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Note: This is the 2022–2023 eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or .
Note: This is the 2022–2023 eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or .
Interdisciplinary research that draws from the natural and physical sciences is an important aspect of modern biology. The Quantitative Biology option is designed for students with a deep interest in biology who wish to gain a strong grounding in physical sciences and their application to biological questions. The program has two options: an ecology and evolutionary biology stream, and a physical biology stream. Both streams provide a balance of theory and experimental components.
Students may complete this program with a minimum of 68 credits or a maximum of 73 credits depending on whether MATH 222 and CHEM 212 are completed.
It is highly recommended that freshman BIOL, CHEM, MATH, and PHYS courses be selected with the Program Adviser to ensure they meet the core requirements of the Quantitative Biology option.
This program is recommended for U1 students achieving a CGPA of 3.20 or better; and entering CEGEP students with a Math/Science R-score of 28.0 or better.
Biology (Sci) : An introduction to molecular and cell biology from a physical perspective. Techniques and methodologies, both experimental and computational, are included in the presentation of each thematic module.
Terms: Fall 2022
Instructors: Hendricks, Adam; Watt, Alanna; Reyes Lamothe, Rodrigo; Weber, Stephanie (Fall)
Prerequisite(s): BIOL 112; CHEM 110 and CHEM 120; MATH 140, MATH 141 and MATH 133; PHYS 131 and PHYS 142; or the equivalents of these courses.
Corequisite(s): MATH 222 or equivalent
Restriction(s): Not open to students who have taken or are taking ANAT 212, BIOC 212, BIOL 200, and BIOL 201, or BIEN 219. Only open to students in Bioengineering, Computer Science-Biology, Biology-Mathematics, Biology-Quantitative Biology, Chemistry-Biophysical Chemistry, and Physics-Biological Physics Options.
This course is meant to prepare students for related 300-level courses in Biology, Chemistry, Engineering and Physics.
Biology (Sci) : An introduction to biology research and communication with a focus on cell and molecular biology. Through conducting a series of project-based experiments and writing a final report, molecular and synthetic biology techniques such as gene cloning, manipulation, protein isolation and characterization and how research is conducted, analyzed and communicated will be addressed. In addition, an introduction to bioinformatics methods and their role in analysis will be provided.
Terms: Fall 2022, Winter 2023
Instructors: Reyes Lamothe, Rodrigo; Harrison, Paul; Leroux, Maxime (Fall) Hayer, Arnold; Harrison, Paul; Leroux, Maxime (Winter)
Fall or Winter
1 hour lecture and one 6-hour laboratory
Prerequisites: BIOL 200, BIOL 201 (or ANAT 212/BIOC 212); or BIOL 219
Restrictions: Not open to students who have taken or are taking BIOC 300, or BIOC 220 and BIOC 320. Requires departmental approval.
For approval email hugo.zheng [at] mcgill.ca. Specify your ID number as well as the term and two lab day preferences.
Biology (Sci) : Overview of concepts and current research in quantitative biology; theoretical ecology and evolution, computational biology, and physical biology.
Terms: Fall 2022
Instructors: Hayer, Arnold; Francois, Paul; Kleinman, Claudia; Oeffinger, Marlene; Ehrlicher, Allen; Hendricks, Michael; Bui, Khanh Huy; Weber, Stephanie; Reznikov, Natalie; Gerhold, Abigail (Fall)
Fall
Prerequisites: BIOL 219; or BIOL 200 plus BIOL 201 or ANAT 212 or BIOC 212; CHEM 212; COMP 202 or COMP 204 or COMP 250; MATH 222; or permission of instructor.
Restriction: Only open to U2 students in the following programs: B.Sc.; Major and Honours in Biology; Quantitative Biology, B.Sc.; Major and Honours Computer Science and Biology, B.Sc.; Major Biology and Mathematics, B.Sc.; Major Physiology and Mathematics, B.Sc.; Major Physiology and Physics, B.Sc.; Major and Honours Chemistry; Biophysical Chemistry, and B.Sc.; Major and Honours Physics; Biological Physics.
Chemistry : A survey of reactions of aliphatic and aromatic compounds including modern concepts of bonding, mechanisms, conformational analysis, and stereochemistry.
Terms: Fall 2022, Winter 2023, Summer 2023
Instructors: Pavelka, Laura; Sirjoosingh, Pallavi; Vlaho, Danielle; Gauthier, Jean-Marc (Fall) Vlaho, Danielle; Gauthier, Jean-Marc; Pavelka, Laura; Luedtke, Nathan (Winter) Pavelka, Laura; Vlaho, Danielle; Huot, Mitchell (Summer)
Fall, Winter, Summer
Prerequisite: CHEM 110 or equivalent.
Corequisite: CHEM 120 or equivalent.
Restriction: Not open to students who are taking or have taken CHEM 211 or equivalent
Each lab section is limited enrolment
Note: Some CEGEP programs provide equivalency for this course. For more information, please see the Department of Chemistry's Web page ().
**Due to the intensive nature of this course, the standard add/drop and withdrawal deadlines do not apply. Add/drop is the second lecture day and withdrawal is the fourth lecture day.
Computer Science (Sci) : Introduction to computer programming in a high level language: variables, expressions, primitive types, methods, conditionals, loops. Introduction to algorithms, data structures (arrays, strings), modular software design, libraries, file input/output, debugging, exception handling. Selected topics.
Terms: Fall 2022, Winter 2023, Summer 2023
Instructors: Campbell, Jonathan (Fall) M'hiri, Faten (Winter) M'hiri, Faten (Summer)
3 hours
Prerequisite: a CEGEP level mathematics course
Restrictions: Not open to students who have taken or are taking COMP 204, COMP 208, or GEOG 333; not open to students who have taken or are taking COMP 206 or COMP 250.
COMP 202 is intended as a general introductory course, while COMP 204 is intended for students in life sciences, and COMP 208 is intended for students in physical sciences and engineering.
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 2022, Winter 2023, Summer 2023
Instructors: Paquette, Elliot; Wrobel, Konrad (Fall) Trudeau, Sidney (Winter) Barill, Gavin (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.
Terms: Fall 2022, Winter 2023
Instructors: Macdonald, Jeremy; Pichot, Mikael (Fall) Macdonald, Jeremy (Winter)
Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Terms: Fall 2022, Winter 2023, Summer 2023
Instructors: Berk, Aaron (Fall) Bélanger-Rioux, Rosalie (Winter) Roth, Charles (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.
Terms: Fall 2022, Winter 2023, Summer 2023
Instructors: Nadarajah, Tharshanna; Sajjad, Alia (Fall) Asgharian, Masoud; Sajjad, Alia (Winter) Kelome, Djivede (Summer)
Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Terms: Fall 2022, Winter 2023
Instructors: Nadarajah, Tharshanna (Fall) Nadarajah, Tharshanna (Winter)
Fall and Winter
Prerequisite: MATH 323 or equivalent
Restriction: Not open to students who have taken or are taking MATH 357
You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
*Students who have taken the equivalent of CHEM 212 or MATH 222 can make up the credits with a complementary 3 or 4 credit course in consultation with a stream adviser.
**Students who have sufficient knowledge of programming should take COMP 250 Introduction to Computer Science rather than COMP 202.
Biology (Sci) : Introduction to basic principles, and to modern advances, problems and applications in the genetics of higher and lower organisms with examples representative of the biological sciences.
Terms: Winter 2023
Instructors: Moon, Nam Sung; Nilson, Laura; Schoen, Daniel J; Hipfner, David; Champetier, Serge (Winter)
Biology (Sci) : An introduction to the fundamental processes of ecology and evolution that bear on the nature and diversity of organisms and the processes that govern their assembly into ecological communities and their roles in ecosystem function.
Terms: Fall 2022
Instructors: Price, Neil; Abouheif, Ehab; Sunday, Jennifer (Fall)
Physics : Translational motion under Newton's laws; forces, momentum, work/energy theorem. Special relativity; Lorentz transforms, relativistic mechanics, mass/energy equivalence. Topics in rotational dynamics. Noninertial frames.
Terms: Fall 2022
Instructors: Guo, Hong (Fall)
Physics : The laws of thermodynamics and their consequences. Thermodynamics of P-V-T systems and simple heat engines. Free, driven, and damped harmonic oscillators. Coupled systems and normal modes. Fourier methods. Wave motion and dispersion. The wave equation.
Terms: Winter 2023
Instructors: Hilke, Michael (Winter)
21 credits from one of the following two streams:
Biology
Biology (Sci) : Unified view of form and function in animals and plants. Focus on how the laws of chemistry and physics illuminate biological processes relating to the acquisition of energy and materials and their use in movement, growth, development, reproduction and responses to environmental stress.
Terms: Winter 2023
Instructors: Sakata, Jon; Barrett, Rowan; Soper, Fiona (Winter)
Biology (Sci) : Introduction to modern methods used in organismal biology, including ecological sampling, experimental methods and statistics. Particular emphasis is on ways of thinking about the design of sampling programs and the analyses of data to test hypotheses using observational or experimental data.
Terms: Fall 2022
Instructors: Pollock, Laura; Larsson, Hans Carl; Leung, Brian; Turney, Shaun (Fall)
Fall
1. 2 hours lecture, 2. 3 hours laboratory
Prerequisite: BIOL 111 or equivalent
Biology (Sci) : A comprehensive introduction to evolutionary biology. It covers both short-term and long-term evolutionary processes. Topics include the history of life, the origin of species, adaptation, natural selection and sexual selection.
Terms: Fall 2022
Instructors: Bell, Graham; Turney, Shaun (Fall)
Biology (Sci) : Principles of population, community, and ecosystem dynamics: population growth and regulation, species interactions, dynamics of competitive interactions and of predator/prey systems; evolutionary dynamics.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Field Courses - 3 credits from the following list or any other field course with permission:
Biology (Sci) : Field studies of ferns, fern allies, conifers and flowering plants; the use of keys for plant identification.
Terms: Summer 2023
Instructors: Millien, Virginie; Lapointe, Mélanie (Summer)
Prerequisite: BIOL 111 or permission
Restriction: Not open to students who have taken PLNT 358
Note: Taught at the Gault Nature Reserve. Contact instructor for specific dates, logistics: (virginie.millien [at] mcgill.ca).
This course is offered in the summer.
This course, given at the University’s Gault Nature Reserve in Mont St. Hilaire, has an additional fee of $471.42 which includes a hand lens, a textbook, handouts, lodging and supper each day.
Biology (Sci) : Methods of sampling natural populations. Testing hypotheses in nature.
Terms: Summer 2023
Instructors: Reader, Simon; Potvin, Catherine; Barrett, Rowan (Summer)
Prerequisites: BIOL 206 and BIOL 215, or equivalents, or permission of the instructor.
Note: This course has an additional fee. The Department of Biology subsidizes a portion of the cost for this activity.
The field portion of this course is given at the University’s Gault Nature Reserve in Mont St. Hilare over a two-week period in the summer term. In the summer, students prepare a report based on projects carried out during this field portion. There is an additional fee of $668.32 that covers room and board and handouts. This fee could be refundable if the department approves it.
Biology (Sci) : A study of the physical, chemical and biological properties of lakes and other inland waters, with emphasis on their functioning as systems.
Terms: Fall 2022
Instructors: Gregory-Eaves, Irene; Iversen, Lars Lonsmann (Fall)
Fall
3 hours lecture
Prerequisites: BIOL 206 and BIOL 215 or permission of instructor.
Restrictions: Not open to students who have taken or are taking ENVB 315.
This course, involving two field weekends, has an additional fee of $343.03, which includes room and board and transportation. The fee is refundable during the period where a student can drop the course with full refund. The Department of Biology subsidizes a portion of the cost for this activity.
6 credits chosen from the following list of courses at the 400 level or above:
* Students choose either both BIOL 596 and BIOL 597, or BIOL 598.
Biology (Sci) : A study of the physical, chemical and biological properties of lakes and other inland waters, with emphasis on their functioning as systems.
Terms: Fall 2022
Instructors: Gregory-Eaves, Irene; Iversen, Lars Lonsmann (Fall)
Fall
3 hours lecture
Prerequisites: BIOL 206 and BIOL 215 or permission of instructor.
Restrictions: Not open to students who have taken or are taking ENVB 315.
This course, involving two field weekends, has an additional fee of $343.03, which includes room and board and transportation. The fee is refundable during the period where a student can drop the course with full refund. The Department of Biology subsidizes a portion of the cost for this activity.
Biology (Sci) : Study of theoretical ecology and of mathematical tools available to explore the dynamical behaviour of model populations, communities and ecosystems. Models addressing major ecological theories including population stability, community dynamics and ecosystem functioning, epidemic and disturbance dynamics, spatial models, game theory.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Biology (Sci) : Explains how the selection of undirected variation accounts for some of the leading features of the natural world. Its main focus is evolutionary change and adaptation, but it will also include material from ecological, economic, biochemical and computer systems. It emphasizes experimental studies of evolution.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Fall
3 hours of lecture
Prerequisite: BIOL 304 or permission of instructor.
Biology (Sci) : Discussion of relevant theoretical and applied issues in conservation biology. Topics: biodiversity, population viability analysis, community dynamics, biology of rarity, extinction, habitat fragmentation, social issues.
Terms: Fall 2022
Instructors: Chapman, Lauren; Gonzalez, Andrew (Fall)
Biology (Sci) : An overview of the molecular genetic tools used to investigate ecological and evolutionary processes in natural populations. The use of molecular tools in studies of population structure, parentage, kinship, species boundaries, phylogenetics. Special topics include conservation genetics, population genetics, and ecological genomics.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Biology (Sci) : The origin, maintenance and roles of biological diversity within ecological communities.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Biology (Sci) : Causes and consequences of biological invasion, as well as risk assessment methods and management strategies for dealing with invasive species.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Biology (Sci) : Evolutionary ecology is the study of evolutionary change in natural populations. General predictive approaches in evolutionary ecology, including population genetics, quantitative genetics, optimality, and game theory will be examined. Emphasis will be placed on the mathematical underpinnings of each approach, particularly as they relate to classic and contemporary problems.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Biology (Sci) : This course focuses on experimental design as it relates to statistical analyses to prepare individuals for data collection. Instructors will provide information on basic statistical principles and require students to prepare presentations about their experiments, write summaries of their research, and discuss and critique journal articles.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Prerequisite: BIOL 373 or equivalent and permission of instructor
Biology (Sci) : This course will concentrate on the practical application of data analytical approaches with particular experimental questions in mind. Techniques presented will include statistical methods such as linear models, multivariate statistics, data reduction, information theory.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Biology (Sci) : This course will address issues related to experimental design and multivariate statistical analysis. The first third of the course will focus on experimental design, and the remainder of the course will focus on multivariate approaches to data analysis. The course is designed to inform students on best practices to analytically address their experimental questions.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Biology (Sci) : Emerging physical approaches and quantitative measurement techniques are providing new insights into longstanding biological questions. This course will present underlying physical theory, quantitative measurement techniques, and significant findings in molecular and cellular biophysics. Principles covered include Brownian motion, low Reynolds-number environments, forces relevant to cells and molecules, chemical potentials, and free energies. These principles are applied to enzymes as molecular machines, membranes, DNA, and RNA.
Terms: Winter 2023
Instructors: Reisner, Walter (Winter)
Physics : This interdisciplinary course introduces Statistical Physics illustrated with modern biophysical applications. Principles covered include partition functions, Boltzmann distribution, bosons, fermions, Bose Einstein condensates, Ferni gases, chemical potential, thermodynamical forces, biochemical kinetics, and an introduction to noise and phase transitions in biology.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Physics : De Broglie waves, Bohr atom. Schroedinger equation, wave functions, observables. One dimensional potentials. Schroedinger equation in three dimensions. Angular momentum, hydrogen atom. Spin, experimental consequences.
Terms: Fall 2022
Instructors: Vachon, Brigitte (Fall)
300-level complementary courses: 6 credits from the following:
Biology (Sci) : A survey of current knowledge and approaches in the area of regulation of gene expression, post-transcriptional control of gene expression, and signal transduction.
Terms: Fall 2022
Instructors: Schöck, Frieder; Moon, Nam Sung (Fall)
Biology (Sci) : A consideration of the fundamental processes and principles operating during embryogenesis. Experimental analyses at the molecular, cellular, and organismal levels will be presented and discussed to provide an overall appreciation of developmental phenomena.
Terms: Winter 2023
Instructors: Gerhold, Abigail; Rao, Yong; Dufort, Daniel (Winter)
Biology (Sci) : Neural mechanisms of animal behaviour; neuroethology; cellular neurophysiology, integrative networks within nervous systems; neural control of movement; processing of sensory information.
Terms: Fall 2022
Instructors: Sakata, Jon; Dent, Joseph Alan (Fall)
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 2022
Instructors: Bub, Gil (Fall)
Biology (Sci) : In-depth examination of the structure and function of eukaryotic cells, with an emphasis on experimental design and interpretation. Examination of the molecular mechanisms of various cellular processes, including protein homeostasis, intracellular transport, cytoskeletal dynamics, multicellular organization and cell proliferation.
Terms: Winter 2023
Instructors: Weber, Stephanie; Zetka, Monique (Winter)
500-level complementary courses: 6 credits from the following:
Biology (Sci) : Concepts and mechanisms in advanced cell biology, based on genetic, cell biological, biophysical, and computational studies. Emphasis is placed on processes that are evolutionarily conserved, with examples from model organisms and cell-free (in vitro) approaches.
Terms: Winter 2023
Instructors: Harrison, Paul; Lasko, Paul; Zetka, Monique (Winter)
Winter
3 hours seminar
Prerequisite: BIOL 313 or permission
Biology (Sci) : An analysis of the role and regulation of gene expression in several models of eukaryotic development. The emphasis will be on critical evaluation of recent literature concerned with molecular or genetic approaches to the problems of cellular differentiation and determination. Recent research reports will be discussed in conferences and analyzed in written critiques.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Biology (Sci) : Molecular genetics and molecular, cellular and developmental biology, including signal transduction, cell differentiation and function, genetic diseases in eukaryotes.
Terms: Fall 2022
Instructors: Clarke, Hugh; Dankort, David (Fall)
Biology (Sci) : Fundamental principles of cellular control, with cell cycle control as a major theme. Biological and physical concepts are brought to bear on control in healthy cells..
Terms: Winter 2023
Instructors: Vogel, Jacalyn; Francois, Paul (Winter)
Biology (Sci) : Discussion of fundamental molecular mechanisms underlying the general features of cellular neurobiology. An advanced course based on lectures and on a critical review of primary research papers.
Terms: Fall 2022
Instructors: Hastings, Kenneth E M; Krishnaswamy, Arjun; McPherson, Peter Scott; Poulin, Jean-Francois; Zhou, Yang (Fall)
Quantitative Biology - Theoretical Ecology and Evolutionary Biology, and Physical Biology streams
9 credits from the following:
Recommendations for either Theoretical Ecology and Evolutionary Biology or Physical Biology streams
Biology (Sci) : Independent research project.
Terms: Fall 2022, Winter 2023, Summer 2023
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Fall, Winter or Summer
Prerequisite: BIOL 206 or BIOL 301 or other suitable laboratory course.
Restrictions: Open only to Biology students. Not open to students who have taken BIOL 477.
Note: Before registration, projects must be arranged individually with a PI in the Biology Department. Prior to registration, students fill out the application form at and email or bring it to nancy.nelson [at] mcgill.ca, or Nancy Nelson, Room N7/9B, Stewart Biology Building.
Computer Science (Sci) : Comprehensive overview of programming in C, use of system calls and libraries, debugging and testing of code; use of developmental tools like make, version control systems.
Terms: Fall 2022, Winter 2023
Instructors: D'silva, Joseph (Fall) Errington, Jacob; Vybihal, Joseph P (Winter)
Computer Science (Sci) : Mathematical tools (binary numbers, induction, recurrence relations, asymptotic complexity, establishing correctness of programs), Data structures (arrays, stacks, queues, linked lists, trees, binary trees, binary search trees, heaps, hash tables), Recursive and non-recursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.
Terms: Fall 2022, Winter 2023
Instructors: Alberini, Giulia (Fall) Alberini, Giulia (Winter)
Computer Science (Sci) : Introduction to algorithm design and analysis. Graph algorithms, greedy algorithms, data structures, dynamic programming, maximum flows.
Terms: Fall 2022, Winter 2023
Instructors: Waldispuhl, Jérôme; Alberini, Giulia (Fall) Becerra, David (Winter)
3 hours
COMP 251 uses mathematical proof techniques that are taught in the corequisite course(s). If possible, students should take the corequisite course prior to COMP 251.
COMP 251 uses basic counting techniques (permutations and combinations) that are covered in MATH 240 but not in MATH 235. These techniques will be reviewed for the benefit of MATH 235 students.
Restrictions: Not open to students who have taken or are taking COMP 252.
Computer Science (Sci) : Computer representation of numbers, IEEE Standard for Floating Point Representation, computer arithmetic and rounding errors. Numerical stability. Matrix computations and software systems. Polynomial interpolation. Least-squares approximation. Iterative methods for solving a nonlinear equation. Discretization methods for integration and differential equations.
Terms: Fall 2022
Instructors: Chang, Xiao-Wen (Fall)
Computer Science (Sci) : Concepts and tools for programmatic storage, retrieval, searching, numerical analysis, and visualization of large biological data sets.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
Mathematics & Statistics (Sci) : Sets, functions and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. Rings, ideals and quotient rings. Fields and construction of fields from polynomial rings. Groups, subgroups and cosets; group actions on sets.
Terms: Fall 2022
Instructors: Wise, Daniel (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent
Mathematics & Statistics (Sci) : Introduction to discrete mathematics and applications. Logical reasoning and methods of proof. Elementary number theory and cryptography: prime numbers, modular equations, RSA encryption. Combinatorics: basic enumeration, combinatorial methods, recurrence equations. Graph theory: trees, cycles, planar graphs.
Terms: Fall 2022, Winter 2023
Instructors: Vetta, Adrian Roshan; Fortier, Jérôme (Fall) Fortier, Jérôme; Macdonald, Jeremy (Winter)
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 2022, Winter 2023
Instructors: Roth, Charles (Fall) Fortier, Jérôme (Winter)
Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Terms: Fall 2022
Instructors: Lessard, Jean-Philippe (Fall)
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 2023
Instructors: Bélanger-Rioux, Rosalie (Winter)
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 2022
Instructors: Nave, Jean-Christophe (Fall)
Mathematics & Statistics (Sci) : An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.
Terms: Winter 2023
Instructors: Panayotov, Ivo (Winter)
Mathematics & Statistics (Sci) : Points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area. Power of a point with respect to a circle. Ceva’s theorem. Isometries. Homothety. Inversion.
Terms: Fall 2022
Instructors: Przytycki, Piotr (Fall)
Mathematics & Statistics (Sci) : The formulation and treatment of realistic mathematical models describing biological phenomena through qualitative and quantitative mathematical techniques (e.g. local and global stability theory, bifurcation analysis and phase plane analysis) and numerical simulation. Concrete and detailed examples will be drawn from molecular and cellular biology and mammalian physiology.
Terms: Winter 2023
Instructors: Khadra, Anmar (Winter)
Mathematics & Statistics (Sci) : Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.
Terms: Winter 2023
Instructors: Addario-Berry, Louigi Dana (Winter)
* Students may take COMP 350 OR MATH 317.
**MATH 235 or MATH 240 are required for COMP 251.
Recommendations for Physical Biology stream
BIEN : Forward and reverse engineering of biomolecular systems. Principles of biomolecular thermodynamics and kinetics. Structure and function of the main classes of biomolecules including proteins, nucleic acids, and lipids. Biomolecular systems as mechanical, chemical, and electrical systems. Rational design and evolutionary methods for engineering functional proteins, nucleic acids, and gene circuits. Rational design topics include molecular modeling, positive and negative design paradigms, simulation and optimization of equilibrium and kinetic properties, design of catalysts, sensors, motors, and circuits. Evolutionary design topics include evolutionary mechanisms, fitness landscapes, directed evolution of proteins, metabolic pathways, and gene circuits. Systems biology and synthetic biology.
Terms: Fall 2022
Instructors: Xia, Yu (Fall)
Prerequisite(s): BIEN 200 or permission of instructor.
(3-0-6)
BIEN : Basic mechanics of biological building blocks, focusing on the cytoskeleton, with examples from pathology. At the macromolecular level: weak/variable crosslinking and hydrolysis driven athermal processes. At the cellular/tissue level: cell architecture and function. Discussion of modern analytical techniques capable of single-molecule to tissue scale measurements.
Terms: Winter 2023
Instructors: Ehrlicher, Allen (Winter)
BIEN : Fundamental principles of mass transport and its application to a variety of biological systems. Membrane permeability and diffusive transport. Convection. Transport across cell membranes. Ion channels. Blood rheology. Active transport. Intra- and inter-cellular transport.
Terms: Winter 2023
Instructors: Oprea, Laurentiu (Winter)
BIEN : Introduction to the interdisciplinary field of biomedical uses of nanotechnology. Emphasis on emerging nanotechnologies and biomedical applications including nanomaterials, nanoengineering, nanotechnology-based drug delivery systems, nano-based imaging and diagnostic systems, nanotoxicology and immunology, and translating nanomedicine into clinical investigation.
Terms: Fall 2022
Instructors: Kinsella, Matt (Fall)
BIEN : Microscopy techniques with application to biology and medicine. Practical introduction to optics and microscopy from the standpoint of biomedical research. Discussion of recent literature; hands-on experience. Topics include: optics, contrast techniques, advanced microscopy, and image analysis.
Terms: Winter 2023
Instructors: Hendricks, Adam (Winter)
Prerequisite: Permission of instructor.
(3-1-5)
Chemistry : Modern spectroscopic techniques for structure determination. The chemistry of alcohols, ethers, carbonyl compounds, and amines, with special attention to mechanistic aspects. Special topics.
Terms: Fall 2022, Winter 2023, Summer 2023
Instructors: Vlaho, Danielle; Gauthier, Jean-Marc; Pavelka, Laura; Auclair, Karine (Fall) Pavelka, Laura; Vlaho, Danielle; Gauthier, Jean-Marc (Winter) Pavelka, Laura; Vlaho, Danielle; Huot, Mitchell (Summer)
Fall, Winter
Prerequisite: CHEM 212 or equivalent.
Restriction: Not open to students who have taken an equivalent Organic 2 at CEGEP (see Æ»¹ûÒùÔº Basic Math and Sciences Equivalence Table at ) or who have or are taking CHEM 234.
**Due to the intensive nature of this course, the standard add/drop and withdrawal deadlines do not apply. Add/drop is the second lecture day and withdrawal is the fourth lecture day.
Physics : Properties of electromagnetic fields, dipole and quadropole fields and their interactions, chemical binding of molecules, electromagnetic properties of materials, Maxwell's equations and properties of electromagnetic waves, propagation of waves in media.
Terms: Fall 2022
Instructors: Chiang, Hsin Cynthia (Fall)
Fall
2 hours lectures
Prerequisites: CEGEP Physics, MATH 222
Physics : Introductory laboratory work and data analysis as related to mechanics, optics and thermodynamics. Introduction to computers as they are employed for laboratory work, for data analysis and for numerical computation. Previous experience with computers is an asset, but is not required.
Terms: Fall 2022
Instructors: Vachon, Brigitte (Fall)
Physics : Maxwell's equations. The wave equation. The electromagnetic wave, reflection, refraction, polarization. Guided waves. Transmission lines and wave guides. Vector potential. Radiation. The elemental dipole; the half-wave dipole; vertical dipole; folded dipoles; Yagi antennas. Accelerating charged particles.
Terms: Winter 2023
Instructors: Gervais, Guillaume (Winter)
Physics : Fundamental concepts of optics, including applications and modern developments. Light propagation in media; geometric optics and optical instruments; polarization and coherence properties of light; interference and interferometry; diffraction theory and applications in spectrometry and imaging; Gaussian beams, Fourier optics and photonic band structure. A laboratory component provides hands-on experience in optical setup design, construction and testing of concepts introduced in lectures.
Terms: Fall 2022
Instructors: Cooke, David (Fall)
Physics : An advanced biophysics course, with a special emphasis on stochastic and out of equilibrium physical processes in living matter.
Terms: Winter 2023
Instructors: Bourassa, François (Winter)
Physics : Topics include scanning probe microscopy, chemical self-assembly, computer modelling, and microfabrication/micromachining.
Terms: Fall 2022
Instructors: Grutter, Peter H (Fall)
Fall
Restriction: U3 or graduate students in Physics, Chemistry, or Engineering, or permission of the instructor.
* PHYS 242 is required for PHYS 342 and PHYS 434.
Recommendations for Theoretical Ecology and Evolutionary Biology stream
Biology (Sci) : Ecological bases of the natural causes and consequences of current global environmental changes, including how biodiversity and ecosystem processes are defined and measured, how they vary in space and time, how they are affected by physical and biological factors, and how they affect each other and human societies.
Terms: Winter 2023
Instructors: Pollock, Laura; Iversen, Lars Lonsmann (Winter)
Biology (Sci) : Presents evolutionary genetics within an ecological context. Covers theoretical and applied topics together with relevant data from natural populations of plant and animals.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.
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 2022
Instructors: Hundemer, Axel W (Fall)
Mathematics & Statistics (Sci) : Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
Terms: Winter 2023
Instructors: Norin, Sergey (Winter)
Mathematics & Statistics (Sci) : Multiple regression estimators and their properties. Hypothesis tests and confidence intervals. Analysis of variance. Prediction and prediction intervals. Model diagnostics. Model selection. Introduction to weighted least squares. Basic contingency table analysis. Introduction to logistic and Poisson regression. Applications to experimental and observational data.
Terms: Fall 2022
Instructors: Nadarajah, Tharshanna (Fall)
Mathematics & Statistics (Sci) : Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used.
Terms: Fall 2022
Instructors: Neslehova, Johanna (Fall)
Mathematics & Statistics (Sci) : Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.
Terms: Winter 2023
Instructors: Yang, Archer Yi (Winter)
Physics : This interdisciplinary course introduces Statistical Physics illustrated with modern biophysical applications. Principles covered include partition functions, Boltzmann distribution, bosons, fermions, Bose Einstein condensates, Ferni gases, chemical potential, thermodynamical forces, biochemical kinetics, and an introduction to noise and phase transitions in biology.
Terms: This course is not scheduled for the 2022-2023 academic year.
Instructors: There are no professors associated with this course for the 2022-2023 academic year.