# Bachelor of Science - Mathematics and Economics Major

The major in mathematics and economics requires the completion of at least 66 credits in economics, mathematics and statistics, of which a maximum of 30 credits must be at the upper level (3000 and 4000 levels) and no less than six credits must be at the 4000 level.

###### Lower level requirements (36 credits)
MATH 1130 Calculus 1 for Engineering (3,1.5,0)

#### MATH 1130 Calculus 1 for Engineering (3,1.5,0)

Credits: 3 credits
Delivery: Campus

Students build a strong mathematical foundation for engineering by learning ideas, methods and applications of single-variable differential calculus. Limits and derivatives are defined and calculated, derivatives are interpreted as slopes and rates of change, and derivatives are then applied to many sorts of problems, such as finding maximum and minimum values of functions.
Prerequisite: Admission to the Engineering program.
Note: Students can get credit for only one of the following MATH 1130, MATH 1140, MATH 1141, MATH 1150, MATH 1157, MATH 1170 or MATH 1171.

or
MATH 1140 Calculus 1 (3,1.5,0) or (5,0,0)

#### MATH 1140 Calculus 1 (3,1.5,0) or (5,0,0)

Credits: 3 credits
Delivery: Campus

Students study differential calculus for functions of one variable, with applications emphasizing the physical sciences. Topics include calculation and interpretation of limits and derivatives; curve sketching; optimization and related-rate problems; l'Hospital's rule; linear approximation and Newton's method. Prerequisites: Pre-calculus 12 with a minimum grade of 67% (C+) or MATH 0610 with a minimum grade of C- or MATH 0630 with a minimum grade of C- or MATH 0633 with a minimum grade of C- or MATH 1000 with a minimum grade of C- or MATH 1001 with a minimum grade of C-
Note: Students can get credit for only one of the following MATH 1130, MATH 1140, MATH 1141, MATH 1150, MATH 1157, MATH 1170 or MATH 1171.

MATH 1230 Calculus 2 for Engineering (3,1.5,0)

#### MATH 1230 Calculus 2 for Engineering (3,1.5,0)

Credits: 3 credits
Delivery: Campus

Students learn the ideas and techniques of single-variable integral calculus from an engineering perspective. Integrals are defined, evaluated and used to calculate areas, volumes, arc lengths and physical quantities such as force, work and centres of mass. Differential equations are introduced and used to model various physical phenomena. Ideas about infinite series are pursued, including some convergence tests, with particular emphasis on Taylor series.
Prerequisite: MATH 1130 with a minimum grade of C.
Note: Students will get credit for only one of MATH 1230, MATH 1240, MATH 1241 or MATH 1250.

or
MATH 1240 Calculus 2 (3,1.5,0) or (5,0,0)

#### MATH 1240 Calculus 2 (3,1.5,0) or (5,0,0)

Credits: 3 credits
Delivery: Campus

This course covers integral calculus for functions of one variable, with applications emphasizing the physical sciences. Topics include Riemann sums, definite and indefinite integrals, techniques of integration, improper integrals, applications of integration (including area, volume, arc length, probability and work), separable differential equations, and series. Prerequisites: MATH 1130 with a minimum grade of C- or MATH 1140 with a minimum grade of C- or MATH 1141 with a minimum grade of C- or MATH 1150 with a minimum grade of C- or MATH 1157 with a minimum grade of C-
Note: Students will get credit for only one of MATH 1230, MATH 1240, MATH 1241 or MATH 1250.

MATH 1700 Discrete Mathematics 1 (3,1.5,0)

#### MATH 1700 Discrete Mathematics 1 (3,1.5,0)

Credits: 3 credits
Delivery: Campus

This course is an introduction to the foundation of modern mathematics including basic set theory; solution to recurrence relations; logic and quantifiers; properties of integers; mathematical induction; introduction to graphs and trees; Boolean algebra and finite state machines. Students will apply the critical thinking skills developed in Mathematics to derive meaning from complex problems. Prerequisites: Pre-calculus 12 with a minimum C+ or Foundations of Math 12 with a minimum C+ or MATH 0600 with a minimum grade of B or MATH 0610 with a minimum grade of C- or MATH 0630 with a minimum grade of C- or MATH 0633 with a minimum grade of C- or MATH 0650 with a minimum grade of C-
Note: Students can get credit for only one of the following MATH 1220, COMP 1390, MATH 1390, MATH 1700 or MATH 1701.

ECON 1900 Principles of Microeconomics (3,0,0)

#### ECON 1900 Principles of Microeconomics (3,0,0)

Credits: 3 credits
Delivery: Campus

Students examine the interactions between individuals and firms in various types of markets. Topics include a definition of economics; demand and supply analysis; consumer theory; production and cost; market structure including perfect competition, monopoly, monopolistic competition, and oligopoly; market efficiency and market failure; resource markets; and international trade.
Prerequisite: Foundations of Mathematics 11 or Pre-calculus Math 11 with a minimum B OR MATH 0510 or MATH 0530 or equivalent. Completion of one Foundations of Mathematics 12, or Pre-calculus 12 is highly recommended
Note: Students cannot receive credit for both ECON 1900 and ECON 1901

ECON 1950 Principles of Macroeconomics (3,0,0)

#### ECON 1950 Principles of Macroeconomics (3,0,0)

Credits: 3 credits
Delivery: Campus

Students examine economic behaviour at the aggregate level, and the measurement and determination of national income. Topics include an introduction to economics; measuring macroeconomic variables including gross domestic product, unemployment, and inflation; the Keynesian model; aggregate demand and supply; money and banking; the money market; fiscal policy; monetary policy and the central bank; exchange rates and the balance of payments; and economic growth.
Prerequisite: Foundations of Mathematics 11 or Pre-calculus Math 11 with a minimum B or MATH 0510 or MATH 0530 or equivalent. Completion of one Foundations of Mathematics 12, or Pre-calculus 12 is highly recommended

STAT 2000 Probability and Statistics (3,1.5,0)

#### STAT 2000 Probability and Statistics (3,1.5,0)

Credits: 3 credits
Delivery: Campus

This course is intended for math or science students. Students are introduced to probability and statistical reasoning. Students will learn to both calculate and interpret quantities relating to descriptive statistics; correlation; regression; probability; and probability distributions including the binomial and normal. Students will learn different facets of sampling and experimental design and the construction and appropriate inference from confidence intervals and hypothesis tests including analysis of variance. Students will apply their knowledge in groups to investigate and resolve divergent views on data analysis. .
Prerequisite: MATH 1140 with a score of C- or MATH 1130 with a score of C- or MATH 1150 with a score of C- or MATH 1157 or MATH 1170 with a score of C- or MATH 1171 with a score of C-
Note: Students cannot receive credit for more than one of BIOL 3000, ECON 2320, GEOG 2700, PSYC 2100, PSYC 2101, STAT 1200, STAT 1201, and STAT 2000

or
ECON 2320 Economics and Business Statistics 1 (3,0,0)

#### ECON 2320 Economics and Business Statistics 1 (3,0,0)

Credits: 3 credits
Delivery: Campus

Students are introduced to statistics with an emphasis on its applications in business and economics. Topics include descriptive statistics and numerical measures; an introduction to probability; discrete and continuous probability distributions; sampling and sampling distributions; interval estimations; and testing hypotheses and statistical inferences.
Prerequisite: ECON 1220 or ECON 1900 and ECON 1950
Note:Students cannot receive credit for more than one of MATH 1200, STAT 1200, STAT 2000, ECON 2320, PSYC 2100, SOCI 2710, BIOL 3000, and SOCI 3710

MATH 2110 Calculus 3 (3,1.5,0)

#### MATH 2110 Calculus 3 (3,1.5,0)

Credits: 3 credits
Delivery: Campus

The concepts of single-variable calculus are extended to higher dimensions by using vectors as variables. Topics include vector geometry and the analytic geometry of lines, planes and surfaces; calculus of curves in two or three dimensions, including arc length and curvature; calculus of scalar-valued functions of several variables, including the gradient, directional derivatives and the Chain Rule; Lagrange multipliers and optimization problems; double integrals in rectangular and polar coordinates. Prerequisites: MATH 1230 with a minimum grade of C or MATH 1240 with a minimum grade of C or MATH 1241 with a minimum grade of C.
Note: Students will get credit for only one of MATH 2110, MATH 2111 or MATH 2650.

MATH 2120 Linear Algebra 1 (3,1.5,0)

#### MATH 2120 Linear Algebra 1 (3,1.5,0)

Credits: 3 credits
Delivery: Campus

Students are introduced to linear algebra. Topics include vector spaces, Matrix algebra and matrix inverse, systems of linear equations and row-echelon form, bases and dimension, orthogonality, geometry of n-dimensional space, eigenvalues and eigenvectors, linear transformations. Prerequisites: MATH 1220 or MATH 1230 or MATH 1240 or MATH 1241 or MATH 1250 or MATH 1700 or MATH 1701 all with a minimum grade of C.
Note: Students will only receive credit for one MATH 1300, MATH 2120 or MATH 2121.

MATH 2240 Differential Equations 1 (3,1.5,0)

#### MATH 2240 Differential Equations 1 (3,1.5,0)

Credits: 3 credits
Delivery: Campus

This course examines ordinary differential equations and related initial-value problems, and emphasizes their many applications in science and engineering. Students discuss methods for solving such equations either exactly or approximately. Topics include first-order equations; higher order linear equations; modelling with differential equations; systems of linear equations; and phase plane analysis of nonlinear systems. Prerequisites: MATH 1240 or MATH 1241 and MATH 2110 or 2111 and MATH 2120 or MATH 2121, all with a minimum grade of C. NOTE: MATH 2110 or 2111 and MATH 2120 or MATH 2121 may be taken as co-requisites with MATH 2240.

MATH 2700 Discrete Mathematics 2 (3,1.5,0)

#### MATH 2700 Discrete Mathematics 2 (3,1.5,0)

Credits: 3 credits
Delivery: Campus

Student will further develop concepts in discrete mathematics building on ideas introduced in first year. Topics include combinatorial arguments and proofs, deriving and solving recurrence relations; generating functions; inclusion-exclusion; functions and relations; and graph theory with an emphasis on algorithmic aspects.
Prerequisite: MATH 1220 or COMP 1390 or MATH 1390 or MATH 1700 or MATH 1701 all with a minimum grade of C.

ECON 2900 Intermediate Microeconomics 1 (3,0,0)

#### ECON 2900 Intermediate Microeconomics 1 (3,0,0)

Credits: 3 credits
Delivery: Campus

Students examine at a more advanced level how individuals and firms interact in various types of markets. Topics include consumer and producer behaviour; partial equilibrium analysis for perfectly competitive markets; and aspects of monopoly and imperfectly competitive markets. This course prepares students for advanced courses in economics.
Prerequisite: ECON 1900 or ECON 1901 and MATH 1170
Note: Students cannot credit for more than one of ECON 2900, BUEC 2040, BUEC 2041

ECON 2950 Intermediate Macroeconomics 1 (3,0,0)

#### ECON 2950 Intermediate Macroeconomics 1 (3,0,0)

Credits: 3 credits
Delivery: Campus

Students complete an advanced, in-depth examination of economic behaviour at the aggregate level. Topics include the determination and distribution of output in the long run; the classical dichotomy and neutrality of money; the measurement, problems, and determinants of unemployment and inflation in the long run; and the role of capital accumulation, population growth, and technology in growth theory.
Prerequisite: ECON 1950 or ECON 1951

###### Upper level requirements (30 credits)
ECON 3200 Introduction to Mathematical Economics (3,0,0)

#### ECON 3200 Introduction to Mathematical Economics (3,0,0)

Credits: 3 credits
Delivery: Campus

Students examine the mathematical methods and tools most commonly used in analyzing economic problems. Topics include a review of set theory, functions, and limits; linear models and matrix algebra; application of single and multivariable calculus; unconstrained and constrained optimization; integration and difference and differential equations; application of dynamic analysis; and linear and non-linear programing.
Prerequisite: ECON 1900; ECON 1950; MATH 1170 or equivalent

ECON 3900 Intermediate Microeconomics 2 (3,0,0)

#### ECON 3900 Intermediate Microeconomics 2 (3,0,0)

Credits: 3 credits
Delivery: Campus

Students continue to study intermediate topics in partial and general equilibrium analysis. Topics include consumer choice under different scenarios, factor markets, game theory, imperfect competition, general equilibrium analysis and welfare economics, public goods, and externalities.
Prerequisite: ECON 2900; MATH 1170 or equivalent

ECON 3950 Intermediate Macroeconomics 2 (3,0,0)

#### ECON 3950 Intermediate Macroeconomics 2 (3,0,0)

Credits: 3 credits
Delivery: Campus

Students continue to study short-run macroeconomic theory and its applications to contemporary policy issues. Topics include an overview of macroeconomics; macroeconomic data; the open economy; economic fluctuations; aggregate demand, including investment savings-liquidity preference money supply (IS-LM) curves; aggregate supply, including the Phillips curve; economic stabilization and the effectiveness of fiscal and monetary policy; and money supply and demand.
Prerequisite: ECON 2950

ECON 4320 Econometrics (3,0,0)

#### ECON 4320 Econometrics (3,0,0)

Credits: 3 credits
Delivery: Campus

Students are introduced to econometric models and the application of classical regression techniques to estimate socio-economic relationships. Topics include an introduction to econometrics; simple linear regression; interval estimation and hypothesis testing; predictions, goodness of fit, and modeling issues; multiple regression; non-linear relationships; heteroscedasticity; dynamic models, autocorrelation, and forecasting; simultaneous equations; and qualitative dependent variables. General econometric computer software is used to reinforce course concepts.
Prerequisite: ECON 2330 or ECON 3330 or equivalent

ECON 4330 Forecasting in Business and Economics (3,0,0)

#### ECON 4330 Forecasting in Business and Economics (3,0,0)

Credits: 3 credits
Delivery: Campus

Students apply a variety of forecasting methods to solve problems in business and economics. Topics include qualitative forecasting methods; the forecasting process, data considerations, and model selection; moving averages and exponential smoothing; multiple regression and time series decomposition; Box-Jenkins methodology to fit autoregressive conditional heteroscedasticity (ARCH); time-varying volatility and autoregressive integrated moving average (ARIMA) and vector autoregressive models; combining forecasting results; and implementing forecasting.
Prerequisite: ECON 2330 or ECON 3330 or equivalent
Exclusion: BUEC 4330

Depending on a student's interests and qualifications, one of the following streams should be chosen:

###### Mathematics stream
STAT 3060 Applied Regression Analysis (3,1,0)

#### STAT 3060 Applied Regression Analysis (3,1,0)

Credits: 3 credits
Delivery: Campus

Students are exposed to the concepts of regression analysis with an emphasis on application. Students will learn how to appropriately conduct residual analysis, perform diagnostics, apply transformations, select and check models, and augment regression such as with weighted least squares and nonlinear models. Students may learn additional topics such as inverse, robust, ridge and logistic regression.
Prerequisite: MATH 1300 or MATH 2121 or MATH 2120, STAT 2000

MATH 3160 Differential Equations 2 (3,1,0)

#### MATH 3160 Differential Equations 2 (3,1,0)

Credits: 3 credits
Delivery: Campus

This course begins with an introduction to Fourier series and Fourier transforms. Next, series solutions of ordinary differential equations are examined. Power series methods are applied to obtain solutions near ordinary points and regular singular points. Students then consider Sturm-Liouville boundary value problems and series of eigenfunctions. Initial value and boundary value problems involving partial differential equations are then examined. Solutions are found using the methods of separation of variables, Green's functions and integral transforms. Physical applications discussed include the heat/diffusion equation, wave equation and Laplace's equation. Prerequisites: MATH 2240-Differential Equations with a minimum grade of C
Exclusion: Students will only receive credit for one of MATH 3160 or PHYS 3120.

MATH 3400 Introduction to Linear Programming (3,1,0)

#### MATH 3400 Introduction to Linear Programming (3,1,0)

Credits: 3 credits
Delivery: Campus

This course introduces the theory and applications of linear programming. Topics include: the graphic method, the simplex algorithm, the revised simplex method, duality theory, and sensitivity analysis. Some special linear programming problems such as transportation, network flows, and game theory are explored. Prerequisites: MATH 2120 or MATH 2121 with a minimum grade of C

MATH 4410 Modelling of Discrete Optimization Problems (3,1,0)

#### MATH 4410 Modelling of Discrete Optimization Problems (3,1,0)

Credits: 3 credits
Delivery: Campus

Real-world optimization problems are formulated in order to be resolved by standard techniques involving linear programming, integer programming, network flows, dynamic programming and goal programming. Additional techniques may include post-optimality analysis, game theory, nonlinear programming, and heuristic techniques. Prerequisites: MATH 3400-Intro to Linear Programming with a minimum grade of C

Upper level MATH elective (3000 or 4000 level)
###### Statistics stream
MATH 3020 Introduction to Probability (3,1,0)

#### MATH 3020 Introduction to Probability (3,1,0)

Credits: 3 credits
Delivery: Campus

This course provides a theoretical foundation for the study of statistics. Topics include basic notions of probability, random variables, probability distributions (both single-variable and multi-variable), expectation and conditional expectation, limit theorems and random number generation.
Prerequisite: MATH 2110 or 2111 with a minimum grade of C-

MATH 3030 Introduction to Stochastic Processes (3,1,0)

#### MATH 3030 Introduction to Stochastic Processes (3,1,0)

Credits: 3 credits
Delivery: Campus

Students examine simple random processes, including discrete and continuous Markov chains, Poisson processes and Brownian motion. Renewal theory is also discussed.
Prerequisite: MATH 3020 Required Seminar: MATH 3030S

MATH 3050
MATH 3060
STAT 4040 Analysis of Variance (3,1,0)

#### STAT 4040 Analysis of Variance (3,1,0)

Credits: 3 credits
Delivery: Campus

Students discuss the analysis of variance for standard experimental designs. Topics include single factor designs, fixed and random effects, block designs, hierarchical designs, multiple comparisons, factorial designs, mixed models, general rules for analysis of balanced designs, and analysis of covariance. Co-Requisite: STAT 3060 Required Seminar: STAT 4040S

###### General stream
STAT 3060 Applied Regression Analysis (3,1,0)

#### STAT 3060 Applied Regression Analysis (3,1,0)

Credits: 3 credits
Delivery: Campus

Students are exposed to the concepts of regression analysis with an emphasis on application. Students will learn how to appropriately conduct residual analysis, perform diagnostics, apply transformations, select and check models, and augment regression such as with weighted least squares and nonlinear models. Students may learn additional topics such as inverse, robust, ridge and logistic regression.
Prerequisite: MATH 1300 or MATH 2121 or MATH 2120, STAT 2000

Plus at least four of:
MATH 3020 Introduction to Probability (3,1,0)

#### MATH 3020 Introduction to Probability (3,1,0)

Credits: 3 credits
Delivery: Campus

This course provides a theoretical foundation for the study of statistics. Topics include basic notions of probability, random variables, probability distributions (both single-variable and multi-variable), expectation and conditional expectation, limit theorems and random number generation.
Prerequisite: MATH 2110 or 2111 with a minimum grade of C-

MATH 3030 Introduction to Stochastic Processes (3,1,0)

#### MATH 3030 Introduction to Stochastic Processes (3,1,0)

Credits: 3 credits
Delivery: Campus

Students examine simple random processes, including discrete and continuous Markov chains, Poisson processes and Brownian motion. Renewal theory is also discussed.
Prerequisite: MATH 3020 Required Seminar: MATH 3030S

STAT 3050 Introduction to Statistical Inference (3,1,0)

#### STAT 3050 Introduction to Statistical Inference (3,1,0)

Credits: 3 credits
Delivery: Campus

This course examines the theory behind statistical inference. Students will review probability theory, sampling distributions, methods of estimation, and hypothesis testing. Students will learn more advanced inferential techniques such as maximum likelihood estimation, bootstrapping, Bayesian methods, likelihood ratio testing, and confidence intervals. There will be an emphasis on the theory of these approaches in addition to their application.
Prerequisite: STAT 2000 with a minimum grade of C and MATH 3020 with a minimum grade of C or instructor permission.

MATH 3160 Differential Equations 2 (3,1,0)

#### MATH 3160 Differential Equations 2 (3,1,0)

Credits: 3 credits
Delivery: Campus

This course begins with an introduction to Fourier series and Fourier transforms. Next, series solutions of ordinary differential equations are examined. Power series methods are applied to obtain solutions near ordinary points and regular singular points. Students then consider Sturm-Liouville boundary value problems and series of eigenfunctions. Initial value and boundary value problems involving partial differential equations are then examined. Solutions are found using the methods of separation of variables, Green's functions and integral transforms. Physical applications discussed include the heat/diffusion equation, wave equation and Laplace's equation. Prerequisites: MATH 2240-Differential Equations with a minimum grade of C
Exclusion: Students will only receive credit for one of MATH 3160 or PHYS 3120.

MATH 3400 Introduction to Linear Programming (3,1,0)

#### MATH 3400 Introduction to Linear Programming (3,1,0)

Credits: 3 credits
Delivery: Campus

This course introduces the theory and applications of linear programming. Topics include: the graphic method, the simplex algorithm, the revised simplex method, duality theory, and sensitivity analysis. Some special linear programming problems such as transportation, network flows, and game theory are explored. Prerequisites: MATH 2120 or MATH 2121 with a minimum grade of C

STAT 4040 Analysis of Variance (3,1,0)

#### STAT 4040 Analysis of Variance (3,1,0)

Credits: 3 credits
Delivery: Campus

Students discuss the analysis of variance for standard experimental designs. Topics include single factor designs, fixed and random effects, block designs, hierarchical designs, multiple comparisons, factorial designs, mixed models, general rules for analysis of balanced designs, and analysis of covariance. Co-Requisite: STAT 3060 Required Seminar: STAT 4040S