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MATH 1000 Pre-Calculus (5,0,0)MATH 1000 Pre-Calculus (5,0,0)Credits: 3 credits This course provides the mathematical foundation for an introductory calculus course. Topics include equations and inequalities; functions, models, and graphs; polynomial and rational functions; exponential and logarithmic functions; trigonometric functions, identities and equations.
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MATH 1070 Mathematics for Business and Economics (3,1.5,0)MATH 1070 Mathematics for Business and Economics (3,1.5,0)Credits: 3 credits This course is designed for Business and Economics students. Topics include linear and non-linear functions and models applied to cost, revenue, profit, demand and supply, systems of equations (linear and nonlinear), matrices, linear programming, difference equations, and mathematics of finance (including simple and compound interest, annuities, mortgages, and loans).
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MATH 1100 Finite Math with Applications 1 (3, 1.5, 0)MATH 1100 Finite Math with Applications 1 (3, 1.5, 0)Credits: 3 credits This course is intended primarily for Liberal Arts or Tourism students. Students solve problems that have direct relevance in the “real world." Topics to be covered include sets, counting, probability, matrices, linear programming, and math of finance.
Prerequisites: Foundations of Math 11 with a minimum grade of 67% (C+) or Pre-Calculus 11 with a minimum grade of 67% (C+) or Foundations of Math 12 with a minimum grade of 60% (C) or MATH 0510 with a minimum grade of C- or MATH 0520 with a minimum grade of C- or MATH 0523 with a minimum grade of C- or MATH 0650 with a minimum grade of C-
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MATH 1130 Calculus 1 for Engineering (3,1.5,0)MATH 1130 Calculus 1 for Engineering (3,1.5,0)Credits: 3 credits 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.
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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 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-
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MATH 1150 Calculus for the Biological Sciences 1 (5,0,0)MATH 1150 Calculus for the Biological Sciences 1 (5,0,0)Credits: 3 credits Students study differential calculus for functions of one variable, with applications emphasizing the biological sciences. Topics include calculation and interpretation of limits and derivatives, curve sketching, and optimization problems. MATH 1140 is recommended rather than MATH 1150 for students planning to take second-year MATH courses.
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MATH 1170 Calculus for Business and Economics (3,1.5,0)MATH 1170 Calculus for Business and Economics (3,1.5,0)Credits: 3 credits This course is intended for Business and Economics students. Topics include calculation and interpretation of derivatives, curve sketching, optimization (applied to business and economics), multivariable functions (including partial derivatives, optimization and Lagrange multipliers).
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MATH 1220 Logic and Foundations ( 3,1.5,0)MATH 1220 Logic and Foundations ( 3,1.5,0)Credits: 3 credits Students are introduced to mathematics at the university level by learning some fundamental concepts of mathematics in a rigorous manner, using theorems and proofs. The topics in the course are vital for subsequent mathematics courses. Topics include propositional logic, properties of integers, relations and functions, mathematical induction and recurrence relations, axiomatic set theory, inclusion/exclusion and pigeonhole principles, and cardinality. This course is intended for students who plan to major in Mathematics or a combined Mathematics major.
Prerequisites: MATH 1140 with a minimum grade of C- or MATH 1141 with a minimum grade of C- or permission of the instructor/chair.
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MATH 1230 Calculus 2 for Engineering (3,1.5,0)MATH 1230 Calculus 2 for Engineering (3,1.5,0)Credits: 3 credits 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.
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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 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-
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MATH 1250 Calculus for the Biological Sciences 2 (5,0,0)MATH 1250 Calculus for the Biological Sciences 2 (5,0,0)Credits: 3 credits This course covers integral calculus for functions of one variable, with applications emphasizing the biological sciences. Topics include Riemann sums, definite and indefinite integrals, techniques of integration, improper integrals, first-order differential equations and slope fields, applications (including area, probability, logistic growth and predator-prey systems), and series. MATH 1240 is recommended instead of MATH 1250 for students planning to take 2nd-year MATH courses.
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-
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MATH 1300 Linear Algebra for Engineers (3,1.5,0)MATH 1300 Linear Algebra for Engineers (3,1.5,0)Credits: 3 credits This course is designed for engineering students, with applications chosen accordingly. Topics include real vectors in two and three dimensions, systems of linear equations and row-echelon form, span and linear dependence, linear transformations and matrices, determinants, complex numbers, eigenvalues and eigenvectors, and orthogonality and Gram-Schmidt orthogonalization.
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MATH 1420 Mathematics for Visual Arts (3,1.5,0)MATH 1420 Mathematics for Visual Arts (3,1.5,0)Credits: 3 credits Students explore mathematical concepts and techniques that are useful in a visual arts context. Topics include real numbers, ratios, geometry, and perspective.
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MATH 1540 Technical Mathematics 1 (3,1.5,0)MATH 1540 Technical Mathematics 1 (3,1.5,0)Credits: 3 credits Students are instructed in mathematical concepts that are relevant to architecture, design, and engineering. Topics include trigonometry, an introduction to two- and three- dimensional vectors, functions and graphs, solving linear and quadratic equations, coordinate geometry, areas and volumes of standard geometric shapes, elementary statistics and probability, and problem solving.
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MATH 1640 Technical Mathematics 2 (3,1.5,0)MATH 1640 Technical Mathematics 2 (3,1.5,0)Credits: 3 credits This is a calculus course for students in the Architectural and Engineering Technology program. Topics include systems of linear equations and matrices; differentiation and integration, with applications to curve sketching, extreme values and optimization; related rates; areas; volumes.
Prerequisites:
MATH 1540
and
Admission to the Architectural and Engineering Technology program |
MATH 1650 Mathematics for Computing Science (3,1.5,0)MATH 1650 Mathematics for Computing Science (3,1.5,0)Credits: 3 credits This course surveys several mathematical concepts used in Computing Science. Topics include logic; circuits; number systems; vector and matrix algebra; systems of linear equations; linear transformations; counting; discrete and continuous probabilities; statistics and random variables; decision analysis and asymptotic notation.
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- or MATH 1000 with a minimum grade of C- or MATH 1001 with a minimum grade of C-
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MATH 1700 Discrete Mathematics 1 (3,1.5,0)MATH 1700 Discrete Mathematics 1 (3,1.5,0)Credits: 3 credits 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-
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MATH 1900 Principles of Mathematics for Teachers (3,1.5,0)MATH 1900 Principles of Mathematics for Teachers (3,1.5,0)Credits: 3 credits This course is designed for students who wish to enter the Elementary Teaching Program, emphasizes conceptual understanding of elementary mathematical methods and ideas. Topics include problem solving, numbers and number theory, operations, geometry, measurement, proportional reasoning and probability. Additional topics may be included at the discretion of the instructor.
Prerequisites: Foundations of Math 11 with a minimum 67% (C+) or Pre-calculus 11 with a minimum 67% (C+) or MATH 0510 with a minimum grade of C- or MATH 0520 with a minimum grade of C- or MATH 0550 with a minimum grade of C-
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MATH 2110 Calculus 3 (3,1.5,0)MATH 2110 Calculus 3 (3,1.5,0)Credits: 3 credits 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.
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MATH 2120 Linear Algebra 1 (3,1.5,0)MATH 2120 Linear Algebra 1 (3,1.5,0)Credits: 3 credits 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.
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MATH 2200 Introduction to Analysis (3,1.5,0)MATH 2200 Introduction to Analysis (3,1.5,0)Credits: 3 credits Students learn some basic concepts of analysis in a mathematically rigorous manner, using theorems and proofs. Topics include the real number system, suprema and infima, completeness, real functions, and an introduction to continuity and limits using epsilon and delta.
Prerequisites: MATH 1240 or MATH 1241 or MATH 1230 and MATH 1220 or MATH 1700 or MATH 1701, with a minimum grade of C for all.
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MATH 2210 Introduction to Algebra (3,1.5,0)Credits: 3 credits Algebra in one of the main branches of Mathematics. This course offers some fundamental concepts of algebra in a mathematically rigorous manner. Topics include congruence and modular arithmetic, complex numbers, De Moivre’s Theorem, rings and ring homomorphisms, integral domains and fields, polynomial arithmetic, reducibility and irreducibility, and congruence in the ring of polynomials. |
MATH 2240 Differential Equations 1 (3,1.5,0)MATH 2240 Differential Equations 1 (3,1.5,0)Credits: 3 credits 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 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.
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MATH 3000 Complex Variables (3,1,0)MATH 3000 Complex Variables (3,1,0)Credits: 3 credits Students are introduced to the classical complex function theory, a cornerstone of mathematics. Topics include: complex derivatives and the Cauchy-Riemann equations; the complex exponential function and related elementary functions; integration along curves and Cauchy's theorems; Taylor and Laurent series; zeros and singularities; residues; and evaluation of integrals using the residue theorem.
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MATH 3020 Introduction to Probability (3,1,0)MATH 3020 Introduction to Probability (3,1,0)Credits: 3 credits 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.
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MATH 3030 Introduction to Stochastic Processes (3,1,0)MATH 3030 Introduction to Stochastic Processes (3,1,0)Credits: 3 credits Students examine simple random processes, including discrete and continuous Markov chains, Poisson processes and Brownian motion. Renewal theory is also discussed.
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MATH 3070 Linear Algebra 2 (3,1,0)MATH 3070 Linear Algebra 2 (3,1,0)Credits: 3 credits Fundamental ideas about vector spaces and subspaces, bases and dimension, linear transformations and matrices are studied in more depth than in MATH 2120. Topics include matrix diagonalization and its applications, invariant subspaces, inner product spaces and Gram-Schmidt orthogonalization, linear operators of various special types (normal, self-adjoint, unitary, orthogonal, projections), and the finite-dimensional spectral theorem.
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MATH 3080 Euclidean Geometry (3,1,0)MATH 3080 Euclidean Geometry (3,1,0)Credits: 3 credits Students are encountered with an examination of the axiomatic development of geometry, and some possible variations in axioms, and then move to a study of classical Euclidean geometry, including geometric transformations and their relevance for computer graphics. There may be some discussion of non-Euclidean geometries, such as projective geometry or hyperbolic geometry.
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MATH 3120 Elementary Number Theory (3,1,0)MATH 3120 Elementary Number Theory (3,1,0)Credits: 3 credits Students begin the course with integer divisibility and the related ideas of prime numbers, unique prime factorization, and congruence. Attention is then directed to arithmetic functions, including the Euler totient function. The Chinese Remainder Theorem and quadratic reciprocity are studied, and some Diophantine equations are considered. Lastly continued fractions and primitive roots may be discussed.
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MATH 3160 Differential Equations 2 (3,1,0)MATH 3160 Differential Equations 2 (3,1,0)Credits: 3 credits 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
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MATH 3170 Calculus 4 (3,1,0)MATH 3170 Calculus 4 (3,1,0)Credits: 3 credits The concept of a definite integral is extended to double and triple integrals and the calculus of vector fields are studied. Topics include triple integrals in rectangular, cylindrical and spherical coordinates, general change of variables in double and triple integrals, vector fields, line integrals, conservative fields and path independence, Green's theorem, surface integrals, Stokes' theorem and the divergence theorem, with applications in physics.
Prerequisites: a minimum grade of C in MATH 2110 or MATH 2111
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MATH 3200 Real Variables (3,1,0)MATH 3200 Real Variables (3,1,0)Credits: 3 credits The core of this course is a careful study of continuity and limits of real functions and convergence of real sequences and series, in addition to basic topology of the real line. Limit points and subsequences are discussed, leading to the Bolzano-Weierstrass theorem and the concept of a compact set. Metric spaces are introduced.
Prerequisites: a minimum grade of C in MATH 2200 and a minimum grade of C in one of MATH 3070, MATH 3080, MATH 3120 or MATH 3220. |
MATH 3220 Abstract Algebra (3,1,0)MATH 3220 Abstract Algebra (3,1,0)Credits: 3 credits Students in this course study some abstract algebraic structures. The main structures are groups and rings. Topics include groups and subgroups, cyclic groups, permutation groups, group homomorphisms and quotient groups, rings and ring homomorphisms, integral domains, ideals and quotient rings, prime and maximal ideals, and fields.
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MATH 3400 Introduction to Linear Programming (3,1,0)MATH 3400 Introduction to Linear Programming (3,1,0)Credits: 3 credits 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
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MATH 3510 Problem Solving Applied Math (3,1,0)MATH 3510 Problem Solving Applied Math (3,1,0)Credits: 3 credits This course provides learners with a systematic approach to problem solving. Students use a variety of analytical techniques to solve problems drawn from various disciplines. This course is of interest to students in any program where numerical problems may occur.
Prerequisites: MATH 1140 or MATH 1141 or MATH 1150 or MATH 1157 or MATH 1170 or MATH 1171 or MATH 1650 or MATH 1651 or MATH 1700 or MATH 1701 or STAT 1200 or STAT 1201 or STAT 2000 with a minimum grade of C -, or MATH 1220 with a minimum grade of C.
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MATH 3650 Numerical Analysis (3,1,0)MATH 3650 Numerical Analysis (3,1,0)Credits: 3 credits This course introduces standard numerical methods, including algorithms for solving algebraic equations (linear and nonlinear, single equations and systems) and for polynomial approximation and interpolation.
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MATH 3700 Introduction to the History of Mathematics (3,1,0)MATH 3700 Introduction to the History of Mathematics (3,1,0)Credits: 3 credits Students trace the development of numeration, arithmetic, geometry, algebra and other areas of mathematics, from their beginnings to their modern forms. The historical context of each mathematical development is emphasized by requiring students to solve problems using techniques that were available at the time.
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MATH 4240 Differential Geometry (4,0,0)MATH 4240 Differential Geometry (4,0,0)Credits: 3 credits Students in this course study the foundation of modern differential geometry. Topics include curves, Frenet-Serret trihedron, surfaces, fundamental forms, Gauss map, Gaussian curvature, Theorema Egregium, Geodesics,Gauss-Bonnet Theorem.
Prerequisites: MATH 2120 or MATH 2121 and MATH 2110 or MATH 2111 , all 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 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
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MATH 4430 Introduction to Graph Theory (4,0,0)MATH 4430 Introduction to Graph Theory (4,0,0)Credits: 3 credits An introductory course deals mostly with non-algorithmic topics, including connectivity, Eulerian graphs, Hamiltonian graphs, planarity and Kuratowski's Theorem, matchings, graph colouring, and extremal graphs. Applications of graphs are discussed.
Prerequisites:
MATH 2700-Discrete Mathematics 2 with a minimum grade of C
or
A minimum grade of C in at least 12 credits of Mathematics or Statistics courses numbered 2000 or higher. |
MATH 4650 Topology (4,0,0)Credits: 3 credits This course is an introduction to the fundamentals of topology. Topics include topological spaces, continuous functions, homeomorphism, base for a topology, open and closed sets, interior and closure, connectedness and local connectedness, compactness, quotient and product topology, separation axioms, Urysohn Lemma, and Tietze Extension Theorem. |
STAT 1200 Introduction to Statistics (3,1.5,0)STAT 1200 Introduction to Statistics (3,1.5,0)Credits: 3 credits Students are introduced to statistical reasoning in this course. Students will learn to 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. Students will learn to make appropriate inferences from confidence intervals and hypothesis tests including analysis of variance.
Prerequisites: Foundations of Mathematics 11 with a minimum grade of C+ or Pre-calculus 11 with a minimum grade of C+ or equivalent or Foundations of Math 12 or equivalent with a minimum grade of C+ or MATH 0510 with a minimum score of C- or MATH 0523 with a minimum score of C- or equivalent. MATH 1100 or MATH 1101 is recommended.
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STAT 2000 Probability and Statistics (3,1.5,0)STAT 2000 Probability and Statistics (3,1.5,0)Credits: 3 credits 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. .
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STAT 3050 Introduction to Statistical Inference (3,1,0)STAT 3050 Introduction to Statistical Inference (3,1,0)Credits: 3 credits 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.
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STAT 3060 Applied Regression Analysis (3,1,0)STAT 3060 Applied Regression Analysis (3,1,0)Credits: 3 credits 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.
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STAT 4040 Analysis of Variance (3,1,0)STAT 4040 Analysis of Variance (3,1,0)Credits: 3 credits 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 |
STAT 4310 Introduction to Multivariate Analysis (3,0,1)STAT 4310 Introduction to Multivariate Analysis (3,0,1)Credits: 3 credits Students analyze and interpret multivariate data in a number of different contexts. Topics include linear models, analysis of variance and covariance, multivariate analysis of variance, principle component analysis, and tree models. Students explore techniques for exploratory data analysis, model identification, and diagnostic checking. The course involves extensive use of software tools to apply the various analytical approaches.
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STAT 4990 ***Selected Topics in Statistics (3,1,0)STAT 4990 ***Selected Topics in Statistics (3,1,0)Credits: 3 credits Students consider, in depth, a selection of topics drawn from Statistics. The particular topics may vary each time the course is offered.
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