6 credits selected as follows:

• PHGY 209 Mammalian Physiology 1 (3 credits)

  Offered by: Physiology (Faculty of Science)

  Overview

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

  Terms: Fall 2013

  Instructors: Ann Wechsler, Phil Gold, David S Ragsdale (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
• PHGY 210 Mammalian Physiology 2 (3 credits)

  Offered by: Physiology (Faculty of Science)

  Overview

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

  Terms: Winter 2014

  Instructors: John H White, Ann Wechsler, Tomoko Takano (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

3 credits, one of:

• MATH 248 Honours Advanced Calculus (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Partial derivatives; implicit functions; Jacobians; maxima and minima; Lagrange multipliers. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line integrals; Green's theorem; the divergence theorem. Stokes' theorem; irrotational and solenoidal fields; applications.

  Terms: Fall 2013

  Instructors: There are no professors associated with this course for the 2013-2014 academic year.

  • Fall and Winter and Summer
  • Prerequisites: MATH 133 and MATH 222 or consent of Department.
  • Restriction: Intended for Honours Mathematics, Physics and Engineering students
  • Restriction: Not open to students who have taken or are taking MATH 314
• MATH 314 Advanced Calculus (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.

  Terms: Fall 2013, Winter 2014

  Instructors: There are no professors associated with this course for the 2013-2014 academic year.

  • Prerequisites: MATH 133, MATH 222
  • Restriction: Not open to students who have taken or are taking MATH 248

3 credits, one of:

• MATH 315 Ordinary Differential Equations (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

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

  Terms: Fall 2013, Winter 2014

  Instructors: Charles Roth (Fall) Gantumur Tsogtgerel (Winter)

  • Prerequisite: MATH 222.
  • Corequisite: MATH 133.
  • Restriction: Not open to students who have taken or are taking MATH 325.
• MATH 325 Honours Ordinary Differential Equations (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.

  Terms: Fall 2013, Winter 2014

  Instructors: Charles Roth (Winter)

  • Fall and Winter
  • (3-0-6)
  • Prerequisite: MATH 222.
  • Restriction: Intended for Honours Mathematics, Physics and Engineering programs.
  • Restriction: Not open to students who have taken MATH 263 (formerly MATH 261), MATH 315

U2 Required Courses (24 credits)

• MATH 242 Analysis 1 (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

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

  Terms: Fall 2013

  Instructors: There are no professors associated with this course for the 2013-2014 academic year.

  • Fall
  • Prerequisite: MATH 141
• MATH 243 Analysis 2 (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Infinite series; series of functions; power series. The Riemann integral in one variable. A rigorous development of the elementary functions.

  Terms: Winter 2014

  Instructors: There are no professors associated with this course for the 2013-2014 academic year.

  • Winter
  • Prerequisite: MATH 242
• MATH 323 Probability (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.

  Terms: Fall 2013, Winter 2014

  Instructors: William J Anderson (Winter)

  • Prerequisites: MATH 141 or equivalent.
  • Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
  • Restriction: Not open to students who have taken or are taking MATH 356
• MATH 326 Nonlinear Dynamics and Chaos (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.

  Terms: Fall 2013

  Instructors: There are no professors associated with this course for the 2013-2014 academic year.

  • Fall
  • Prerequisites: MATH 222, MATH 223
  • Restriction: Not open to students who have taken or are taking MATH 376
• PHGY 311 Channels, Synapses & Hormones (3 credits)

  Offered by: Physiology (Faculty of Science)

  Overview

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

  Terms: Fall 2013

  Instructors: Ellis Cooper, Riaz Farookhi, Ali Haghighi (Fall)

  • Fall
  • 3 hours of lectures per week; 1-3 hours optional lab/demonstration/tutorial arranged for a maximum of 3 afternoons per term
  • Prerequisite: PHGY 209 or permission of the instructor.
• PHGY 312 Respiratory, Renal, & Cardiovascular Physiology (3 credits)

  Offered by: Physiology (Faculty of Science)

  Overview

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

  Terms: Winter 2014

  Instructors: John W Hanrahan, Jacopo Mortola, Alvin Shrier (Winter)

  • Winter
  • 3 hours of lectures per week; 1-3 hours optional lab/demonstration/tutorial arranged for a maximum of 3 Wednesday afternoons per term
  • Prerequisites: PHGY 209 and PHGY 210 or equivalent, PHGY 311 or permission of the instructor
• PHGY 313 Blood, Gastrointestinal, & Immune Systems Physiology (3 credits)

  Offered by: Physiology (Faculty of Science)

  Overview

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

  Terms: Winter 2014

  Instructors: Julio Martinez Trujillo, Mark D Blostein, Volker Manfred Blank (Winter)

  • Winter
  • 3 hours of lectures per week; 1-3 hours optional lab/demonstration/tutorial arranged for a maximum of 3 Wednesday afternoons per term
  • Prerequisites: PHGY 209 and PHGY 210 or equivalent, PHGY 311 or permission of the instructor
• PHGY 314 Integrative Neuroscience (3 credits)

  Offered by: Physiology (Faculty of Science)

  Overview

  Physiology : In depth presentation of experimental results and hypotheses underlying our current understanding of how single neurons and ensembles of neurons encode sensory information, generate movement, and control cognitive functions such as emotion, learning, and memory, during voluntary behaviours.

  Terms: Fall 2013

  Instructors: Kathleen E Cullen, Julio Martinez Trujillo, Christopher Pack (Fall)

  • Fall
  • 3 hours of lectures per week
  • Prerequisites: PHGY 209

U2 or U3 Required Courses (6 credits)

• MATH 437 Mathematical Methods in Biology (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : The formulation and treatment of realistic mathematical models describing biological phenomena through qualitative and quantitative mathematical techniques (e.g. local and global stability theory, bifurcation analysis and phase plane analysis) and numerical simulation. Concrete and detailed examples will be drawn from molecular and cellular biology and mammalian physiology.

  Terms: This course is not scheduled for the 2013-2014 academic year.

  Instructors: There are no professors associated with this course for the 2013-2014 academic year.

  • Taught in alternate years (Fall)
  • Prerequisites: MATH 315 or MATH 325, and MATH 323 or MATH 356, a CEGEP or higher level computer programming course
  • Corequisite: MATH 326 or MATH 376
• PHYS 413 Physical Basis of Physiology (3 credits)

  Offered by: Physics (Faculty of Science)

  Overview

  Physics : Analytic and computer simulation techniques are used to examine the role of nonlinearities and time delays in determining the dynamic behaviour of physiological control systems and their relation to normal and pathophysiological states. Examples drawn from the control of respiration, cellular proliferation and differentiation, biochemical feedback networks, thermoregulatory mechanisms, and neural feedback.

  Terms: Fall 2013

  Instructors: Michael C Mackey (Fall)

  • 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

U3 Required Courses (18 credits)

• BMDE 519 Biomedical Signals and Systems (3 credits)

  Offered by: Biomedical Engineering (Faculty of Engineering)

  Overview

  Biomedical Engineering : An introduction to the theoretical framework, experimental techniques and analysis procedures available for the quantitative analysis of physiological systems and signals. Lectures plus laboratory work using the Biomedical Engineering computer system. Topics include: amplitude and frequency structure of signals, filtering, sampling, correlation functions, time and frequency-domain descriptions of systems.

  Terms: Fall 2013

  Instructors: Robert E Kearney (Fall)

  • (3-0-6)
  • Prerequisites: Satisfactory standing in U3 Honours Physiology; or U3 Major in Physics-Physiology; or U3 Major Physiology-Mathematics; or permission of instructor
• MATH 319 Introduction to Partial Differential Equations (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

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

  Terms: Winter 2014

  Instructors: Peter Bartello (Winter)

  • Winter
  • Prerequisites: MATH 223 or MATH 236, MATH 314, MATH 315
• MATH 324 Statistics (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

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

  Terms: Fall 2013, Winter 2014

  Instructors: William J Anderson (Fall)

  • 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.
• PHGY 461D1 Experimental Physiology (4.5 credits)

  Offered by: Physiology (Faculty of Science)

  Overview

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

  Terms: Fall 2013

  Instructors: Ann Wechsler, Linda H Cooper (Fall)

  • Fall
  • Restrictions: Departmental approval required. This course is a requirement for U3 students in the Honours Physiology program, the Major Program in Physiology and Mathematics, and the Major program in Physiology and Physics, and is open to a limited number of other U3 Physiology students.
  • Students must register for both PHGY 461D1 and PHGY 461D2.
  • No credit will be given for this course unless both PHGY 461D1 and PHGY 461D2 are successfully completed in consecutive terms
• PHGY 461D2 Experimental Physiology (4.5 credits)

  Offered by: Physiology (Faculty of Science)

  Overview

  Physiology : See PHGY 461D1 for course description.

  Terms: Winter 2014

  Instructors: Ann Wechsler (Winter)

  • Winter
  • Prerequisite: PHGY 461D1
  • No credit will be given for this course unless both PHGY 461D1 and PHGY 461D2 are successfully completed in consecutive terms