# 13.22 Mathematics and Statistics

At most 9 credit hours in Mathematics will be given for courses successfully completed from the following list subject to normal credit restrictions: Mathematics 1000, 1005, 1031, 1050, 1051, 1052, 1053, 1080, 1081, 1090, 109A/B, 1150, 1151. Students who have already obtained credit for 6 or more Mathematics credit hours numbered 2000 or above are not permitted to register for Mathematics 1052 or 1053, nor can they receive credit for either of these courses.

At Grenfell Campus, students who have completed high school mathematics may enter directly into Mathematics 1052 or 1053. However, placement in other first-year mathematics courses is based upon a student’s pre-requisite level of proficiency in mathematics as demonstrated in a manner that is acceptable to the School of Science and the Environment. This may be through a combination of credit and grades earned in recognized high school or undergraduate mathematics courses or through scores earned in the University’s Mathematics Placement Test (MPT) or Calculus Placement Test (CPT), or recognized, standardized examinations such as International Baccalaureate (IB), Advanced Placement (AP), or the College Board’s Subject Area Test in Mathematics Level I (SATM1) examinations. Students registering for first year mathematics courses online or through the St. John’s Campus should consult the Faculty of Science, Course Descriptions, Mathematics for placement information.

Mathematics courses are designated by MATH and Statistics courses are designated by STAT.

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**MATH 1000 Calculus I **

is an introduction to differential calculus, including algebraic, trigonometric, exponential, logarithmic, inverse trigonometric and hyperbolic functions. Applications include kinematics, related rates problems, curve sketching and optimization.

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**MATH 1001 Calculus II **

is an introduction to integral calculus, including Riemann sums and the Fundamental Theorem of Calculus, techniques of integration, improper integrals and first order differential equations. Applications include: area between curves, volumes of solids of revolution, probability functions and modelling with differential equations.

1.5

MATH 1000 or the former MATH 1081

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**MATH 1052 Mathematics for Business **

covers topics which include elementary algebra and functions, sets, elementary probability, matrices, systems of equations, and linear programming.

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**MATH 1053 Classical Mathematics **

covers topics which include logic, permutations, combinations, mathematical systems, elementary number theory, and geometry.

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**MATH 109A and 109B Introductory Algebra and Trigonometry **

is a two-semester course which provides students with the essential prerequisite elements for the study of an introductory course in calculus, at a slower pace than MATH 1090. Topics include algebra, functions and their graphs, exponential and logarithmic functions, trigonometry, polynomials, and rational functions.

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**MATH 1090 Algebra and Trigonometry **

provides students with the essential prerequisite elements for the study of an introductory course in calculus. Topics include algebra, functions and their graphs, exponential and logarithmic functions, trigonometry, polynomials, and rational functions.

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**MATH 2000 Calculus III **

is an introduction to infinite sequences and series, and to the differential and integral calculus of multivariate functions. Topics include tests for the convergence of infinite series, power series, Taylor and Maclaurin series, complex numbers including Euler's formula, partial differentiation, and double integrals in Cartesian and polar coordinates.

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**MATH 2050 Linear Algebra I **

includes the topics of Euclidean n-space, vector operations in 2- and 3-space, complex numbers, linear transformations on n-space, matrices, determinants, and systems of linear equations.

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**MATH 2051 Linear Algebra II **

includes the topics of real and complex vector spaces, basis, dimension, change of basis, eigenvectors, inner products, and diagonalization of Hermitian matrices.

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**MATH 2090 Mathematics of Finance **

covers the following topics: simple and compound interest and discount, forces of interest and discount, equations of value, annuities and perpetuities, amortization schedules and sinking funds, bonds and other securities, contingent payments.

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**MATH 2130 Technical Writing in Mathematics **

is a project oriented course combining mathematical investigation and technical writing. By using computer programming, graphical and typesetting tools, students will explore mathematical concepts and will produce technical reports of professional quality. The latter will combine elements of writing and graphics to convey technical ideas in a clear and concise manner.

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**MATH 2260 Ordinary Differential Equations I **

introduces first and second order differential equations, systems of first order differential equations and Laplace transforms. These will be studied with both analytic techniques as well as using a computer algebra system to generate symbolic and numerical solutions. Applications include oscillatory motion and population and epidemic models.

the former MATH 3260

MATH 2000

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**MATH 2320 Discrete Mathematics **

covers basic concepts of mathematical reasoning: logic and quantifiers, methods of proof, sets and set operations, functions and relations, equivalence relations and partial orders, countable and uncountable sets. These concepts will be illustrated through the congruence and divisibility of integers, induction and recursion, principles of counting, permutations and combinations, the Binomial Theorem, and elementary probability.

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**MATH 2330 Euclidean Geometry **

is an introduction to Euclidean geometry of the plane. It covers the geometry of triangles and circles, including results such as the Euler line, the nine-point circle and Ceva’s theorem. It also includes straight-edge and compass constructions, isometries of the plane, the three reflections theorem, and inversions on circles.

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**STAT 2500 Statistics for Business and Arts Students **

covers descriptive statistics (including histograms, stem-and-leaf plots and box plots), elementary probability, random variables, the binomial distribution, the normal distribution, sampling distribution, estimation and hypothesis testing including both one and two sample tests, paired comparisons, correlation and regression, related applications.

1.5

3 credit hours in Mathematics or Statistics courses, or a combination of placement test and high school Mathematics scores acceptable to the School of Science and the Environment

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**STAT 2550 Statistics for Science Students **

is an introduction to basic statistics methods with an emphasis on applications to the sciences. Material includes descriptive statistics, elementary probability, binomial distribution, Poisson distribution, normal distribution, sampling distribution, estimation and hypothesis testing (both one and two sample cases), chi-square test, one way analysis of variance, correlation and simple linear regression.

1.5

Statistical computer package will be used in the laboratory, but no prior computing experience is assumed

MATH 1000 or the former MATH 1081

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**MATH 3000 Real Analysis I **

covers the structure of the real numbers, sequences and limits, compactness, continuity, uniform continuity, differentiation, and the Mean Value Theorem.

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**MATH 3132 Numerical Analysis I **

includes a discussion of round-off error, the solution of linear systems, iterative methods for nonlinear equations, interpolation and polynomial approximation, least squares approximation, fast Fourier transform, numerical differentiation and integration, and numerical methods for initial value problems.

Computer Science 3731

1.5

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**MATH 3202 Vector Calculus **

deals with functions of several variables. Lagrange multipliers, vector valued functions, directional derivatives, gradient, divergence, curl, transformations, Jacobians, inverse and implicit function theorems, multiple integration including change of variables using polar, cylindrical and spherical co-ordinates, Green’s theorem. Stokes’ theorem, divergence theorem, line integrals, arc length.

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**MATH 3240 Applied Graph Theory **

examines algorithms and complexity, definitions and basic properties of graphs, Eulerian and Hamiltonian chains, shortest path problems, graph colouring, planarity, trees, network flows, with emphasis on applications including scheduling problems, tournaments, and facilities design.

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**MATH 3320 Abstract Algebra **

is an introduction to groups and group homomorphisms including cyclic groups, cosets, Lagrange's theorem, normal subgroups and quotient groups, introduction to rings and ring homomorphisms including ideals, prime and maximal ideals, quotient rings, integral domains and fields.

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**MATH 3340 Introductory Combinatorics **

includes Topics such as distributions, the binomial and multinomial theorems, Stirling numbers, recurrence relations, generating functions and the inclusion-exclusion principle. Emphasis will be on applications.

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**MATH 3370 Introductory Number Theory **

is perfect numbers and primes, divisibility, Euclidean algorithm, greatest common divisors, primes and the unique factorization theorem, congruences, cryptography (secrecy systems), Euler-Fermat theorems, power residues, primitive roots, arithmetic functions, Diophantine equations, topics above in the setting of the Gaussian integers.

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**STAT 3410 Mathematical Statistics I **

is basic probability concepts, combinatorial analysis, conditional probability, independence, random variable, distribution function, mathematical expectation, Chebyshev's inequality, distribution of two random variables, binomial and related distributions, Poisson, gamma, normal, bivariate normal, t, and F distributions, transformations of variables including the moment-generating function approach.

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**MATH 4132 Introduction to Optimization **

is an introduction to optimization, analytic methods for functions of one variable and for functions of several variables, classical maxima and minima, necessary and sufficient conditions, constrained optimization, equality and inequality constraints, Kuhn-Tucker conditions, introduction to the calculus of variations, linear programming, simplex algorithm.

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**MATH 4160 Partial Differential Equations I **

covers two point boundary value problems, Fourier series, Sturm-Liouville theory, canonical forms, classification and solution of linear second order partial differential equations in two independent variables, separation of variable, integral transform methods.

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**MATH 4191 Modelling in Life Sciences **

is an introduction to population dynamics modelling and epidemiological modelling via ordinary and partial differential equations. Topics include basic non-spatial single species models, pollution models, non-spatial models of interacting populations, chemostat models, disease dynamics models, spatial population dynamics via reaction-diffusion equations, steady state solutions, modelling of invasive species, notions of critical domain size and spreading speed, extending classical models to two-compartment and spatially heterogenous settings.

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**MATH 4242 Algorithms and Complexity **

is a study of the correctness and complexity of algorithms, with particular focus on algorithms important in mathematics. Topics may include sorting and binary search, string searching, integer multiplication and exponentiation, matrix multiplication, geometric problems such as closest pair of points and convex hull, probabilistic and approximative algorithms. This course discusses polynomial reductions and NP-completeness.

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**MATH 4251 Advanced Matrix Analysis **

is an advanced course in linear algebra and matrix theory with applications in quantum information. Topics include spectral theorem, singular value decomposition, variational characterizations of eigenvalues of Hermitian matrices, vector and matrix norms, characterizations of positive definite matrices, trace inequalities and entropy.

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**MATH 4292-4299 Special Topics in Mathematics **

are courses offered on a one-time basis which cover a specific mathematical topic.

permission of the Chair of Mathematics

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**MATH 4305 Mathematical Logic **

starts with a brief overview of basic set theory, followed by an introduction to propositional and predicate logic and basics of model theory (models, theories, compactness theorem) and computability theory (computable and computably enumerable sets, first order arithmetic).

MATH 2320 and 6 credit hours in Mathematics at the 3000-level or higher or permission of the Chair of Mathematics

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**MATH 4340 Combinatorial Analysis **

continues most of the topics started in 3340 with further work on distributions, recurrence relations and generating functions. Generating functions are used to solve recurrence relations in two variables. Also included is a study of Polya's theorem with applications.

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**MATH 4343 Combinatorial Game Theory **

is an introduction to the study of two-player strategy games of perfect information and no chance. Topics include canonical form; group and poset structure of short games; Sprague-Grundy Theory of impartial games; and monoids of games under misère play. Computer programming will be used to analyze games computationally.

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**MATH 4345 Advanced Graph Theory **

includes topics which may be chosen from matchings, factorizations, adjacency matrices, eigenvalues of graphs, strongly regular graphs, independent sets and cliques, cuts and connectivity, graph products, graph homomorphisms, edge colourings, domination, and graph searching.

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**MATH 4950 Senior Project **

is a course in which, under the guidance of a faculty member, students conduct a study of an area of mathematics. Students are required to submit a report and give a presentation.

permission of Program Chair

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**MATH 495A/B Honours Project in Mathematics **

is a two-semester course that requires the student, under the supervision of a faculty member, to prepare a dissertation in an area of mathematics. In addition to a written project, an oral presentation will be given by the student at the end of the second semester.

6

Permission of the Program Chair and admission to an honours program

AN = Additional notes. AR = Attendance requirement as noted. CH = Credit hours: unless otherwise noted, a course normally has a credit value of 3 credit hours. CO = Co-requisite(s): course(s) listed must be taken concurrently with or successfully completed prior to the course being described. CR = Credit restricted: The course being described and the course(s) listed are closely related but not equivalent. Credit is limited to one of these courses. Normally, these courses cannot be substituted, one for the other, to satisfy program requirements. EQ = Equivalent: the course being described and the course(s) listed are equal for credit determination. Credit is limited to one of these courses. These courses can be substituted, one for the other, to satisfy program requirements. |
LC = Lecture hours per week: lecture hours are 3 per week unless otherwise noted. LH = Laboratory hours per week. OR = Other requirements of the course such as tutorials, practical sessions, or seminars. PR = Prerequisite(s): course(s) listed must be successfully completed prior to commencing the course being described. UL = Usage limitation(s) as noted. |

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