Minor Programs

Civil Engineering students can choose to either broaden their background or attain in-depth coverage of a particular subject by enrolling in a Minor Program. Minors are coherent sequences of courses that may be taken in addition to the courses required for the BEng degree.

Minor programs normally consist of 18 to 24 credits, allowing up to 12 credits of overlap with a degree program. The real credit cost to the students is typically 9 to 15 credits, representing one semester beyond the BEng degree program. All courses in a Minor program must be passed with a grade of C or better.

In particular, Civil Engineering students are most inclined to enrol in the following Minor programs:

Arts Minor (B.Eng.) (24 credits)
Offered by: Engineering - Dean's Office听(Faculty of Engineering) 听听
Degree: Bachelor of Engineering
Program credit weight: 24

Program 听Description

Minor Adviser: Faculty Student Adviser in the Engineering Student Centre (Frank Dawson Adams Building, Room 22)

B.Sc.(Arch.), and B.Eng., students may obtain the Arts Minor as part of their B.Eng., or B.Sc.(Arch.) degree by completing 24 credits, as described below.

Students must select courses for this Minor in consultation with one of the Advisers indicated above.

All courses in the Minor must be passed with a grade of C or better.

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Requirements

24 credits as follows:
1. At least two areas of concentration in the Faculty of Arts must be chosen, with a minimum of 6 credits in any one area.
2. At least 12 credits must be at the 300 level or higher.
In general, B.Eng. students may use courses from the Complementary Studies lists (Group A and Group B) in their program that are offered by the Faculty of Arts to satisfy some of these requirements. No more than 9 credits of these courses can be credited toward the Arts Minor.

Computer Science Minor (B.Eng.) (25 credits)

Offered by: Computer Science听(Faculty of Science) 听听
Degree: Bachelor of Engineering
Program credit weight: 25

Program 听Description

24-26 credits

This program gives students in Engineering an introduction to core computer science concepts. The Minor is open to B.Eng. and B.Sc.(Arch.) students in Engineering who have already taken 贰颁厂贰听202 Introduction to Software Development., 颁翱惭笔听202 Foundations of Programming., or 颁翱惭笔听208 Computer Programming for Physical Sciences and Engineering .. This program is not open to students in the B.Eng.; Co-op in Software Engineering program. All courses in the Minor must be passed with a grade of C or better. The Minor program may be completed in 24-26 credits, of which no more than 6 credits may overlap with the primary program. Students who are interested in this Minor should consult with the Undergraduate Program CooThis program gives students in Engineering an introduction to core computer science concepts. The Minor is open to B.Eng. and B.Sc.(Arch.) students in Engineering who have already taken 贰颁厂贰听202 Introduction to Software Development., 颁翱惭笔听202 Foundations of Programming., or 颁翱惭笔听208 Computer Programming for Physical Sciences and Engineering .. This program is not open to students in the B.Eng.; Co-op in Software Engineering program. All courses in the Minor must be passed with a grade of C or better. The Minor program may be completed in 24-26 credits, of which no more than 6 credits may overlap with the primary program. Students who are interested in this Minor should consult with the Undergraduate Program Coordinator in the School of Computer Science for administrative matters, and should consult with both the Minor Adviser in Computer Science and with their department adviser for approval of their course selection. Forms must be submitted and approved before the end of the drop/add period of the student's final term

Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.

Required Courses (3 credits)

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Course	Title	Credits
COMP 206	Introduction to Software Systems.	3
Introduction to Software Systems. Terms offered: this course is not currently offered. 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.

Complementary Courses (21-23 credits)

3 credits from the following:

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Course	Title	Credits
COMP 250	Introduction to Computer Science.	3
Introduction to Computer Science. Terms offered: this course is not currently offered. Mathematical tools (binary numbers, induction,recurrence relations, asymptotic complexity,establishing correctness of programs). Datastructures (arrays, stacks, queues, linked lists,trees, binary trees, binary search trees, heaps,hash tables). Recursive and non-recursivealgorithms (searching and sorting, tree andgraph traversal). Abstract data types. Objectoriented programming in Java (classes andobjects, interfaces, inheritance). Selected topics.
ECSE 250	Fundamentals of Software Development.	3
Fundamentals of Software Development. Terms offered: this course is not currently offered. Software development practices in the context of object-oriented programming. Elementary data structures such as lists, stacks and trees. Recursive and non-recursive algorithms: searching and sorting, tree and graph traversal. Asymptotic notation: Big O. Introduction to tools and practices employed in commercial software development.

3 credits from the following:

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Course	Title	Credits
COMP 302	Programming Languages and Paradigms.	3
Programming Languages and Paradigms. Terms offered: this course is not currently offered. Programming language design issues and programming paradigms. Binding and scoping, parameter passing, lambda abstraction, data abstraction, type checking. Functional and logic programming.
COMP 303	Software Design.	3
Software Design. Terms offered: this course is not currently offered. Principles, mechanisms, techniques, and tools for object-oriented software design and its implementation, including encapsulation, design patterns, and unit testing.

3-4 credits from the following:

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Course	Title	Credits
COMP 273	Introduction to Computer Systems.	3
Introduction to Computer Systems. Terms offered: this course is not currently offered. Number representations, combinational and sequential digital circuits, MIPS instructions and architecture datapath and control, caches, virtual memory, interrupts and exceptions, pipelining.
ECSE 324	Computer Organization.	4
Computer Organization. Terms offered: this course is not currently offered. Basic computer structures; instruction set architecture; assembly language; input/output; memory; software; processor implementation; computer arithmetic. Lab work involving assembly language level programming of single-board computers.

3-4 credits from the following:

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Course	Title	Credits
CHEE 390	Computational Methods in Chemical Engineering.	3
Computational Methods in Chemical Engineering. Terms offered: this course is not currently offered. Linear systems of algebraic equations, Gaussian elimination; non-linear algebraic systems: Taylor series, incremental search, bisection method, linear interpolation, Newton-Raphson's method; differentiation and integration; initial value problems: Euler's and Runge Kutta's methods, stiff equations, adaptive solvers; boundary value problems; curve fitting; numerical optimization; probability theory and stochastic simulation: Monte Carlo method.
CIVE 320	Numerical Methods.	4
Numerical Methods. Terms offered: this course is not currently offered. Numerical procedures applicable to civil engineering problems: integration, differentiation, solution of initial-value problems, solving linear and non-linear systems of equations, boundary-value problems for ordinary-differential equations, and for partial-differential equations.
COMP 350	Numerical Computing.	3
Numerical Computing. Terms offered: this course is not currently offered. 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.
ECSE 343	Numerical Methods in Engineering.	3
Numerical Methods in Engineering. Terms offered: this course is not currently offered. Number representation and numerical error. Symbolic vs. numerical computation. Curve fitting and interpolation. Numerical differentiation and integration. Optimization. Data science pipelines and data-driven approaches. Preliminary machine learning. Solutions of systems of linear equations and nonlinear equations. Solutions of ordinary and partial differential equations. Applications in engineering, physical simulation, CAD, machine learning and digital media.
MATH 317	Numerical Analysis.	3
Numerical Analysis. Terms offered: this course is not currently offered. Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
MECH 309	Numerical Methods in Mechanical Engineering.	3
Numerical Methods in Mechanical Engineering. Terms offered: this course is not currently offered. Numerical techniques for problems commonly encountered in Mechanical Engineering are presented. Chebyshev interpolation, quadrature, roots of equations in one or more variables, matrices, curve fitting, splines and ordinary differential equations. The emphasis is on the analysis and understanding of the problem rather than the details of the actual numerical program.

9 credits from:

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Course	Title	Credits
COMP 251	Algorithms and Data Structures.	3
Algorithms and Data Structures. Terms offered: this course is not currently offered. Data Structures: priority queues, balanced binary search trees, hash tables, graphs. Algorithms: topological sort, connected components, shortest paths, minimum spanning trees, bipartite matching, network flows. Algorithm design: greedy, divide and conquer, dynamic programming, randomization. Mathematicaltools: proofs of asymptotic complexity and program correctness, Master theorem.
MATH 240	Discrete Structures.	3
Discrete Structures. Terms offered: this course is not currently offered. 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.

COMP courses at the 300 level or above except 颁翱惭笔听396 Undergraduate Research Project., 颁翱惭笔听400 Project in Computer Science.

It is strongly recommended that students take 颁翱惭笔听251 Algorithms and Data Structures., as it is a prerequisite of many later computer science courses.

Construction Engineering and Management Minor (B.Eng.) (24 credits)

Offered by: Civil Engineering (Faculty of Engineering)听听听
Degree: Bachelor of Engineering
Program credit weight: 24

Program 听Description

This Minor covers construction project management, law related to construction, labour-management relations, financial accounting and project finance, in addition to topics in other construction-related fields, architecture or mining engineering.

All courses in the Minor must be passed with a grade of C or better.

A maximum of 12 credits of coursework in the student's major may double-count with the Minor.

Minor Adviser: Prof. L. Chouinard, Macdonald Engineering Building, Room 491 (Telephone: 514-398-6446)

Minor program credit weight: 24 credits

Note: This Minor is particularly designed for Civil Engineering students, but is open to all B.Eng. and B.Sc.(Arch.) students.

All courses in the Minor must be passed with a grade of C or better.

Prerequisites

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Course	Title	Credits
CIVE 208	Civil Engineering System Analysis.	3
Civil Engineering System Analysis. Terms offered: this course is not currently offered. Introduction to civil engineering systems; system modelling process; systems approach and optimization techniques; application of linear programming; simplex method; duality theory; sensitivity analysis; transportation problem; assignment problem; network analysis including critical path method; integer linear programming method.
CIVE 302	Probabilistic Systems.	3
Probabilistic Systems. Terms offered: this course is not currently offered. An introduction to probability and statistics with applications to Civil Engineering design. Descriptive statistics, common probability models, statistical estimation, regression and correlation, acceptance sampling.
COMP 208	Computer Programming for Physical Sciences and Engineering .	3
Computer Programming for Physical Sciences and Engineering . Terms offered: this course is not currently offered. Programming and problem solving in a high level computer language: variables, expressions, types, functions, conditionals, loops, objects and classes. Introduction to algorithms such as searching and sorting. Modular software design, libraries, file input and output, debugging. Emphasis on applications in Physical Sciences and Engineering, such as root finding, numerical integration, diffusion, Monte Carlo methods.
FACC 300	Engineering Economy.	3
Engineering Economy. Terms offered: Summer 2025 Introduction to the basic concepts required for the economic assessment of engineering projects. Topics include: accounting methods, marginal analysis, cash flow and time value of money, taxation and depreciation, discounted cash flow analysis techniques, cost of capital, inflation, sensitivity and risk analysis, analysis of R and D, ongoing as well as new investment opportunities.

Required Courses: Management and Law (15 credits)

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Course	Title	Credits
CIVE 324	Sustainable Project Management.	3
Sustainable Project Management. Terms offered: this course is not currently offered. Lifecycle approach to project and construction management. Sustainable practices are introduced at all project stages: Team formation, materials and equipment use, cost estimation and economic valuation, financing, scheduling, quality control and safety, monitoring and performance assessment, decision-making.
FACC 220	Law for Architects and Engineers.	3
Law for Architects and Engineers. Terms offered: this course is not currently offered. Aspects of the law which affect architects and engineers. Definition and branches of law; Federal and Provincial jurisdiction, civil and criminal law and civil and common law; relevance of statutes; partnerships and companies; agreements; types of property, rights of ownership; successions and wills; expropriation; responsibility for negligence; servitudes/easements, privileges/liens, hypothecs/ mortgages; statutes of limitations; strict liability of architect, engineer and builder; patents, trade marks, industrial design and copyright; bankruptcy; labour law; general and expert evidence; court procedure and arbitration.
INDR 294	Introduction to Labour-Management Relations.	3
Introduction to Labour-Management Relations. Terms offered: this course is not currently offered. An introduction to labour-management relations, the structure, function and government of labour unions, labour legislation, the collective bargaining process, and the public interest in industrial relations.
MGCR 211	Introduction to Financial Accounting.	3
Introduction to Financial Accounting. Terms offered: Summer 2025 The role of financial accounting in the reporting of the financial performance of a business. The principles, components and uses of financial accounting and reporting from a user's perspective, including the recording of accounting transactions and events, the examination of the elements of financial statements, the preparation of financial statements and the analysis of financial results.
MGCR 341	Introduction to Finance.	3
Introduction to Finance. Terms offered: Summer 2025 An introduction to the principles, issues, and institutions of Finance. Topics include valuation, risk, capital investment, financial structure, cost of capital, working capital management, financial markets, and securities.

Complementary Courses (9 credits)

3 credits from List A

6 credits from List B

List A

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Course	Title	Credits
ARCH 447	Energy, Environment, and Buildings 2.	3
Energy, Environment, and Buildings 2. Terms offered: this course is not currently offered. Advanced exploration of the interrelationships among energy, environment, and building. Topics include energy efficiency, thermal envelopes, life-cycle design, materials selection, fluid mechanics of natural ventilation, thermal science of passive design, adaptive thermal comfort, the 'air-conditioning trap', the 'embodied carbon blindspot,' and the 'timber-carbon sink'.
ARCH 451	Building Regulations and Safety.	3
Building Regulations and Safety. Terms offered: this course is not currently offered. The study of building codes with specific emphasis on the National Building and National Fire Codes of Canada. Examples of existing buildings with assignments to illustrate regulations. Development of a systematic approach to the implementation of codes during the preliminary design stage of an architectural project.
MIME 322	Fragmentation and Comminution.	3
Fragmentation and Comminution. Terms offered: this course is not currently offered. Principles of drilling, penetration rates, and factors affecting the choice of drilling method. Characteristics of explosives, firing systems and blast patterns. Blasting techniques in surface and underground workings. Special blasting techniques at excavation perimeters. Vibration and noise control. Mechanical and continuous approaches to fragmentation, including longwall shearing and fullface boring. Economics of drill/blast practice, interface with transport and crushing systems, drivers for mine-to-mill integration including energy considerations. Modelling of fragment and particle size distributions; comminution as a transfer function. Comminution technology: crushing, grinding, size classification. Integrated analysis of fragmentation and comminution operations.
MIME 333	Materials Handling.	3
Materials Handling. Terms offered: this course is not currently offered. Physical and mechanical characteristics of materials related to loading, transport and storage. Dynamics of particles, systems and rigid bodies, mass-acceleration, work-energy, impulse-momentum. Types and selection of excavation and haulage equipment. Layout of haul roads. Rail transport. Conveyor belts and chain conveyors. Mine hoists. Layout of mine shafts.

List B

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Course	Title	Credits
CIVE 446	Construction Engineering.	3
Construction Engineering. Terms offered: this course is not currently offered. Project management principles; construction equipment economics, selection, operation; characteristics of building, heavy, marine, underground and route construction projects; international projects.
CIVE 527	Renovation and Preservation: Infrastructure.	3
Renovation and Preservation: Infrastructure. Terms offered: this course is not currently offered. Maintenance, rehabilitation, renovation and preservation of infrastructure; infrastructure degradation mechanisms; mechanical, chemical and biological degradation; corrosion of steel; condition surveys and evaluation of buildings and bridges; repair and preservation of materials, techniques and strategies; codes and guidelines; case studies, sustainable development; group project.
ECSE 461	Electric Machinery.	3
Electric Machinery. Terms offered: this course is not currently offered. Electric and magnetic circuits. Notions of electromechanical energy conversion applied to electrical machines. Basic electrical machines - transformers, direct-current motors, synchronous motors and generators, three phase and single phase induction machines. Elements of modern electronically controlled electric drive systems.
FINE 445	Real Estate Finance.	3
Real Estate Finance. Terms offered: this course is not currently offered. Fundamentals of mortgages from the viewpoint of both consumer and the firm. Emphasis on legal, mathematical and financial structure, provides a micro basis for analysis of the functions and performance of the mortgage market, in conjunction with the housing market.
MIME 520	Stability of Rock Slopes.	3
Stability of Rock Slopes. Terms offered: this course is not currently offered. Properties of structural discontinuities. Influence of geological structures on slope stability. Kinematic analysis. Limit equilibrium methods. Empirical methods. Numerical modelling. Slope stabilization and monitoring. Case studies.
MIME 521	Stability of Underground Openings.	3
Stability of Underground Openings. Terms offered: this course is not currently offered. The properties of rock masses and stability classification systems. The influence and properties of geological structural features. Stability related to the design of underground openings and mining systems. Site investigations. Methods of stabilization.
MPMC 321	M茅canique des roches et contr么le des terrains. ¹	3
M茅canique des roches et contr么le des terrains. Terms offered: this course is not currently offered. Pressions de terrains au pourtour des excavations: solutions analytiques et num茅riques. Stabilit茅 des excavations souterraines et 脿 ciel ouvert: analyse des instabilit茅s structurales par projection st茅r茅ographique m茅ridienne, analyse des instabilit茅s caus茅es par les exc猫s de contraintes. Sout猫nement. Surveillance. 脡tudes de cas.

¹: Course offered in French at 脡cole Polytechnique in Montreal

Economics Minor (B.Eng.) (18 credits)

Offered by: Economics (Faculty of Arts)听听
Degree: Bachelor of Engineering
Program credit weight: 18

Program 听Description

The B.Eng.; Minor in Economics focuses on such economic topics as: how societies decide what to produce, how much of it, what determines prices, exchange rates, interest rates, and levels of inflation. How economies function internally and on a global scale, what drives consumers, and how public policy and global events affect markets. A maximum of 9 credits of coursework in the student's major may be double counted with the Minor.

Required Courses (18 credits)

6 credits from the following:

Expand allContract all Course List

Course	Title	Credits
ECON 230D1	Microeconomic Theory.	3
Microeconomic Theory. Terms offered: this course is not currently offered. The introductory course for Economics Major students in microeconomic theory. In depth and critical presentation of the theory of consumer behaviour, theory of production and cost curves, theory of the firm, theory of distribution, welfare economics and the theory of general equilibrium.
ECON 230D2	Microeconomic Theory.	3
Microeconomic Theory. Terms offered: this course is not currently offered. See ECON 230D1 for course description.
ECON 250D1	Introduction to Economic Theory: Honours.	3
Introduction to Economic Theory: Honours. Terms offered: this course is not currently offered. An intermediate level microeconomics course. Includes theory of exchange, theory of consumer behaviour, theory of production and cost curves, theory of the firm, theory of distribution; general equilibrium and welfare economics. The assumptions underlying the traditional neo-classical approach to economic theory will be carefully specified.
ECON 250D2	Introduction to Economic Theory: Honours.	3
Introduction to Economic Theory: Honours. Terms offered: this course is not currently offered. See ECON 250D1 for course description.

12 credits from:

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Course	Title	Credits
ECON 209	Macroeconomic Analysis and Applications.	3
Macroeconomic Analysis and Applications. Terms offered: Summer 2025 A university-level introduction to national income determination, money and banking, inflation, unemployment and economic policy.
ECON 225	Economics of the Environment.	3
Economics of the Environment. Terms offered: this course is not currently offered. A study of the application of economic theory to questions of environmental policy. Particular attention will be given to the measurement and regulation of pollution, congestion and waste and other environmental aspects of specific economies.
ECON 303	Canadian Economic Policy.	3
Canadian Economic Policy. Terms offered: this course is not currently offered. Major theories of how economic policy is made and goes on to use economic tools of analysis to investigate selected policy problems of current interest.
ECON 304	Financial Instruments and Institutions.	3
Financial Instruments and Institutions. Terms offered: this course is not currently offered. Economic analysis of initiating, assembling, pricing and marketing equities of bonds, bills and complex financial instruments; financial innovation; its implications for financial stability and market failure; banks as brokers, underwriters, market makers and international allocators of credit; strategies of private and public agents operating in financial markets, monetary history.
ECON 305	Industrial Organization.	3
Industrial Organization. Terms offered: this course is not currently offered. The course analyzes the structure, conduct, and performance of industries, particularly but not exclusively in Canada. Topics include effects of mergers, barriers to entry, product line and promotion policies, vertical integration, and R D policies of firms.
ECON 306	Labour Markets and Wages.	3
Labour Markets and Wages. Terms offered: this course is not currently offered. Examination of the implications on wage structures of differences in job conditions, levels and type training, long-term employment relationships, unionization etc. A variety of socioeconomic policy issues including subsidies for higher education, government regulation of workplace safety, and the role and treatment of women in today's labour force are explored.
ECON 308	Governmental Policy Towards Business.	3
Governmental Policy Towards Business. Terms offered: this course is not currently offered. Covers the major public policies toward business in Canada, such as competition policy, regulation, public ownership and privatization, industrial policies, and trade policies. Includes comparison with policies of other countries, especially the U.S. Readings will include some legal decisions.
ECON 313	Economic Development 1.	3
Economic Development 1. Terms offered: Summer 2025 Microeconomic theories of economic development and empirical evidence on population, labour, firms, poverty. Inequality and environment.
ECON 314	Economic Development 2.	3
Economic Development 2. Terms offered: this course is not currently offered. Macroeconomic development issues, including theories of growth, public finance, debt, currency crises, corruption, structural adjustment, democracy and global economic organization.
ECON 316	The Underground Economy.	3
The Underground Economy. Terms offered: this course is not currently offered. The origins, structure and operation of the "underground" sectors of modern economies around the world. Topics include the causes of black marketeering in Western economies; international contraband trade in guns and drugs; money laundering through the world financial system.
ECON 326	Ecological Economics.	3
Ecological Economics. Terms offered: this course is not currently offered. Macroeconomic and structural aspects of the ecological crisis. A course in which subjects discussed include the conflict between economic growth and the laws of thermodynamics; the search for alternative economic indicators; the fossil fuels crisis; and "green'' fiscal policy.
ECON 332	Macroeconomic Theory: Majors 1. ¹	3
Macroeconomic Theory: Majors 1. Terms offered: this course is not currently offered. A review of basic economic concepts and tools with an in depth and critical presentation of the fundamental areas of macroeconomic theory. Topics include: the measurement of economic aggregates, economic growth, and the consumption-savings decision and other basic elements of a business cycle.
ECON 333	Macroeconomic Theory - Majors 2. ¹	3
Macroeconomic Theory - Majors 2. Terms offered: this course is not currently offered. A review of basic economic concepts and tools with an in depth and critical presentation of the fundamental areas of macroeconomic theory. Topics include: money and banking and business cycles, stabilization policy, and international finance.
ECON 335	The Japanese Economy.	3
The Japanese Economy. Terms offered: this course is not currently offered. The first part of the course covers the economic institutions in, changing structure of, and public policies employed by the Japanese economy. The second part probes the economic "logic" of the Japanese capitalist system, explores its relationship to the ideas of Joseph Schumpeter, and makes comparisons with the American economy.
ECON 336	The Chinese Economy.	3
The Chinese Economy. Terms offered: this course is not currently offered. Examination of the growth and transformation of the Chinese economy and the domestic and international implications.
ECON 337	Introductory Econometrics 1.	3
Introductory Econometrics 1. Terms offered: this course is not currently offered. The practical application of quantitative methods in statistical investigations.
ECON 347	Economics of Climate Change.	3
Economics of Climate Change. Terms offered: this course is not currently offered. The course focuses on the economic implications of, and problems posed by, predictions of global warming due to anthropogenic emissions of greenhouse gases. Attention is given to economic policies such as carbon taxes and tradeable emission permits and to the problems of displacing fossil fuels with new energy technologies.
ECON 405	Natural Resource Economics.	3
Natural Resource Economics. Terms offered: this course is not currently offered. Topics include: Malthusian and Ricardian Scarcity; optimal depletion of renewable and non-renewable resources; exploration, risk and industry structure, and current resources, rent and taxation. Current public policies applied to the resource industries, particularly those of a regulatory nature.
ECON 406	Topics in Economic Policy.	3
Topics in Economic Policy. Terms offered: this course is not currently offered. Selected policy issues are investigated using economic theory. For details on topics covered in the current year, consult the instructor.
ECON 408	Public Sector Economics 1.	3
Public Sector Economics 1. Terms offered: this course is not currently offered. Theoretical and empirical economic analysis of the public sector with an emphasis on public goods and government spending. Study of Canadian institutions in international perspective.
ECON 409	Public Sector Economics 2.	3
Public Sector Economics 2. Terms offered: this course is not currently offered. Theoretical and empirical economic analysis of the public sector with an emphasis on taxation. Study of Canadian institutions in international perspective.
ECON 411	Economic Development: A World Area.	3
Economic Development: A World Area. Terms offered: this course is not currently offered. An advanced course in the economic development of a pre-designated underdeveloped country or a group of countries.
ECON 416	Topics in Economic Development 2.	3
Topics in Economic Development 2. Terms offered: this course is not currently offered. This course gives students a broad overview of the economics of developing countries. The course covers micro and macro topics, with particular emphasis on the economic analysis at the micro level.
ECON 420	Topics in Economic Theory.	3
Topics in Economic Theory. Terms offered: this course is not currently offered. The course discusses selected topics in micro or macroeconomic theory at an advanced level. Possible topics include welfare economics, general equilibrium, theories of firms, consumer behaviour, intertemporal choice, uncertainty, game theory, etc.
ECON 426	Labour Economics.	3
Labour Economics. Terms offered: this course is not currently offered. The determinants of labour supply, demand and the structure of earnings are considered. The economic effects of government policies, such as minimum wage laws, unemployment insurance, welfare and training programs and subsidies to higher education are analyzed. A rigorous theoretical and "hands on'' empirical approach is emphasized.
ECON 434	Current Economic Problems.	3
Current Economic Problems. Terms offered: this course is not currently offered. A discussion of contemporary economic problems. Topics will reflect economic issues of current interest.
ECON 440	Health Economics.	3
Health Economics. Terms offered: this course is not currently offered. The organization and performance of Canada's health care system are examined from an economist's perspective. The system is described and its special features analyzed. Much attention is given to the role of government in the system and to financing arrangements for hospital and medical services. Current financial problems are discussed.
ECON 468	Econometrics 1 - Honours.	3
Econometrics 1 - Honours. Terms offered: this course is not currently offered. The statistical basis of econometric modelling and treatment of the linear regression model; simple time series models; procedures for inference in linear cases; an introduction to methods for dealing with endogeneity and non-constant variance.
ECON 469	Econometrics 2 - Honours.	3
Econometrics 2 - Honours. Terms offered: this course is not currently offered. Treatment of asymptotic theory and classical inferential procedures, an introduction to the bootstrap, maximum likelihood, non-linear models, mis-specification testing, non-stationarity and limited dependent variable models.
ECON 525	Project Analysis.	3
Project Analysis. Terms offered: this course is not currently offered. A course in cost benefit analysis for graduate and advanced undergraduate students.
ECON 546	Game Theory.	3
Game Theory. Terms offered: this course is not currently offered. This course introduces students to game theory, the branch of the social sciences that focuses on the formal modelling and analysis of human interactions and strategic behaviour. Basic concepts in cooperative and non-cooperative games are applied to economic models.
MIME 325	Mineral Industry Economics. ²	3
Mineral Industry Economics. Terms offered: this course is not currently offered. Geographical distribution of mineral resources. Production, consumption and prices of minerals. Market structure of selected minerals. Economic evaluation aspects: grade-tonnage considerations; capital and operating cost estimation; assessment of market conditions; estimation of revenue; taxation; sensitivity and risk analyses; economic optimization of mine development and extraction.
MIME 526	Mineral Economics. ²	3
Mineral Economics. Terms offered: this course is not currently offered. Mineral project evaluation techniques and applications. Topics covered include grade-tonnage relationships, capital and operating cost estimation techniques, assessment of mineral market conditions, taxation, discounted cash flow analysis, risk analysis, and optimization of project specifications with respect to capacity and cutoff grade.

¹: If chosen, students choose either 贰颁翱狈听209 Macroeconomic Analysis and Applications. or 贰颁翱狈听332 Macroeconomic Theory: Majors 1. and 贰颁翱狈听333 Macroeconomic Theory - Majors 2..
²: Note:听Only open to Mining and Materials Engineering students.

Environmental Engineering Minor (B.Eng.) (21 credits)

Offered by: Civil Engineering (Faculty of Engineering)听听听
Degree: Bachelor of Engineering
Program credit weight: 21

Program 听Description

The Minor program is designed to focus on the principles of environmental engineering in all engineering disciplines providing a specialization at the undergraduate level.

The Environmental Engineering Minor is offered by the Department of Civil Engineering for all students in Engineering and in the Department of Bioresource Engineering wishing to pursue studies in this area.

Note: Not all courses listed are offered every year. Students should see the "Courses" section of this Course Catalogue to know if a course is offered.

A maximum of 12 credits of coursework in the student's major may be double-counted with the Minor.

Complementary Courses (21-22 credits)

3-4 credits from the following list:

Expand allContract all Course List

Course	Title	Credits
BREE 327	Bio-Environmental Engineering.	3
Bio-Environmental Engineering. Terms offered: Fall 2025 An introduction to how humans affect the earth's ecosystem and projections for the needs of food, water, air and energy to support the human population. Ecologically-reasonable coping strategies including biofuels, bioprocessing, waste management, and remediation methods.
CIVE 225	Environmental Engineering.	4
Environmental Engineering. Terms offered: this course is not currently offered. Introduction to environmental chemistry; mass balance analyses in engineered and natural systems; water, soil and air pollution characterization and control; water quality parameters; drinking water and wastewater treatment technologies; global climate change: possible causes and effects; risk assessment for pollutant exposure; solid- and hazardous-waste management.

18 credits from Stream A or Stream B:

Stream A

15 credits¹ from the Engineering Course List and 3 credits from the Non-Engineering Course List below

¹: A minimum of 6 credits must be from outside the student's department. A maximum of 6 credits of research project courses may be counted toward this category, provided the project has sufficient environmental engineering content (project requires approval of project supervisor and coordinator of the Minor).

Stream B

9 credits of courses specified from the "Barbados Interdisciplinary Tropical Studies (BITS)" field semester below, provided the project has sufficient environmental engineering content (project requires approval of the Coordinator of the Minor):

Expand allContract all Course List

Course	Title	Credits
AEBI 425	Tropical Energy and Food.	3
Tropical Energy and Food. Terms offered: Summer 2025 Tropical biofuel crops, conversion processes and final products, particularly energy and greenhouse gas balances and bionutraceuticals. Topics include effects of process extraction during refining on biofuel economics, the food versus fuel debate and impact of biofuels and bioproducts on tropical agricultural economics.
AEBI 427	Barbados Interdisciplinary Project.	6
Barbados Interdisciplinary Project. Terms offered: Summer 2025 The planning of projects and research activities related to tropical food, nutrition, or energy at the local, regional, or national scale in Barbados. Projects and activities designed in consultation with university instructors, government, NGO, or private partners, and prepared by teams of 2-3 students working cooperatively with these mentors.

9 credits chosen from the Engineering Course List below, excluding CHEE听496 Environmental Research Project..

Engineering Course List

Courses offered at the MacDonald campus:

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Course	Title	Credits
BREE 217	Hydrology and Water Resources.	3
Hydrology and Water Resources. Terms offered: Winter 2026 Introduction to water resources and hydrologic cycle. Precipitation and hydrologic frequency analysis. Soil water processes, infiltration theory and modeling. Evapotranspiration estimation methods and crop water requirements. Surface runoff estimation as a function of land use modifications. Estimation of peak runoff rates. Unit hydrograph. Design of open channels and vegetated waterways.
BREE 322	Organic Waste Management. ¹	3
Organic Waste Management. Terms offered: Fall 2025 An introduction to engineering aspects of handling, storage and treatment of all biological and food industry wastes. Design criteria will be elaborated and related to characteristics of wastes. Physical, chemical and biological treatment systems.
BREE 416	Engineering for Land Development.	3
Engineering for Land Development. Terms offered: Fall 2025 Engineering aspects of land stewardship and water resource conservation, including: introduction to the hydrologic cycle and agricultural water use; computation of soil loss by water erosion; conservation farming practices; reservoirs and embankments; water and sediment control structures; stream restoration and water supply; wetlands and wetland design; irrigation principles and design; pumps and pumping; introduction to drainage and water table management.
BREE 518	Ecological Engineering.	3
Ecological Engineering. Terms offered: Winter 2026 Concepts and practice of ecological engineering: the planned creation or management of a community of organisms, their nonliving surroundings, and technological components to provide services. Survey of applications such as constructed wetlands, aquatic production systems, green infrastructure for urban storm water management, environmental restoration. Taught cooperatively with a parallel course at University of Nebraska-Lincoln. Online collaboration with an interdisciplinary, international team is an important component of the course.
BREE 533	Water Quality Management.	3
Water Quality Management. Terms offered: Fall 2025 The water phases of terrestrial ecological systems and the processes that link them. Physical, chemical, and biological properties of water, and water quality standards. The fate and transport of pollutants in rivers and streams, lakes, and wetlands. Methods to quantify soil carbon and nitrogen cycle to predict nutrient leaching. Impacts of human activities (e.g., agricultural drainage) on water quality and measures to improve drainage water quality. Assess the effectiveness of proposed engineering measures or management practices in improving or maintaining water quality of a real site/water body using numerical methods or a computer modelling approach.

¹: Not open to students who have passed CIVE听323 Hydrology and Water Resources..

Courses offered at the Downtown campus:

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Course	Title	Credits
ARCH 377	Energy, Environment, and Buildings 1.	3
Energy, Environment, and Buildings 1. Terms offered: this course is not currently offered. Exploration of the interrelationship between energy, environment, and building. Climate analysis and design, daylighting, electrical systems, plumbing and water conservation, and conveyance systems.
ARCH 515	Sustainable Design.	3
Sustainable Design. Terms offered: this course is not currently offered. This course will address sustainable design theory and applications in the built environment with students from a variety of fields (architecture, urban planning, engineering, sociology, environmental studies, economics, international studies). Architecture will provide the focus for environmental, socio-cultural and economic issues.
CHEE 351	Separation Processes.	3
Separation Processes. Terms offered: this course is not currently offered. Concepts underlying equilibrium based separation, design of processes and equipment for distillation, absorption/stripping, liquid extraction, washing, and leaching. Consideration of mass transfer effects.
CHEE 370	Elements of Biotechnology.	3
Elements of Biotechnology. Terms offered: this course is not currently offered. Biological macromolecules; cell structure and metabolism; industrially significant microbes; enzyme kinetics; introduction to molecular biology and genetic engineering, laboratory exercises.
CHEE 496	Environmental Research Project.	3
Environmental Research Project. Terms offered: this course is not currently offered. Independent study and experimental work on environmental topic(s) chosen by consultation between the student and professor. Students must find a supervisor amongst department faculty before registering for this course.
CHEE 591	Environmental Bioremediation.	3
Environmental Bioremediation. Terms offered: this course is not currently offered. The presence and role of microorganisms in the environment, the role of microbes in environmental remediation either through natural or human-mediated processes, the application of microbes in pollution control and the monitoring of environmental pollutants.
CHEE 593	Industrial Water Pollution Control.	3
Industrial Water Pollution Control. Terms offered: this course is not currently offered. Wastewater constituents of concern; legislation pertinent to wastewater treatment; wastewater sampling and analysis techniques; process analysis and selection; physical, chemical and biological processes; advanced wastewater treatment methods; integration of sciences and engineering principles to design wastewater treatment processes.
CIVE 225	Environmental Engineering.	4
Environmental Engineering. Terms offered: this course is not currently offered. Introduction to environmental chemistry; mass balance analyses in engineered and natural systems; water, soil and air pollution characterization and control; water quality parameters; drinking water and wastewater treatment technologies; global climate change: possible causes and effects; risk assessment for pollutant exposure; solid- and hazardous-waste management.
CIVE 323	Hydrology and Water Resources. ¹	3
Hydrology and Water Resources. Terms offered: this course is not currently offered. Precipitation, evaporation and transpiration. Streamflow, storage reservoirs, flood routing. Groundwater hydrology. Ecohydrology. Statistical analysis in hydrology, stochastic modelling. Simulations using hydrologic models. Case studies in flood damage mitigation, surface and ground water management, and water-energy-food nexus.
CIVE 421	Municipal Systems.	3
Municipal Systems. Terms offered: this course is not currently offered. Design of water-related municipal services; sources of water and intake design; estimation of water demand and wastewater production rates; design, construction and maintenance of water distribution, wastewater and stormwater collection systems; pumps and pumping stations; pipe materials, network analysis and optimization; storage; treatment objectives for water and wastewater.
CIVE 428	Water Resources and Hydraulic Engineering.	3
Water Resources and Hydraulic Engineering. Terms offered: this course is not currently offered. Application of continuity, energy and momentum equations to open channel flow; design of channels considering uniform flow and flow resistance, non-uniform flow and longitudinal profiles; design of channel controls and transitions; unsteady flow and flood routing; river ice engineering; sediment transport and river morphology; sustainability in river engineering; industry standard numerical models.
CIVE 430	Water Treatment and Pollution Control.	3
Water Treatment and Pollution Control. Terms offered: this course is not currently offered. Principles of water and sewage treatment. Water and sewage characteristics; design of conventional unit operations and processes; laboratory analyses of potable and waste waters.
CIVE 520	Groundwater Hydrology.	3
Groundwater Hydrology. Terms offered: this course is not currently offered. Fundamentals of subsurface hydrological processes. Field data and simulation under parameter uncertainty. Numerical modelling. Quantifying groundwater resources and groundwater flow to wells. Groundwater sustainability from a multidisciplinary perspective including engineering and policy.
CIVE 550	Water Resources Management.	3
Water Resources Management. Terms offered: this course is not currently offered. State-of-the-art water resources management techniques; case studies of their application to Canadian situations; identification of major issues and problem areas; interprovincial and international river basins; implications of development alternatives; institutional arrangements for planning and development of water resources; and, legal and economic aspects.
CIVE 555	Environmental Data Analysis.	3
Environmental Data Analysis. Terms offered: this course is not currently offered. Application of statistical principles to design of measurement systems and sampling programs. Introduction to experimental design. Graphical data analysis. Description of uncertainty. Hypothesis tests. Model parameter estimation methods: linear and nonlinear regression methods. Trend analysis. Statistical analysis of censored data. Statistics of extremes.
CIVE 557	Microbiology for Environmental Engineering.	3
Microbiology for Environmental Engineering. Terms offered: this course is not currently offered. Microbiological concepts applied to the practice of environmental engineering and biotechnologies including the following topics: cellular and pathway organizations, evolution, growth, gene expression, horizontal gene transfer, metabolic microbial diversity, ecosystem structures, and quantitative mathematical modelling.
CIVE 561	Greenhouse Gas Emissions.	3
Greenhouse Gas Emissions. Terms offered: this course is not currently offered. Greenhouse gas inventories at various scales from national to institutional. Emission estimation methods including field measurements and engineering calculations for anthropogenic sources including fossil fuel combustion from transportation and energy production, cement production, hydroelectric reservoirs, oil and gas systems, landfills, wastewater treatment and sewer systems, and agriculture. Technical and policy options for reducing greenhouse gas emissions. Group project.
CIVE 572	Computational Hydraulics.	3
Computational Hydraulics. Terms offered: this course is not currently offered. Computation of unsteady flows in open channels; abrupt waves, flood waves, tidal propagations; method of characteristics; mathematical modelling of river and coastal currents.
CIVE 573	Hydraulic Structures.	3
Hydraulic Structures. Terms offered: this course is not currently offered. Hydraulic aspects of the theory and design of hydraulic structures. Storage dams, spillways, outlet works, diversion works, drop structures, stone structures, conveyance and control structures, flow measurement and culverts.
CIVE 574	Fluid Mechanics of Water Pollution.	3
Fluid Mechanics of Water Pollution. Terms offered: this course is not currently offered. Mixing, dilution and dispersion of pollutants discharged into lakes, rivers, estuaries and oceans; salinity intrusion in estuaries and its effects on dispersion; biochemical oxygen demand and dissolved oxygen as water quality indicators; thermal pollution; oil pollution.
CIVE 577	River Engineering.	3
River Engineering. Terms offered: this course is not currently offered. Fluvial geomorphology; sediment properties; river turbulence; mechanics of the entrainment, transportation and deposition of solids by fluids; threshold of movement; bed forms; suspended load, bed load and total load equations; stable channel design and regime rivers; river modelling; river engineering; and river management.
CIVE 584	Mechanics of Groundwater Flow.	3
Mechanics of Groundwater Flow. Terms offered: this course is not currently offered. Origins and types of groundwater; Darcy's law; hydraulic anisotropy; conservation laws; fundamental equations of porous media flow; Laplace's and Poisson's equations: analytical solution of potential flow problems; determination of hydraulic conductivity; flow in unconfined and confined acquifers; seepage modelling; unsaturated flow; transient flows in porous media; introduction to computational methods.
MECH 447	Combustion.	3
Combustion. Terms offered: this course is not currently offered. Equilibrium analysis of reacting systems, Hugoniot analysis, flame propagation mechanisms, introduction to chemical kinetics, models for laminar flame propagation, ignition, quenching, flammability limits, turbulent flames, flame instability mechanisms, detonations, solid and liquid combustion.
MECH 534	Air Pollution Engineering.	3
Air Pollution Engineering. Terms offered: this course is not currently offered. Pollutants from power production and their effects on the environment. Mechanisms of pollutant formation in combustion. Photochemical pollutants and smog, atmospheric dispersion. Pollutant generation from internal combustion engines and stationary power plants. Methods of pollution control (exhaust gas treatment, absorption, filtration, scrubbers, etc.).
MECH 535	Turbomachinery and Propulsion.	3
Turbomachinery and Propulsion. Terms offered: this course is not currently offered. Introduction to propulsion: turboprops, turbofans and turbojets. Review of thermodynamic cycles. Euler turbine equation. Velocity triangles. Axial-flow compressors and pumps. Centrifugal compressors and pumps. Axial-flow turbines. Loss mechanisms. Dimensional analysis of turbomachines. Performance maps. 3-D effects. Introduction to numerical methods in turbomachines. Prediction of performance of gas turbines.
MECH 560	Eco-design and Product Life Cycle Assessment .	3
Eco-design and Product Life Cycle Assessment . Terms offered: this course is not currently offered. Fundamentals of both product and process engineering with an emphasis on life cycle models and sustainability. Practical and theoretical topics, methodologies, principles, and techniques. Practical methods such as Life Cycle Analysis, eco-design strategies, streamlined Life Cycle Assessment, environmental impact assessment, and Life Cycle Engineering. Introduction to important product development theories and life cycle assessment theories.
MIME 422	Mine Ventilation.	3
Mine Ventilation. Terms offered: Summer 2025 Statutory regulations and engineering design criteria. Occupational health hazards of mine gases, dusts, etc. Ventilation system design. Natural and mechanical ventilation. Measuring and modelling air flow in ventilation networks. Calculation of head losses. Selection of mine ventilation fans. Air heating and cooling. Aspects of economics.
MIME 428	Environmental Mining Engineering.	3
Environmental Mining Engineering. Terms offered: Summer 2025 Effect of mining on the environment: ecology, legislation, effluents and wastes, environmental impact. Acid mine drainage: prediction, treatment, prevention, control. Mineral processing agents. Solid wastes. Mine site closure, reclamation and monitoring. Economic aspects. Environmental practices.
MIME 512	Corrosion and Degradation of Materials.	3
Corrosion and Degradation of Materials. Terms offered: this course is not currently offered. Electrochemical theory of metal corrosion, Evans Diagrams, corrosion rate controlling mechanisms, mixed corrodents, alloying effects, passivation. Discussion and analysis of the various forms of corrosion. Corrosion prevention methods. Oxidation of alloys-mechanisms and kinetics. Degradation of ceramics and polymers. Case studies.
MIME 556	Sustainable Materials Processing.	3
Sustainable Materials Processing. Terms offered: this course is not currently offered. Sustainability, population and environment impact, environmental impact indicators, materials flows, enthalpy flows, the carbon cycle, materials intensity, energy intensity, global warming potential, acidification potential, FACTOR-Two, -Four and -Ten, life-cycle-inventory/assessment, end-of-pipe strategies, supply-chain and flow-sheet redesign, recycling, waste treatment and materials case studies.
MPMC 328	Environnement et gestion des rejets miniers.	3
Environnement et gestion des rejets miniers. Terms offered: Summer 2025 Effets du milieu de travail sur l'homme (hygi猫ne du travail) : l茅gislation; contraintes thermiques, probl猫mes de bruit, de contaminants gazeux et de poussi猫res; techniques de mesures. Effets de l'exploitation d'une mine sur le milieu (environnement et 茅cologie) : l茅gislation; 茅tudes d'impacts; effluents miniers: origine, nature et traitement des effluents; entreposage des r茅sidus; restauration des sites.
SEAD 515	Climate Change Adaptation and Engineering Infrastructure .	3
Climate Change Adaptation and Engineering Infrastructure . Terms offered: this course is not currently offered. Climate resilience and sustainability of engineering systems such as the built environment and engineering infrastructure in the context of a changing climate, possible mitigation and adaptation strategies and associated challenges and opportunities. Review of the basic principles that underpin the science of climate change; the role of global and regional climate models in predicting the behaviour of the climate system in response to different forcing scenarios, and the use of climate model outputs in support of across scale climate-resilience of various engineering systems including infrastructure systems.
SEAD 520	Life Cycle-Based Environmental Footprinting .	3
Life Cycle-Based Environmental Footprinting . Terms offered: this course is not currently offered. Introduction to Life Cycle-Based Environmental Footprinting and the application of basic methods for life-cycle environmental inventory and impacts modeling. LCA theory and quantitative analysis, approaches for assessing and reducing the environmental impacts of product, process, and technology systems. System boundary and functional unit design approaches, process-based and input-output-based methods for modeling mass and energy flows in life-cycle systems. How LCA can facilitate sustainable technology innovation and deployment, behavioural and societal changes, and policies, standards and regulations.
SEAD 550	Decision-Making for Sustainability in Engineering and Design.	3
Decision-Making for Sustainability in Engineering and Design. Terms offered: this course is not currently offered. Role and importance of engineering decisions of environmental, social, and economic problems and the application of decision-making approaches and tools to engineering sustainability. Multi-criteria decision-making, uncertainty analysis, game theory, sustainability metrics, life cycle analysis evaluation and impact assessment methodologies, design problem formulation, stage-dependent strategies, case studies.
URBP 506	Environmental Policy and Planning.	3
Environmental Policy and Planning. Terms offered: this course is not currently offered. Analytical and institutional approaches for understanding and addressing environmental issues at various scales; characteristics of environmental issues, science-policy-politics interactions relating to the environment, and implications for policy; sustainability, and the need for and challenges associated with interdisciplinary perspectives; externalities and their regulation; public goods; risk perception and implications; the political-institutional context and policy instruments; cost-benefit analysis; multiple-criteria decision-making approaches; multidimensional life-cycle analysis; policy implementation issues; conflict resolution; case studies.

¹: Not open to students who have passed BREE听217 Hydrology and Water Resources..

Non-Engineering Course List

Courses offered at the MacDonald campus:

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Course	Title	Credits
ENVB 210	The Biophysical Environment.	3
The Biophysical Environment. Terms offered: Fall 2025 With reference to the ecosystems in the St Lawrence lowlands, the principles and processes governing climate-landform-water-soil-vegetation systems and their interactions will be examined in lecture and laboratory. Emphasis on the natural environment as an integrated system.
LSCI 230	Introductory Microbiology. ¹	3
Introductory Microbiology. Terms offered: Winter 2026 The occurrence and importance of microorganisms in the biosphere. Principles governing growth, death and metabolic activities of microorganisms. An introduction to the microbiology of soil, water, plants, food, humans and animals.
MICR 331	Microbial Ecology. ¹	3
Microbial Ecology. Terms offered: Winter 2026 The ecology of microorganisms, primarily bacteria and archaea, and their roles in biogeochemical cycles. Microbial interactions with the environment, plants, animals and other microbes emphasizing the underlying genetics and physiology. Diversity, evolution (microbial phylogenetics) and the application of molecular biology in microbial ecology.
MICR 341	Mechanisms of Pathogenicity.	3
Mechanisms of Pathogenicity. Terms offered: Fall 2025 A study of the means by which bacteria cause disease in animals and humans. Includes response of host to invading bacteria, bacterial attachment and penetration processes, and modes of actions of exotoxins and endotoxins.
RELG 270	Religious Ethics and the Environment.	3
Religious Ethics and the Environment. Terms offered: this course is not currently offered. Environmental potential of various religious traditions and secular perspectives, including animal rights, ecofeminism, and deep ecology.
SOIL 331	Environmental Soil Physics.	3
Environmental Soil Physics. Terms offered: this course is not currently offered. This course addresses physical properties and processes in soil, state and transport of matter and energy affecting environment and agriculture (State: soil texture, structure, temperature, water; Transport: water flow, chemical transport, heat and gas flow), mass and energy balance in soil, effect of various environmental events on soil physical properties, management of physical properties and processes for various practical agricultural, hydrological and environmental applications including land reclamation.

¹: Not open to students who have passedCHEE听370 Elements of Biotechnology..

Courses offered at the Downtown campus:

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Course	Title	Credits
ANTH 206	Environment and Culture.	3
Environment and Culture. Terms offered: this course is not currently offered. Introduction to ecological anthropology, focusing on social and cultural adaptations to different environments, human impact on the environment, cultural constructions of the environment, management of common resources, and conflict over the use of resources.
BIOL 205	Functional Biology of Plants and Animals.	3
Functional Biology of Plants and Animals. Terms offered: this course is not currently offered. 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.
BIOL 432	Limnology.	3
Limnology. Terms offered: this course is not currently offered. A study of the physical, chemical and biological properties of lakes and other inland waters, with emphasis on their functioning as systems.
CMPL 580	Environment and the Law.	3
Environment and the Law. Terms offered: this course is not currently offered. Environmental law, with emphasis on ecological, economic, political, and international dimensions.
ECON 225	Economics of the Environment.	3
Economics of the Environment. Terms offered: this course is not currently offered. A study of the application of economic theory to questions of environmental policy. Particular attention will be given to the measurement and regulation of pollution, congestion and waste and other environmental aspects of specific economies.
ECON 326	Ecological Economics.	3
Ecological Economics. Terms offered: this course is not currently offered. Macroeconomic and structural aspects of the ecological crisis. A course in which subjects discussed include the conflict between economic growth and the laws of thermodynamics; the search for alternative economic indicators; the fossil fuels crisis; and "green'' fiscal policy.
ECON 347	Economics of Climate Change.	3
Economics of Climate Change. Terms offered: this course is not currently offered. The course focuses on the economic implications of, and problems posed by, predictions of global warming due to anthropogenic emissions of greenhouse gases. Attention is given to economic policies such as carbon taxes and tradeable emission permits and to the problems of displacing fossil fuels with new energy technologies.
EPSC 549	Hydrogeology.	3
Hydrogeology. Terms offered: this course is not currently offered. Introduction to groundwater flow through porous media. Notions of fluid potential and hydraulic head. Darcy flux and Darcy's Law. Physical properties of porous media and their measurement. Equation of groundwater flow. Flow systems. Hydraulics of pumping and recharging wells. Notions of hydrology. Groundwater quality and contamination. Physical processes of contaminant transport.
GEOG 200	Geographical Perspectives: World Environmental Problems.	3
Geographical Perspectives: World Environmental Problems. Terms offered: this course is not currently offered. Introduction to geography as the study of nature and human beings in a spatial context. An integrated approach to environmental systems and the human organization of them from the viewpoint of spatial relationships and processes. Special attention to environmental problems as a constraint upon Third World development.
GEOG 201	Introductory Geo-Information Science.	3
Introductory Geo-Information Science. Terms offered: this course is not currently offered. An introduction to Geographic Information Systems. The systematic management of spatial data. The use and construction of maps. The use of microcomputers and software for mapping and statistical work. Air photo and topographic map analyses.
GEOG 203	Environmental Systems.	3
Environmental Systems. Terms offered: this course is not currently offered. An introduction to system-level interactions among climate, hydrology, soils and vegetation at the scale of drainage basins, including the study of the global geographical variability in these land-surface systems. The knowledge acquired is used to study the impact on the environment of various human activities such as deforestation and urbanisation.
GEOG 205	Global Change: Past, Present and Future.	3
Global Change: Past, Present and Future. Terms offered: this course is not currently offered. An examination of global change, from the Quaternary Period to the present day involving changes in the physical geography of specific areas. Issues such as climatic change and land degradation will be discussed, with speculations on future environments.
GEOG 302	Environmental Management 1.	3
Environmental Management 1. Terms offered: this course is not currently offered. An ecological analysis of the physical and biotic components of natural resource systems. Emphasis on scientific, technological and institutional aspects of environmental management. Study of the use of biological resources and of the impact of individual processes.
GEOG 308	Remote Sensing for Earth Observation.	3
Remote Sensing for Earth Observation. Terms offered: this course is not currently offered. A conceptual view of remote sensing and the underlying physical principles. Covers ground-based, aerial, satellite systems, and the electromagnetic spectrum, from visible to microwave. Emphasis on application of remotely sensed data in geography including land cover change and ecological processes.
GEOG 321	Climatic Environments.	3
Climatic Environments. Terms offered: this course is not currently offered. The earth-atmosphere system, radiation and energy balances. Surface-atmosphere exchange of energy, mass and momentum and related atmospheric processes on a local and regional scale. Introduction to measurement theory and practice in micrometeorology.
GEOG 404	Environmental Management 2.	3
Environmental Management 2. Terms offered: this course is not currently offered. Practical application of environmental planning, analysis and management techniques with reference to the needs and problems of developing areas. Special challenges posed by cultural differences and traditional resource systems are discussed. This course involves practical field work in a developing area (Kenya or Panama).
MIMM 211	Introductory Microbiology.	3
Introductory Microbiology. Terms offered: this course is not currently offered. A general treatment of microbiology bearing specifically on the biological properties of microorganisms. Emphasis will be on procaryotic cells. Basic principles of microbial genetics are also introduced.

Management (for Non-Management Students) (Minor) (18 credits)

Offered by:听Management (Desautels Faculty of Management)听听听
Program credit weight:听18

Program Description

The Minor Management consists of 18 credits of Management courses and is currently offered to non-Management students in the following Faculties: Arts, Engineering, Science, Agricultural & Environmental Sciences, Music, Religious Studies, and Kinesiology.

This Minor is designed to provide non-management students with the opportunity to obtain basic knowledge in various aspects of management.

Complementary Courses (18 credits)

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Course	Title	Credits
MGCR 211	Introduction to Financial Accounting.	3
Introduction to Financial Accounting. Terms offered: Summer 2025 The role of financial accounting in the reporting of the financial performance of a business. The principles, components and uses of financial accounting and reporting from a user's perspective, including the recording of accounting transactions and events, the examination of the elements of financial statements, the preparation of financial statements and the analysis of financial results.
MGCR 222	Introduction to Organizational Behaviour.	3
Introduction to Organizational Behaviour. Terms offered: Summer 2025 Individual motivation and communication style; group dynamics as related to problem solving and decision making, leadership style, work structuring and the larger environment. Interdependence of individual, group and organization task and structure.
MGCR 271	Business Statistics. ¹	3
Business Statistics. Terms offered: this course is not currently offered. Statistical concepts and methodology, their application to managerial decision-making, real-life data, problem-solving and spreadsheet modeling. Topics include: descriptive statistics; normal distributions, sampling distributions and estimation, hypothesis testing for one and two populations, goodness of fit, analysis of variance, simple and multiple regression.
MGCR 293	Managerial Economics. ²	3
Managerial Economics. Terms offered: Summer 2025 The course focuses on the application of economic theory to management problems and the economic foundations of marketing, finance, and production. Attention is given to the following topics: price and cost analysis; demand and supply analysis, conditions of competition.
MGCR 331	Information Technology Management .	3
Information Technology Management . Terms offered: Summer 2025 Introduction to principles and concepts of information systems in organizations. Topics include information technology, transaction processing systems, decision support systems, database and systems development. Students are required to have background preparation on basic micro computer skills including spreadsheet and word-processing.
MGCR 341	Introduction to Finance. ³	3
Introduction to Finance. Terms offered: Summer 2025 An introduction to the principles, issues, and institutions of Finance. Topics include valuation, risk, capital investment, financial structure, cost of capital, working capital management, financial markets, and securities.
MGCR 352	Principles of Marketing.	3
Principles of Marketing. Terms offered: Summer 2025 Introduction to marketing principles, focusing on problem solving and decision making. Topics include: the marketing concept; marketing strategies; buyer behaviour; Canadian demographics; internal and external constraints; product; promotion; distribution; price. Lectures, text material and case studies.
MGCR 372	Operations Management. ³	3
Operations Management. Terms offered: Summer 2025 Design, planning, establishment, control, and improvement of the activities/processes that create a firm's final products and/or services. The interaction of operations with other business areas will also be discussed. Topics include forecasting, product and process design, waiting lines, capacity planning, inventory management and total quality management.
MGCR 382	International Business.	3
International Business. Terms offered: this course is not currently offered. An introduction to the world of international business. Economic foundations of international trade and investment. The international trade, finance, and regulatory frameworks. Relations between international companies and nation-states, including costs and benefits of foreign investment and alternative controls and responses. Effects of local environmental characteristics on the operations of multi-national enterprises.

¹: 3 credits of statistics: Students who have taken an equivalent Statistics course in another faculty may not count those credits towards the Minor; an additional 3-credit complementary course must be chosen from the course list above.
²: Students who have taken an equivalent Economics course in another faculty may not count those credits toward the Minor; an additional 3-credit complementary course must be chosen from the course list above.
³: Prerequisite: MGCR 271, Business Statistics, or another equivalent Statistics course approved by the Program Advisor.

9 credits selected from any Management courses not already chosen from the first list or any 300- or 400-level Management courses for which prerequisites have been met.

Note: Students should select their Statistics course only after consulting the "Course Overlap" section in the Faculty of Arts, the "Course Overlap" section in the Faculty of Science, and the "Course Overlap" section in the Desautels Faculty of Management to avoid overlapping Statistics courses.

Materials Engineering Minor (B.Eng.) (24 credits)

Offered by:听Mining & Materials Engineering (Faculty of Engineering)听听
Degree:听Bachelor of Engineering
Program credit weight:听24

Program 听Description

Minor Adviser: Prof. Richard Chromik (Minor Coordinator), Wong Building, Room 2620

Engineering students may obtain a Materials Engineering Minor by completing 24 credits chosen from the required and complementary courses listed below. By a careful selection of complementary courses, Engineering students may obtain this Minor with a minimum of 15 additional credits.

Required Courses (15 credits)

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Course	Title	Credits
CHEE 380	Materials Science. ¹	3
Materials Science. Terms offered: this course is not currently offered. Structure/property relationship for metals, ceramics, polymers and composite materials. Atomic and molecular structure, bonds, electronic band structure and semi-conductors. Order in solids: crystal structure, disorders, solid phases. Mechanical properties and fracture, physico-chemical properties, design. Laboratory exercises.
CHEE 484	Materials Engineering.	3
Materials Engineering. Terms offered: this course is not currently offered. Processes for forming and producing engineering materials such as amorphous, semicrystalline, textured and crystal-oriented substances and composites. Phase transformations, nucleation and growth. Effect of processing variables on the properties of the finished article. Process of blending and alloying. Shaping and joining operations. Vessel equipment design for chemical engineering applications.
MIME 260	Materials Science and Engineering. ¹	3
Materials Science and Engineering. Terms offered: this course is not currently offered. Structure properties and fabrication of metals, polymers, ceramics, composites; engineering properties: tensile, fracture, creep, oxidation, corrosion, friction, wear; fabrication and joining methods; principles of materials selection.
MIME 345	Applications of Polymers.	3
Applications of Polymers. Terms offered: Summer 2025 Applications of synthetic and natural polymers and composites as engineering materials, e.g. in biomedical, automotive and aerospace applications. Thermoplastics, thermosets and elastomers. Animal and plant origin, degradable and non-degradable polymers. Particulate and fibre reinforced polymer matrix composites. Manufacturing routes, and characterization tools for their physical, thermal, mechanical and chemical properties.
MIME 465	Metallic and Ceramic Powders Processing.	3
Metallic and Ceramic Powders Processing. Terms offered: this course is not currently offered. Powder metallurgy and ceramic processing. Fabrication, characterization and properties of powders. Powder consolidation techniques. Sintering and densification mechanisms. Properties of porous compacts. Design of fabrication process. Particularities and classification of ceramic systems.
MIME 467	Electronic Properties of Materials.	3
Electronic Properties of Materials. Terms offered: Summer 2025 Electrons as particles and waves, Schrodinger's Equation, electrical and thermal conductivity, semiconductors, semiconductor devices, fundamentals of magnetism, superconductivity and superconductive materials, dielectric materials, optical properties of materials, LASERs and waveguides. Advanced materials and their technological applications. An introduction to quantum mechanics will be included which will be the foundation upon which energy band diagrams will be built and understood.

¹: Students choose either CHEE听380 Materials Science. or MIME听260 Materials Science and Engineering..

Complementary Courses

9 credits from the following:

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Course	Title	Credits
MECH 530	Mechanics of Composite Materials.	3
Mechanics of Composite Materials. Terms offered: this course is not currently offered. Fiber-reinforced composites. Stress, strain, and strength of composite laminates and honeycomb structures. Failure modes and failure criteria. Environmental effects. Manufacturing processes. Design of composite structures. Computer modelling of composites. Computer techniques are utilized throughout the course.
MIME 360	Phase Transformations: Solids.	3
Phase Transformations: Solids. Terms offered: this course is not currently offered. Free energy (equilibrium) and kinetic (non-equilibrium) considerations, phase diagrams and TTT diagrams, solid state diffusion, diffusional (nucleation and growth) and shear (martensitic) transformations.
MIME 512	Corrosion and Degradation of Materials.	3
Corrosion and Degradation of Materials. Terms offered: this course is not currently offered. Electrochemical theory of metal corrosion, Evans Diagrams, corrosion rate controlling mechanisms, mixed corrodents, alloying effects, passivation. Discussion and analysis of the various forms of corrosion. Corrosion prevention methods. Oxidation of alloys-mechanisms and kinetics. Degradation of ceramics and polymers. Case studies.
MIME 560	Joining Processes.	3
Joining Processes. Terms offered: this course is not currently offered. Physics of joining; interfacial requirements; energy sources, chemical, mechanical and electrical; homogeneous hot-joining, arc-, Mig-, Tig-, gas-, thermite- and Plasma-welding; Autogeneous hot-joining, forge-, pressure-, friction-, explosive-, electron beam- and laser-welding; Heterogeneous hot-joining, brazing, soldering, diffusion bonding; Heterogeneous cold joining, adhesives, mechanical fastening; Filler materials; Joint metallurgy; Heat affected zone, non-metallic systems; joint design and economics; defects and testing methods.
MIME 561	Advanced Materials Design.	3
Advanced Materials Design. Terms offered: this course is not currently offered. Advanced topics in materials design problems. Discussion and laboratory work, supplemented by detailed technical reports. Special attention is given to selection, design and failure problems in various materials systems.
MIME 563	Hot Deformation of Metals.	3
Hot Deformation of Metals. Terms offered: this course is not currently offered. High temperature deformation processing of metallic materials. Topics include static and dynamic recrystallization, recovery, precipitation; effect of deformation on phase transformations and microstructural evolution during industrial processing. Mathematical modelling of microstructural evolution.
MIME 569	Electron Beam Analysis of Materials.	3
Electron Beam Analysis of Materials. Terms offered: this course is not currently offered. Emphasis on operation of scanning and transmission electron microscopes. Topics covered are electron/specimen interactions, hardware description; image contrast description; qualitative and quantitative (ZAF) x-ray analysis; electron diffraction pattern analysis.

Mathematics Minor (B.Eng.) (18 credits)

Offered by: Mathematics and Statistics (Faculty of Science)听听听
Degree: Bachelor of Engineering
Program credit weight: 18

Program 听Description

The B.Eng.; Minor in Mathematics provides students with an even stronger foundation in mathematics to further develop their knowledge of this subject. Students enrolled in the B.Eng.; Minor in Mathematics complete a series of mathematics courses offered by the Department of Mathematics and Statistics, or other units offering mathematics courses.

Minor Adviser: Faculty Student Adviser in the McGIll Engineering Student Centre (Student Affairs Office) (Frank Dawson Adams Building, Room 22) AND an adviser designated by the Department of Mathematics and Statistics. (Please consult the Department of Mathematics and Statistics for the name of this adviser.) Selection of courses must be undertaken in conjunction with the Minor Advisers, normally beginning in the U2 year.

Note: The B.Eng.; Minor in Mathematics is open to all students in the Faculty of Engineering (including students registered in the B.Sc.(Arch.)). A maximum of 9 credits of overlap (double-counting) with the degree program is allowed.

Engineering students must obtain a grade of C or better in courses approved for this Minor.

Required Course (3 credits)

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Course	Title	Credits
MATH 242	Analysis 1.	3
Analysis 1. Terms offered: this course is not currently offered. A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.

Complementary Courses (15 credits)

3 credits selected from:

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Course	Title	Credits
MATH 223	Linear Algebra.	3
Linear Algebra. Terms offered: this course is not currently offered. 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.
MATH 247	Honours Applied Linear Algebra.	3
Honours Applied Linear Algebra. Terms offered: this course is not currently offered. 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.

6-12 credits selected from:

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Course	Title	Credits
ECSE 205	Probability and Statistics for Engineers ¹	3
Probability and Statistics for Engineers Terms offered: Summer 2025 Probability: basic probability model, conditional probability, Bayes rule, random variables and vectors, distribution and density functions, common distributions in engineering, expectation, moments, independence, laws of large numbers, central limit theorem. Statistics: descriptive measures of engineering data, sampling distributions, estimation of mean and variance, confidence intervals, hypothesis testing, linear regression.
MATH 204	Principles of Statistics 2.	3
Principles of Statistics 2. Terms offered: this course is not currently offered. The concept of degrees of freedom and the analysis of variability. Planning of experiments. Experimental designs. Polynomial and multiple regressions. Statistical computer packages (no previous computing experience is needed). General statistical procedures requiring few assumptions about the probability model.
MATH 240	Discrete Structures.	3
Discrete Structures. Terms offered: this course is not currently offered. 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.
MATH 243	Analysis 2.	3
Analysis 2. Terms offered: this course is not currently offered. Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.
MATH 264	Advanced Calculus for Engineers.	3
Advanced Calculus for Engineers. Terms offered: Summer 2025 Review of multiple integrals. Differential and integral calculus of vector fields including the theorems of Gauss, Green, and Stokes. Introduction to partial differential equations, separation of variables, Sturm-Liouville problems, and Fourier series.
MATH 271	Linear Algebra and Partial Differential Equations. ²	3
Linear Algebra and Partial Differential Equations. Terms offered: this course is not currently offered. Applied Linear Algebra. Linear Systems of Ordinary Differential Equations. Power Series Solutions. Partial Differential Equations. Sturm-Liouville Theory and Applications. Fourier Transforms.
MATH 316	Complex Variables.	3
Complex Variables. Terms offered: this course is not currently offered. Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
MATH 319	Partial Differential Equations . ²	3
Partial Differential Equations . Terms offered: this course is not currently offered. First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems.
MATH 323	Probability. ¹	3
Probability. Terms offered: Summer 2025 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.
MATH 324	Statistics. ¹	3
Statistics. Terms offered: this course is not currently offered. Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
MATH 326	Nonlinear Dynamics and Chaos.	3
Nonlinear Dynamics and Chaos. Terms offered: this course is not currently offered. 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.
MATH 340	Discrete Mathematics.	3
Discrete Mathematics. Terms offered: this course is not currently offered. Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
MATH 378	Nonlinear Optimization .	3
Nonlinear Optimization . Terms offered: this course is not currently offered. Optimization terminology. Convexity. First- and second-order optimality conditions for unconstrained problems. Numerical methods for unconstrained optimization: Gradient methods, Newton-type methods, conjugate gradient methods, trust-region methods. Least squares problems (linear + nonlinear). Optimality conditions for smooth constrained optimization problems (KKT theory). Lagrangian duality. Augmented Lagrangian methods. Active-set method for quadratic programming. SQP methods.
MATH 417	Linear Optimization.	3
Linear Optimization. Terms offered: this course is not currently offered. An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interior-point methods, quadratic optimization, applications in game theory.
MATH 427	Statistical Quality Control.	3
Statistical Quality Control. Terms offered: this course is not currently offered. Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes.
MATH 447	Introduction to Stochastic Processes.	3
Introduction to Stochastic Processes. Terms offered: this course is not currently offered. 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.
MATH 463	Convex Optimization.	3
Convex Optimization. Terms offered: this course is not currently offered. Introduction to convex analysis and convex optimization: Convex sets and functions, subdifferential calculus, conjugate functions, Fenchel duality, proximal calculus. Subgradient methods, proximal-based methods. Conditional gradient method, ADMM. Applications including data classification, network-flow problems, image processing, convex feasibility problems, DC optimization, sparse optimization, and compressed sensing.
MATH 475	Honours Partial Differential Equations.	3
Honours Partial Differential Equations. Terms offered: this course is not currently offered. First order partial differential equations, geometric theory, classification of second order linear equations, Sturm-Liouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems.
MATH 478	Computational Methods in Applied Mathematics .	3
Computational Methods in Applied Mathematics . Terms offered: this course is not currently offered. Solution to initial value problems: Linear, Nonlinear Finite Difference Methods: accuracy and stability, Lax equivalence theorem, CFL and von Neumann conditions, Fourier analysis: diffusion, dissipation, dispersion, and spectral methods. Solution of large sparse linear systems: iterative methods, preconditioning, incomplete LU, multigrid, Krylov subspaces, conjugate gradient method. Applications to, e.g., weighted least squares, duality, constrained minimization, calculus of variation, inverse problems, regularization, level set methods, Navier-Stokes equations
MATH 563	Honours Convex Optimization .	4
Honours Convex Optimization . Terms offered: this course is not currently offered. Honours level introduction to convex analysis and convex optimization: Convex sets and functions, subdifferential calculus, conjugate functions, Fenchel duality, proximal calculus. Subgradient methods, proximal-based methods. Conditional gradient method, ADMM. Applications including data classification, network-flow problems, image processing, convex feasibility problems, DC optimization, sparse optimization, and compressed sensing.

¹: Students who take ECSE听205 Probability and Statistics for Engineers may not take MATH听323 Probability.听or MATH听324 Statistics..
²: Students may take MATH听271 Linear Algebra and Partial Differential Equations. or MATH听319 Partial Differential Equations . but not both.

0-6 credits chosen from (200- to 500-level) Mathematics and Statistics courses approved for the B.Sc. Major Mathematics or B.Sc. Honours Mathematics programs, or from mathematics courses offered in other units. The courses in this category must be chosen in consultation with, and approved by, the Minor Adviser from the Department of Mathematics and Statistics.

Note: MATH听262 Intermediate Calculus., MATH听263 Ordinary Differential Equations for Engineers. (or any course with substantial overlap in content with these two courses) and/or MATH听338 History and Philosophy of Mathematics. cannot be credited towards this minor.

Technological Entrepreneurship Minor (B.Eng.) (18 credits)

Offered by: Engineering - Dean's Office (Faculty of Engineering)听听
Degree: Bachelor of Engineering
Program credit weight: 18

Program 听Description

This Minor in Technological Entrepreneurship is a collaboration of the Faculty of Engineering and the Desautels Faculty of Management. The program focusses on an entrepreneurial mindset to see opportunity in the world and provide training in an entrepreneurial method to bring opportunities for change to life. This program takes a democratized approach to entrepreneurship, with exposure to the diverse manifestations of entrepreneurship in the world including but not limited to new ventures, social enterprise, tech start-ups, cooperatives, corporate venturing, side hustles, and passion projects. Up to 6 credits of Complementary Studies (Group B., Humanities, and Social Science courses) and/or elective courses may double-count towards the Minor.

Required Courses (9 credits)

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Course	Title	Credits
FACC 500	Technology Business Plan Design.	3
Technology Business Plan Design. Terms offered: this course is not currently offered. This course combines several management functional areas such as marketing, financial, operations and strategy with the skills of creativity, engineering innovation, leadership and communications. Students learn how to design an effective and winning business plan around a technology or engineering project in small, medium or large enterprises.
INTG 215	Entrepreneurship Essentials for Non-Management Students.	3
Entrepreneurship Essentials for Non-Management Students. Terms offered: this course is not currently offered. Fundamental concepts, theories, and practices of entrepreneurship. Focus on identifying opportunities, developing business ideas, and understanding key components of starting and managing a business.
MGPO 362	Fundamentals of Entrepreneurship.	3
Fundamentals of Entrepreneurship. Terms offered: this course is not currently offered. Study of the key aspects involved in starting and managing a new venture: identifying opportunities and analyzing new venture ideas, identifying common causes of failure and strategies for success, understanding intellectual property systems, comparison of multiple modes of funding. Applies to for-profit and not-for-profit start-ups.

Complementary Courses (9 credits)

3 credits from the following:

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Course	Title	Credits
MGCR 211	Introduction to Financial Accounting.	3
Introduction to Financial Accounting. Terms offered: Summer 2025 The role of financial accounting in the reporting of the financial performance of a business. The principles, components and uses of financial accounting and reporting from a user's perspective, including the recording of accounting transactions and events, the examination of the elements of financial statements, the preparation of financial statements and the analysis of financial results.
MGCR 222	Introduction to Organizational Behaviour.	3
Introduction to Organizational Behaviour. Terms offered: Summer 2025 Individual motivation and communication style; group dynamics as related to problem solving and decision making, leadership style, work structuring and the larger environment. Interdependence of individual, group and organization task and structure.
MGCR 331	Information Technology Management .	3
Information Technology Management . Terms offered: Summer 2025 Introduction to principles and concepts of information systems in organizations. Topics include information technology, transaction processing systems, decision support systems, database and systems development. Students are required to have background preparation on basic micro computer skills including spreadsheet and word-processing.
MGCR 341	Introduction to Finance.	3
Introduction to Finance. Terms offered: Summer 2025 An introduction to the principles, issues, and institutions of Finance. Topics include valuation, risk, capital investment, financial structure, cost of capital, working capital management, financial markets, and securities.
MGCR 352	Principles of Marketing.	3
Principles of Marketing. Terms offered: Summer 2025 Introduction to marketing principles, focusing on problem solving and decision making. Topics include: the marketing concept; marketing strategies; buyer behaviour; Canadian demographics; internal and external constraints; product; promotion; distribution; price. Lectures, text material and case studies.
MGCR 372	Operations Management.	3
Operations Management. Terms offered: Summer 2025 Design, planning, establishment, control, and improvement of the activities/processes that create a firm's final products and/or services. The interaction of operations with other business areas will also be discussed. Topics include forecasting, product and process design, waiting lines, capacity planning, inventory management and total quality management.
MGCR 382	International Business.	3
International Business. Terms offered: this course is not currently offered. An introduction to the world of international business. Economic foundations of international trade and investment. The international trade, finance, and regulatory frameworks. Relations between international companies and nation-states, including costs and benefits of foreign investment and alternative controls and responses. Effects of local environmental characteristics on the operations of multi-national enterprises.
MGCR 423	Strategic Management.	3
Strategic Management. Terms offered: Summer 2025 An integrative and interdisciplinary introduction to strategy formation and execution. Concepts, tools, and practical application to understand how firms leverage resources and capabilities to gain competitive advantage in dynamic, contemporary industries. Strategic positioning, organizational design, and managerial action for the long-term success of businesses and positive social and ecological outcomes.
MGCR 460	Social Context of Business.	3
Social Context of Business. Terms offered: Summer 2025 Examination of how business interacts with the larger society. Exploration of the development of modern capitalist society, and the dilemmas that organizations face in acting in a socially responsible manner. Examination of these issues with reference to sustainable development, business ethics, globalization and developing countries, and political activity.

3-6 credits from the following:

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Course	Title	Credits
FACC 501	Technology Business Plan Project.	3
Technology Business Plan Project. Terms offered: this course is not currently offered. Students work in teams to develop a comprehensive business plan project based on a technological or engineering innovation while utilizing site visits.
MGPO 364	Entrepreneurship in Practice.	3
Entrepreneurship in Practice. Terms offered: this course is not currently offered. Provides hands-on experience with the development of an entrepreneurial venture or a contribution to an existing entrepreneurial venture. Involves the creation of a venture development or business plan. Applicable to many kinds of new ventures, both private companies and social enterprises.

0-3 credits from the following:

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Course	Title	Credits
BUSA 465	Technological Entrepreneurship.	3
Technological Entrepreneurship. Terms offered: this course is not currently offered. Concentrating on entrepreneurship and enterprise development, particular attention is given to the start-up, purchasing and management of small to medium-sized industrial firms. The focal point is in understanding the dilemmas faced by entrepreneurs, resolving them, developing a business plan and the maximum utilization of the financial, marketing and human resources that make for a successful operation.
LAWG 570	Innovation for Non-Law Students.	3
Innovation for Non-Law Students. Terms offered: this course is not currently offered. This course provides an introduction to the concept of innovation, its role in the economy, the institutions that foster or hinder it, the laws that promote or undermine it, and its historical, psychological and social context. Through a combination of interactive lectures students will explore the complexity of the subject and its connections with law, the economy, history, sciences and technology and government and firm policies. In addition, through small group projects, students will deploy and extend their knowledge by applying it to a particular proposed innovation.
MGPO 438	Social Entrepreneurship and Innovation.	3
Social Entrepreneurship and Innovation. Terms offered: this course is not currently offered. Explores key concepts associated with social entrepreneurship and social innovation 鈥� the application of principles of entrepreneurship and innovation to solve social problems through social ventures, enterprises and not-for-profit organizations. Focuses on the social economy, including how the market system can be leveraged to create social value.
ORGB 321	Leadership.	3
Leadership. Terms offered: Summer 2025 Leadership theories provide students with opportunities to assess and work on improving their leadership skills. Topics include: the ability to know oneself as a leader, to formulate a vision, to have the courage to lead, to lead creatively, and to lead effectively with others.

Musical Applications of Technology Minor (B.Mus.) (18 credits)

Offered by: Music听(Schulich School of Music)听听听
Degree: Bachelor of Music
Program credit weight: 18

Program Description

The goal of this Minor is to provide instruction in practical and creative applications of technology for musical purposes. This program will help prepare students for production-oriented jobs in the creative arts.

This program is open to students from any discipline and has no prerequisites other than familiarity with computers. Applications will only be considered for fall admission. Late applications will not be accepted and no students will be admitted to the Minor in January. Registration will be limited to available lab space. To apply, submit an online application through the Music website: www.mcgill.ca/music/programs/minor/mat.

Students will be selected on the basis of their previous background or experience in music technology and/or sound recording, their computer programming skills, their expressed interest in the program, and their Cumulative Grade Point Average.

Advising for the Minor is available from the Area Chair for the Music Technology Program. Further information on this program is available on the Music Technology website at: .

Required Courses (12 credits)

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Course	Title	Credits
MUMT 202	Fundamentals of New Media.	3
Fundamentals of New Media. Terms offered: this course is not currently offered. A theoretical and practical introduction to selected areas of music technology. Topics include digital audio and sampling theory, MIDI and sequencing, audio editing and mixing, elementary sound recording, score editing software and current areas of research interest.
MUMT 250	Music Perception and Cognition.	3
Music Perception and Cognition. Terms offered: this course is not currently offered. Basic processes by which the brain transforms sound waves into musical events, dimensions, systems and structures and the processes by which musicians imagine new musical sounds and structures and plan movements that produce music on instruments.
MUMT 302	New Media Production 1.	3
New Media Production 1. Terms offered: this course is not currently offered. Techniques for producing and manipulating music and sound for new media applications. Synthesis techniques including FM, granular and physical modeling. Audio effects including delay, reverberation, dynamics processing, and filtering. Audio compression, HCI and MIR concepts.
PHYS 224	Physics of Music.	3
Physics of Music. Terms offered: this course is not currently offered. An introduction to the physics of music. Properties of sound and their perception as pitch, loudness, and timbre. Dissonance, consonance, and musical intervals and tuning. Physics of sound propagation and reflection. Resonance. Acoustic properties of pipes, strings, bars, and membranes, and sound production in wind, string, and percussion instruments. The human voice. Room reverberation and acoustics. Directional characteristics of sound sources.

Complementary Courses (6 credits)

6 credits selected from:

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Course	Title	Credits
MUMT 301	Music and the Internet.	3
Music and the Internet. Terms offered: this course is not currently offered. A brief history of Internet technologies (protocols, web servers, web browsers) and their relationship to music and musicians (physical vs. virtual music distribution, digital music formats, streaming services). Locating, retrieving, and working with online music information through Web APIs and coding exercises. Basic static website creation for musicians (HTML/CSS/JavaScript). Technology-enhanced music creation.
MUPD 204	Production for Digital Media 1.	3
Production for Digital Media 1. Terms offered: this course is not currently offered. Fundamental video production techniques for music and general applications. Professional video camera operation, lighting and shooting techniques. The lab component of the course includes camera setup and operation during Schulich School of Music productions for live internet streaming. Capture and editing of video, audio, text and graphics for use in creating digital media. Basic techniques of recording audio for video.
MUSR 200	Audio Recording Essentials.	3
Audio Recording Essentials. Terms offered: this course is not currently offered. A basic overview of audio recording. Topics include fundamentals of audio; a historical overview of recorded sound; analog and digital signal flow; listening environment design; listening and analysis; simple recording; connecting audio to a video camera; and audio on the web.
MUSR 232	Introduction to Electronics.	3
Introduction to Electronics. Terms offered: this course is not currently offered. Basics of electricity including: Ohm's law, electronic components, DC circuits, block diagram, amplifiers, filters, power supplies, electrical measurements (frequency levels, distortion). Emphasis will be placed on electronics applied to audio.
MUSR 300D1	Introduction to Music Recording. ¹	3
Introduction to Music Recording. Terms offered: this course is not currently offered. The theory and practice of music recording including a study of recording environments, equipment and studio techniques. The analysis of music scores and recordings with respect to the requirements and possibilities of the recording studio. Studio work will include recording sessions, recording of live concerts, editing, mixing and music p.a.
MUSR 300D2	Introduction to Music Recording. ¹	3
Introduction to Music Recording. Terms offered: this course is not currently offered. See MUSR 300D1 for description.
MUSR 339	Introduction to Electroacoustics.	3
Introduction to Electroacoustics. Terms offered: this course is not currently offered. Basic principles of operation and design of electroacoustical devices and systems; transducers and signal processing devices; magnetic tape sound recording - reproducing systems; disc recording, motion picture sound recording and reproducing systems; practical demonstration of some of these devices and associated measuring, testing and analyzing equipment and techniques.

¹: MUSR听300D1 Introduction to Music Recording./MUSR听300D2 Introduction to Music Recording. has limited enrollment and should be selected together. This course is generally restricted to students in the Sound Recording Qualifying Year program. Students interested in taking this course should contact the Sound Recording Area Coordinator to seek permission to register.

Musical Science and Technology Minor (B.Mus.) (18 credits)

Offered by: Music (Schulich School of Music)听听听听
Degree: Bachelor of Music
Program credit weight: 18

Program Description

This Minor focuses on interdisciplinary topics in science and technology as applied to music. The goal of the program is to help prepare students for commercial jobs in the audio technology sector and/or for subsequent graduate research study. This Minor is designed to serve students who already have a good background in the sciences and prior experience with Math and Computer Science courses.

Applications will only be considered for fall admission. Late applications will not be accepted and no students will be admitted to the Minor in January. Registration will be limited to available lab space. Selection is based on previous experience in math, computer programming, and related sciences, expressed interest in the program, and Cumulative Grade Point Average. To apply, submit an online application through the Music website: www.mcgill.ca/music/programs/minor/mst.

Advising for the Minor is available from the Area Chair for the Music Technology program. Further information on this program is available on the Music Technology website at: .

Required Courses (15 credits)

15 credits, select all of the following:

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Course	Title	Credits
MUMT 203	Introduction to Digital Audio.	3
Introduction to Digital Audio. Terms offered: this course is not currently offered. An introduction to digital audio and the technologies involved in its practical realization and use in computer music. Topics will include audio signals and systems, sampling quantization, signal encoding, compression, transmission and storage, filters, analog-to-digital and digital-to-analog converters, digital audio effects, sound sampling and synthesis techniques.
MUMT 250	Music Perception and Cognition.	3
Music Perception and Cognition. Terms offered: this course is not currently offered. Basic processes by which the brain transforms sound waves into musical events, dimensions, systems and structures and the processes by which musicians imagine new musical sounds and structures and plan movements that produce music on instruments.
MUMT 306	Music and Audio Computing 1.	3
Music and Audio Computing 1. Terms offered: this course is not currently offered. Concepts, algorithms, data structures, and programming techniques for the development of music and audio software, ranging from musical instrument design to interactive music performance systems.
MUMT 307	Music and Audio Computing 2.	3
Music and Audio Computing 2. Terms offered: this course is not currently offered. Theory and implementation of signal processing techniques for sound synthesis and audio effects processing using Matlab, C++, and Max/MSP.
MUMT 501	Digital Audio Signal Processing.	3
Digital Audio Signal Processing. Terms offered: this course is not currently offered. Discrete-time signal processing concepts and techniques. Discrete-time fourier transform and series, linear time-invariant systems, digital filtering, spectral analysis of discrete-time signals, and the z-transform.

Complementary Courses (3 credits)

3 credits selected from:

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Course	Title	Credits
MUMT 502	Senior Project: Music Technology.	3
Senior Project: Music Technology. Terms offered: this course is not currently offered. Independent senior project in Music Technology. Students will design and implement a medium-scale project in consultation with their advisor. Evaluation will be based on concept, background research, implementation, reliability, and documentation.
PHYS 224	Physics of Music.	3
Physics of Music. Terms offered: this course is not currently offered. An introduction to the physics of music. Properties of sound and their perception as pitch, loudness, and timbre. Dissonance, consonance, and musical intervals and tuning. Physics of sound propagation and reflection. Resonance. Acoustic properties of pipes, strings, bars, and membranes, and sound production in wind, string, and percussion instruments. The human voice. Room reverberation and acoustics. Directional characteristics of sound sources.

The full range of Minor Programs and details offered to engineering students about course requirements can be found in the Faculty of Engineering section of 大发彩票平台's eCalendar. Students must consult with their academic advisor before registering in a Minor program.

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Minor Programs

Arts Minor (B.Eng.) (24 credits)

Program 听Description

Requirements

Computer Science Minor (B.Eng.) (25 credits)

Program 听Description

Required Courses (3 credits)

Complementary Courses (21-23 credits)

Construction Engineering and Management Minor (B.Eng.) (24 credits)

Program 听Description

Prerequisites

Required Courses: Management and Law (15 credits)

Complementary Courses (9 credits)

List A

List B

Economics Minor (B.Eng.) (18 credits)

Program 听Description

Required Courses (18 credits)

Environmental Engineering Minor (B.Eng.) (21 credits)

Program 听Description

Complementary Courses (21-22 credits)

Stream A

Stream B

Engineering Course List

Non-Engineering Course List

Management (for Non-Management Students) (Minor) (18 credits)

Program Description

Complementary Courses (18 credits)

Materials Engineering Minor (B.Eng.) (24 credits)

Program 听Description

Required Courses (15 credits)

Complementary Courses

Mathematics Minor (B.Eng.) (18 credits)

Program 听Description

Required Course (3 credits)

Complementary Courses (15 credits)

Technological Entrepreneurship Minor (B.Eng.) (18 credits)

Program 听Description

Required Courses (9 credits)

Complementary Courses (9 credits)

Musical Applications of Technology Minor (B.Mus.) (18 credits)

Program Description

Required Courses (12 credits)

Complementary Courses (6 credits)

Musical Science and Technology Minor (B.Mus.) (18 credits)

Program Description

Required Courses (15 credits)

Complementary Courses (3 credits)

Department and University Information

Civil Engineering