Note: This is the 2019鈥�2020 eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or .
Program Requirements
79 credits
Interdisciplinary research that draws from the natural and physical sciences is an important aspect of modern biology. The Quantitative Biology (QB) Honours 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 through both coursework and a research project. The QB B.Sc. Honours option has two streams: a theoretical ecology and evolutionary biology stream and a physical biology stream. Both streams provide a balance of theory and experimental components that along with a research component will provide outstanding preparation for graduate training. Students must attain a 3.50 CGPA to enter and to complete the Honours program. First Class Honours will be awarded to students in the QB Honours option graduating with a CGPA of 3.75 or greater.
Students may complete this program with a minimum of 74 credits or a maximum of 79 credits depending on whether MATH 222 and CHEM 212 are completed.
Advising notes for U0 students
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.
Required Courses (49 credits)
Bio-Physical Sciences Core (31 credits)
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BIOL 219 Introduction to Physical
Molecular and Cell Biology (4 credits)
Overview
Biology (Sci) : An introduction to molecular and cell biology from a physical perspective. Techniques and methodologies, both experimental and computational, are included in the presentation of each thematic module.
Terms: Fall 2019
Instructors: Hendricks, Adam; Vogel, Jacalyn; Brouhard, Gary; Watt, Alanna (Fall)
Prerequisite(s): BIOL 112; CHEM 110 and CHEM 120; MATH 140, MATH 141 and MATH 133; PHYS 131 and PHYS 142; or the equivalents of these courses.
Corequisite(s): MATH 222 or equivalent
Restriction(s): Not open to students who have taken or are taking ANAT 212, BIOC 212, BIOL 200, and BIOL 201, or BIEN 219. Only open to students in Bioengineering, Computer Science-Biology, Biology-Mathematics, Biology-Quantitative Biology, Chemistry-Biophysical Chemistry, and Physics-Biological Physics Options.
This course is meant to prepare students for related 300-level courses in Biology, Chemistry, Engineering and Physics.
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BIOL 301 Cell and Molecular Laboratory (4 credits)
Overview
Biology (Sci) : An introduction to laboratory techniques with a focus on methods used to investigate fundamental questions in modern cell and molecular biology. Techniques including gene cloning, DNA and protein isolation and manipulation are covered, along with functional analysis of genes and proteins, basic bioinformatics, and computer-based experimental design and data analysis.
Terms: Fall 2019, Winter 2020
Instructors: Zheng, Huanquan; Harrison, Paul; Reyes Lamothe, Rodrigo (Fall) Zheng, Huanquan; Reyes Lamothe, Rodrigo (Winter)
Fall or Winter
1 hour lecture and one 6-hour laboratory
Prerequisites:BIOL 200, BIOL 201 (or ANAT 212/BIOC 212) and BIOL 202; or BIOL 219 and BIOL 202.
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 anne-marie.sdicu [at] mcgill.ca. Specify your ID number as well as the term and two lab day preferences.
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BIOL 395 Quantitative Biology Seminar (1 credit)
Overview
Biology (Sci) : Overview of concepts and current research in quantitative biology; theoretical ecology and evolution, computational biology, and physical biology.
Terms: Fall 2019
Instructors: Hayer, Arnold; Wiseman, Paul; Guichard, Frederic; Michnick, Stephen W.; Brouhard, Gary; Oeffinger, Marlene; Ehrlicher, Allen; Xia, Yu; Hendricks, Adam; Bui, Khanh Huy (Fall)
Fall
Prerequisites: BIOL 219; or BIOL 200 plus BIOL 201 or ANAT 212 or BIOC 212; CHEM 212; COMP 202 or COMP 204 or COMP 250; MATH 222; or permission of instructor.
Restriction: Only open to U2 students in the following programs: B.Sc.; Major and Honours in Biology; Quantitative Biology, B.Sc.; Major and Honours Computer Science and Biology, B.Sc.; Major Biology and Mathematics, B.Sc.; Major Physiology and Mathematics, B.Sc.; Major Physiology and Physics, B.Sc.; Major and Honours Chemistry; Biophysical Chemistry, and B.Sc.; Major and Honours Physics; Biological Physics.
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CHEM 212 Introductory Organic Chemistry 1 (4 credits) *
Overview
Chemistry : A survey of reactions of aliphatic and aromatic compounds including modern concepts of bonding, mechanisms, conformational analysis, and stereochemistry.
Terms: Fall 2019, Winter 2020, Summer 2020
Instructors: Pavelka, Laura; Vlaho, Danielle; Daoust, Michel (Fall) Pavelka, Laura; Luedtke, Nathan; Vlaho, Danielle; Gauthier, Jean-Marc (Winter) Sirjoosingh, Pallavi; Vlaho, Danielle; Pavelka, Laura (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 ().
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COMP 202 Foundations of Programming (3 credits) **
Overview
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 2019, Winter 2020, Summer 2020
Instructors: Patitsas, Elizabeth; Alberini, Giulia (Fall) Alberini, Giulia (Winter) Campbell, Jonathan (Summer)
3 hours
Prerequisite: a CEGEP level mathematics course
Restrictions: COMP 202 and COMP 208 cannot both be taken for credit. COMP 202 is intended as a general introductory course, while COMP 208 is intended for students interested in scientific computation. COMP 202 cannot be taken for credit with or after COMP 250
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MATH 222 Calculus 3 (3 credits) ***
Overview
Mathematics & Statistics (Sci) : Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.
Terms: Fall 2019, Winter 2020, Summer 2020
Instructors: Macdonald, Jeremy; Causley, Broderick (Fall) Fortier, J茅r么me (Winter) Fortier, J茅r么me (Summer)
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MATH 223 Linear Algebra (3 credits) ***
Overview
Mathematics & Statistics (Sci) : Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications.
Terms: Fall 2019, Winter 2020
Instructors: Kelome, Djivede (Fall) Macdonald, Jeremy (Winter)
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MATH 247 Honours Applied Linear Algebra (3 credits) **
Overview
Mathematics & Statistics (Sci) : Matrix algebra, determinants, systems of linear equations. Abstract vector spaces, inner product spaces, Fourier series. Linear transformations and their matrix representations. Eigenvalues and eigenvectors, diagonalizable and defective matrices, positive definite and semidefinite matrices. Quadratic and Hermitian forms, generalized eigenvalue problems, simultaneous reduction of quadratic forms. Applications.
Terms: Winter 2020
Instructors: Hoheisel, Tim (Winter)
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MATH 315 Ordinary Differential Equations (3 credits) +
Overview
Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Terms: Fall 2019, Winter 2020, Summer 2020
Instructors: Nave, Jean-Christophe (Fall) B茅langer-Rioux, Rosalie (Winter) Roth, Charles (Summer)
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MATH 323 Probability (3 credits) ++
Overview
Mathematics & Statistics (Sci) : Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.
Terms: Fall 2019, Winter 2020, Summer 2020
Instructors: Correa, Jose Andres; Alam, Shomoita (Fall) Kelome, Djivede; Wolfson, David B (Winter) Kelome, Djivede (Summer)
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MATH 324 Statistics (3 credits) +++
Overview
Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Terms: Fall 2019, Winter 2020
Instructors: Asgharian-Dastenaei, Masoud (Fall) Luo, Yu; Hurtubise, Jacques Claude (Winter)
Fall and Winter
Prerequisite: MATH 323 or equivalent
Restriction: Not open to students who have taken or are taking MATH 357
You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
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MATH 325 Honours Ordinary Differential Equations (3 credits) +
Overview
Mathematics & Statistics (Sci) : First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.
Terms: Winter 2020
Instructors: Lessard, Jean-Philippe (Winter)
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MATH 356 Honours Probability (3 credits) ++
Overview
Mathematics & Statistics (Sci) : Sample space, probability axioms, combinatorial probability. Conditional probability, Bayes' Theorem. Distribution theory with special reference to the Binomial, Poisson, and Normal distributions. Expectations, moments, moment generating functions, uni-variate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.
Terms: Fall 2019
Instructors: Khalili Mahmoudabadi, Abbas (Fall)
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MATH 357 Honours Statistics (3 credits) +++
Overview
Mathematics & Statistics (Sci) : Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chi-squared goodness of fit test. Introduction to regression analysis and analysis of variance.
Terms: Winter 2020
Instructors: Neslehova, Johanna (Winter)
* Students who have taken the equivalent of CHEM 212 or MATH 222 can make up the credits with complementary 3 or 4 credit courses 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.
*** Students take MATH 223 or MATH 247.
+ Students take MATH 315 or MATH 325.
++ Students take MATH 323 or MATH 356.
+++ Students take MATH 324 or MATH 357.
Note: 6 credits of either MATH or PHYS courses to be taken at the honours level. Honours equivalents of core Math and Physics courses are listed. All 500-level Math courses are considered as honours courses and can be applied to the 6 credit requirement.
Biology (6 credits)
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BIOL 202 Basic Genetics (3 credits)
Overview
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 2020, Summer 2020
Instructors: Moon, Nam Sung; Nilson, Laura; Schoen, Daniel J; Western, Tamara (Winter) Dankort, David; Hipfner, David (Summer)
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BIOL 215 Introduction to Ecology and Evolution (3 credits)
Overview
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 2019
Instructors: Price, Neil; Abouheif, Ehab; Sunday, Jennifer (Fall)
Research Component (6 credits)
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BIOL 468 Independent Research Project 3 (6 credits)
Overview
Biology (Sci) : Independent research project.
Terms: Fall 2019, Winter 2020, Summer 2020
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
Fall, Winter or Summer
Prerequisite: BIOL 206 or BIOL 301 or other suitable laboratory course
Restriction: Open only to Biology students. Not open to students who have taken BIOL 471 or BIOL 471D1/D2.
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.
Physics (6 credits)
6 credits from:
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PHYS 230 Dynamics of Simple Systems (3 credits) *
Overview
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 2019
Instructors: Guo, Hong (Fall)
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PHYS 232 Heat and Waves (3 credits) **
Overview
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 2020
Instructors: Rutledge, Robert (Winter)
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PHYS 251 Honours Classical Mechanics 1 (3 credits) *
Overview
Physics : Newton's laws, work energy, angular momentum. Harmonic oscillator, forced oscillations. Inertial forces, rotating frames. Central forces, centre of mass, planetary orbits, Kepler's laws.
Terms: Fall 2019
Instructors: Gale, Charles (Fall)
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PHYS 253 Thermal Physics (3 credits) **
Overview
Physics : Energy, work, heat; first law. Temperature, entropy; second law. Absolute zero; third law. Equilibrium, equations of state, gases, liquids, solids, magnets; phase transitions.
Terms: Fall 2019
Instructors: Caron-Huot, Simon (Fall)
* Students take PHYS 230 or PHYS 251.
** Students take PHYS 232 or PHYS 253.
Course Requirements for Quantitative Biology Streams
21 credits from one of the following two streams:
Stream 1: Theoretical Ecology and Evolutionary Biology (21 credits)
Biology
12 credits from the following:
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BIOL 205 Biology of Organisms (3 credits)
Overview
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 2020
Instructors: Sakata, Jon; Hargreaves, Anna (Winter)
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BIOL 206 Methods in Biology of Organisms (3 credits)
Overview
Biology (Sci) : Introduction to modern methods used in organismal biology, including ecological sampling, experimental methods and statistics, taxonomic and phylogenetic analysis of biodiversity, experimental behavioural ecology, microbiological methods, and library search procedures.
Terms: Fall 2019
Instructors: Cristescu, Elena; Miller-Nesbitt, Andrea; Larsson, Hans Carl; Lefebvre, Louis; Gonzalez, Andrew (Fall)
Fall
1.5 hours lecture, 3 hours laboratory and local field trip in week 1
Prerequisite: BIOL 111 or equivalent
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BIOL 304 Evolution (3 credits)
Overview
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 2019
Instructors: Bell, Graham (Fall)
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BIOL 308 Ecological Dynamics (3 credits)
Overview
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: Fall 2019
Instructors: Guichard, Frederic (Fall)
Field Courses
3 credits from the following list or any other field course with permission:
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BIOL 240 Monteregian Flora (3 credits)
Overview
Biology (Sci) : Field studies of ferns, fern allies, conifers and flowering plants; the use of keys for plant identification.
Terms: This course is not scheduled for the 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
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鈥檚 Gault Nature Reserve in Mont St. Hilaire, has an additional fee of $445.48 which includes a hand lens, a textbook, handouts, lodging and supper each day.
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BIOL 331 Ecology/Behaviour Field Course (3 credits)
Overview
Biology (Sci) : Methods of sampling natural populations. Testing hypotheses in nature.
Terms: Fall 2019
Instructors: Reader, Simon; Barrett, Rowan; Hargreaves, Anna (Fall)
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BIOL 334 Applied Tropical Ecology (3 credits)
Overview
Biology (Sci) : Relevant to agriculture, forestry, fisheries and conservation of natural resources. Field component taught at the University's Bellairs Research Institute in Barbados, for two weeks in early May. The course is organized in a series of small-group field projects of 2-3 days each. Interested students should contact the Undergraduate Office and fill out an application form.
Terms: Winter 2020
Instructors: Guichard, Frederic; Nilson, Laura; Price, Neil (Winter)
Summer
Prerequisites: BIOL 206; and BIOL 215 or both ENVR 200 and ENVR 202; and permission of the instructor.
This course, given in Barbados, has an additional fee of $1450 to cover the costs of room and board at Bellairs Research Institute, the course pack and all other expenses during the course. It does not cover tuition, airfare, flight insurance, airport taxes, meals in transit, or the cost of supplementary health insurance. 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.
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BIOL 432 Limnology (3 credits)
Overview
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 2019
Instructors: Fussmann, Gregor (Fall)
Fall
2 hours lecture; 2 weekends at field station equivalent to 3 hours laboratory per week
Prerequisites: BIOL 206 and BIOL 215 or permission of instructor.
This course, involving two field weekends, has an additional fee of $332.72, 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.
Restrictions: Not open to students who have taken or are taking ENVB 315.
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.
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BIOL 432 Limnology (3 credits)
Overview
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 2019
Instructors: Fussmann, Gregor (Fall)
Fall
2 hours lecture; 2 weekends at field station equivalent to 3 hours laboratory per week
Prerequisites: BIOL 206 and BIOL 215 or permission of instructor.
This course, involving two field weekends, has an additional fee of $332.72, 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.
Restrictions: Not open to students who have taken or are taking ENVB 315.
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BIOL 434 Theoretical Ecology (3 credits)
Overview
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 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
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BIOL 435 Natural Selection (3 credits)
Overview
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 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
Fall
3 hours of lecture
Prerequisite: BIOL 304 or permission of instructor.
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BIOL 465 Conservation Biology (3 credits)
Overview
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 2019
Instructors: Chapman, Lauren; Gonzalez, Andrew (Fall)
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BIOL 509 Methods in Molecular Ecology (3 credits)
Overview
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 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
- BIOL 510 Advances in Community Ecology (3 credits)
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BIOL 515 Advances in Aquatic Ecology (3 credits)
Overview
Biology (Sci) : Aquatic ecology and the major issues challenging the field.
Terms: This course is not scheduled for the 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
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BIOL 540 Ecology of Species Invasions (3 credits)
Overview
Biology (Sci) : Causes and consequences of biological invasion, as well as risk assessment methods and management strategies for dealing with invasive species.
Terms: Winter 2020
Instructors: Ricciardi, Anthony (Winter)
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BIOL 594 Advanced Evolutionary Ecology (3 credits)
Overview
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 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
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BIOL 596 Advanced Experimental Design (1 credit) *
Overview
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 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
Prerequisite: BIOL 373 or equivalent and permission of instructor
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BIOL 597 Advanced Biostatistics (2 credits) *
Overview
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 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
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BIOL 598 Advanced Design and Statistics (3 credits) *
Overview
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 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
Stream 2: Physical Biology
21 credits
9 credits from:
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BIOL 319 Introduction to Biophysics (3 credits) *
Overview
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 2020
Instructors: Wiseman, Paul (Winter)
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PHYS 319 Introduction to Biophysics (3 credits) *
Overview
Physics : 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 2020
Instructors: Wiseman, Paul (Winter)
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PHYS 329 Statistical Physics with Biophysical Applications (3 credits)
Overview
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: Winter 2020
Instructors: Francois, Paul (Winter)
* Students choose either BIOL 319 or PHYS 319
300-level complementary courses
6 credits from the following:
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BIOL 300 Molecular Biology of the Gene (3 credits)
Overview
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 2019
Instructors: Sch枚ck, Frieder; Moon, Nam Sung (Fall)
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BIOL 303 Developmental Biology (3 credits)
Overview
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 2020
Instructors: Gerhold, Abigail; Rao, Yong; Dufort, Daniel (Winter)
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BIOL 306 Neural Basis of Behaviour (3 credits)
Overview
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 2019
Instructors: Sakata, Jon; Dent, Joseph Alan; Watt, Alanna (Fall)
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BIOL 309 Mathematical Models in Biology (3 credits)
Overview
Biology (Sci) : Application of finite difference and differential equations to problems in cell and developmental biology, ecology and physiology. Qualitative, quantitative and graphical techniques are used to analyze mathematical models and to compare theoretical predictions with experimental data.
Terms: Fall 2019
Instructors: Bub, Gil (Fall)
Fall
3 hours lecture
Prerequisite: one year of calculus. An additional course in calculus is recommended
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BIOL 313 Eukaryotic Cell Biology (3 credits)
Overview
Biology (Sci) : Cell biology of eukaryotes focusing on the assembly and function of cellular structures, the regulation of transcription; the dynamics of the cytoskeleton and its motors; mechanics of cell division; cell cycle and checkpoints; nuclear dynamics; chromosome structure and behaviour and experimental techniques.
Terms: Winter 2020
Instructors: Weber, Stephanie (Winter)
500-level complementary courses
6 credits from the following:
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BIOL 518 Advanced Topics in Cell Biology (3 credits)
Overview
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 2020
Instructors: Reyes Lamothe, Rodrigo; Zetka, Monique (Winter)
Winter
3 hours seminar
Prerequisite: BIOL 313 or permission
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BIOL 520 Gene Activity in Development (3 credits)
Overview
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: Winter 2020
Instructors: Gerhold, Abigail (Winter)
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BIOL 524 Topics in Molecular Biology (3 credits)
Overview
Biology (Sci) : Molecular genetics and molecular, cellular and developmental biology, including signal transduction, cell differentiation and function, genetic diseases in eukaryotes.
Terms: Fall 2019
Instructors: Clarke, Hugh; Dankort, David (Fall)
- BIOL 530 Advances in Neuroethology (3 credits)
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BIOL 551 Principles of Cellular Control (3 credits)
Overview
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 2020
Instructors: Vogel, Jacalyn; Francois, Paul; Reyes Lamothe, Rodrigo; Weber, Stephanie; Hayer, Arnold; Gerhold, Abigail (Winter)
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BIOL 588 Advances in Molecular/Cellular Neurobiology (3 credits)
Overview
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: This course is not scheduled for the 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
Complementary Courses (9 credits)
Recommendations for either Theoretical Ecology and Evolutionary Biology or Physical Biology streams
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COMP 206 Introduction to Software Systems (3 credits)
Overview
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 2019, Winter 2020
Instructors: Vybihal, Joseph P (Fall) Vybihal, Joseph P; D'silva, Joseph (Winter)
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COMP 250 Introduction to Computer Science (3 credits)
Overview
Computer Science (Sci) : Mathematical tools (binary numbers, induction, recurrence relations, asymptotic complexity, establishing correctness of programs), 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 2019, Winter 2020
Instructors: Langer, Michael; Alberini, Giulia (Fall) Alberini, Giulia; Sarrazin Gendron, Roman (Winter)
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COMP 251 Algorithms and Data Structures (3 credits)
Overview
Computer Science (Sci) : Introduction to algorithm design and analysis. Graph algorithms, greedy algorithms, data structures, dynamic programming, maximum flows.
Terms: Fall 2019, Winter 2020
Instructors: Waldispuhl, J茅r么me (Fall) Devroye, Luc P (Winter)
3 hours
Prerequisite: COMP 250
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 and 363, 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.
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COMP 350 Numerical Computing (3 credits) *
Overview
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 2019
Instructors: Panayotov, Ivo; Luan, Sitao (Fall)
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COMP 364 Computer Tools for Life Sciences (3 credits)
Overview
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 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
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MATH 235 Algebra 1 (3 credits) **
Overview
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 2019
Instructors: Wise, Daniel (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent
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MATH 240 Discrete Structures (3 credits) **
Overview
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 2019, Winter 2020
Instructors: Macdonald, Jeremy; Nica, Bogdan (Fall) Macdonald, Jeremy; Lumley, Allysa (Winter)
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MATH 314 Advanced Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.
Terms: Fall 2019, Winter 2020
Instructors: Roth, Charles (Fall) McGregor, Geoffrey; Hurtubise, Jacques Claude (Winter)
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MATH 317 Numerical Analysis (3 credits) *
Overview
Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Terms: Fall 2019
Instructors: Bartello, Peter (Fall)
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MATH 319 Introduction to Partial Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems.
Terms: Winter 2020
Instructors: Laborde, Maxime; Hurtubise, Jacques Claude (Winter)
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MATH 326 Nonlinear Dynamics and Chaos (3 credits)
Overview
Mathematics & Statistics (Sci) : Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Terms: Fall 2019
Instructors: Humphries, Antony Raymond (Fall)
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MATH 327 Matrix Numerical Analysis (3 credits)
Overview
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: This course is not scheduled for the 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
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MATH 348 Euclidean Geometry (3 credits)
Overview
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鈥檚 theorem. Isometries. Homothety. Inversion.
Terms: Fall 2019
Instructors: Lipnowski, Michael (Fall)
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MATH 437 Mathematical Methods in Biology (3 credits)
Overview
Mathematics & Statistics (Sci) : The formulation and treatment of realistic mathematical models describing biological phenomena through qualitative and quantitative mathematical techniques (e.g. local and global stability theory, bifurcation analysis and phase plane analysis) and numerical simulation. Concrete and detailed examples will be drawn from molecular and cellular biology and mammalian physiology.
Terms: Winter 2020
Instructors: Khadra, Anmar (Winter)
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MATH 447 Introduction to Stochastic Processes (3 credits)
Overview
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 2020
Instructors: Steele, Russell (Winter)
* Students may take COMP 350 OR MATH 317.
** MATH 235 or MATH 240 are required for COMP 251.
Recommendations for Physical Biology stream
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BIEN 310 Introduction to Biomolecular Engineering (3 credits)
Overview
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 2019
Instructors: Xia, Yu (Fall)
Prerequisite(s): BIEN 200 or permission of instructor.
(3-0-6)
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BIEN 320 Molecular, Cellular and Tissue Biomechanics (3 credits)
Overview
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 2020
Instructors: Ehrlicher, Allen (Winter)
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BIEN 340 Transport Phenomena in Biological Systems 2 (3 credits)
Overview
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 2020
Instructors: Kamen, Amine (Winter)
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BIEN 510 Engineered Nanomaterials for Biomedical Applications (3 credits)
Overview
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 2019
Instructors: Sudalaiyadum Perumal, Ayyappasamy (Fall)
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BIEN 530 Imaging and Bioanalytical Instrumentation (3 credits)
Overview
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 2020
Instructors: Hendricks, Adam (Winter)
Prerequisite: Permission of instructor.
(3-1-5)
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CHEM 222 Introductory Organic Chemistry 2 (4 credits)
Overview
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 2019, Winter 2020, Summer 2020
Instructors: Vlaho, Danielle; Daoust, Michel; Auclair, Karine; Pavelka, Laura (Fall) Pavelka, Laura; Moitessier, Nicolas; Vlaho, Danielle; Gauthier, Jean-Marc (Winter) Pavelka, Laura; Vlaho, Danielle; Sirjoosingh, Pallavi (Summer)
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PHYS 242 Electricity and Magnetism (2 credits) *
Overview
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 2019
Instructors: Chiang, Hsin Cynthia (Fall)
Fall
2 hours lectures
Prerequisites: CEGEP Physics, MATH 222
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PHYS 257 Experimental Methods 1 (3 credits)
Overview
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 2019
Instructors: Siwick, Bradley (Fall)
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PHYS 342 Majors Electromagnetic Waves (3 credits)
Overview
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 2020
Instructors: Gervais, Guillaume (Winter)
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PHYS 413 Physical Basis of Physiology (3 credits)
Overview
Physics : Analytic and computer simulation techniques are used to examine the role of nonlinearities and time delays in determining the dynamic behaviour of physiological control systems and their relation to normal and pathophysiological states. Examples drawn from the control of respiration, cellular proliferation and differentiation, biochemical feedback networks, thermoregulatory mechanisms, and neural feedback.
Terms: This course is not scheduled for the 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
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PHYS 434 Optics (3 credits)
Overview
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; Fourier optics; selected special topics such as holography, lasers, beam optics, photonic crystals, advanced spectroscopy, stellar interferometry, quantum optics.
Terms: Fall 2019
Instructors: Cooke, David (Fall)
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PHYS 519 Advanced Biophysics (3 credits)
Overview
Physics : An advanced biophysics course, with a special emphasis on stochastic and out of equilibrium physical processes in living matter.
Terms: Winter 2020
Instructors: Francois, Paul (Winter)
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PHYS 534 Nanoscience and Nanotechnology (3 credits)
Overview
Physics : Topics include scanning probe microscopy, chemical self-assembly, computer modelling, and microfabrication/micromachining.
Terms: Fall 2019
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
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BIOL 310 Biodiversity and Ecosystems (3 credits)
Overview
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 2020
Instructors: Sunday, Jennifer; Gonzalez, Andrew; Pollock, Laura (Winter)
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BIOL 324 Ecological Genetics (3 credits)
Overview
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: Fall 2019
Instructors: Schoen, Daniel J (Fall)
Fall
Prerequisite: BIOL 202
Two lectures per week; one required computer lab or conference per week
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MATH 242 Analysis 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Terms: Fall 2019
Instructors: Vetois, Jerome (Fall)
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MATH 340 Discrete
Mathematics (3 credits)
Overview
Mathematics & Statistics (Sci) : Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
Terms: Winter 2020
Instructors: Fortier, J茅r么me (Winter)
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MATH 423 Applied RegressionApplied Regression (3 credits)
Overview
Mathematics & Statistics (Sci) : Least-squares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chi-squared distributions; quadratic forms. General linear hypothesis: F-test and t-test. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.
Terms: Fall 2019
Instructors: Yang, Yi (Fall)
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MATH 524 Nonparametric Statistics (4 credits)
Overview
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: This course is not scheduled for the 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
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MATH 525 Sampling Theory and Applications (4 credits)
Overview
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: This course is not scheduled for the 2019-2020 academic year.
Instructors: There are no professors associated with this course for the 2019-2020 academic year.
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PHYS 329 Statistical Physics with Biophysical Applications (3 credits)
Overview
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: Winter 2020
Instructors: Francois, Paul (Winter)
