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2012-2013 Calendar Proof MATHEMATICS Note: See beginning of Section F for abbreviations, course numbers and coding. MATH 1001 Calculus for Life Sciences 3 ch (4C) Functions, limits, continuity, the concept of derivative, basic rules of differentiation. Derivatives of polynomials, exponential, logarithmic and trigonometric functions. Extreme values and related rates. Introduction to integration, area, volume, average value. Applications to life sciences will be stressed throughout the course. This course is restricted to students in Health Sciences, Nursing, and Biological Sciences. Notes: (1)Credit will be given for only one of MATH 1001 , MATH 1003 , MATH 1823 , or MATH 2853 (2) A minimum grade of B is required in MATH 1001 to take MATH 1013 . Prerequisite: A minimum grade of 60% in New Brunswick high school courses: Trigonometry and 3-Space, advanced Math with an introduction to Calculus, or equivalent. MATH 1003 Introduction to Calculus I 3 ch (4C) Functions and graphs, limits, derivatives of polynominal, log, exponential and trigonometric functions. Curve sketching and extrema of functions. Prerequisite: A grade of at least 60% in New Brunswick high school courses: Trigonometry and 3- space, Advanced Mathematics with an introduction to Calculus or equivalent courses. Students must also pass a Placement Test which is administered by the Department of Mathematical Sciences during Orientation Week in September. See “Note 12 to Admissions Chart” in Section B of this Calendar for further details. Note: Credit will be given for only one of MATH 1001 , MATH 1003, MATH 1823 or MATH 2853 . MATH 1013 Introduction to Calculus II 3 ch (4C) Definition of the integral, fundamental theorem of calculus, techniques of integration, improper integrals. Ordinary differential equations. Taylor polynomials and series. Prerequisite: A grade of C or higher in MATH 1003 . MATH 1503 Introduction to Linear Algebra 3 ch (3C) Lines and Planes, The Geometry and Algebra of vectors, Systems of linear equations, Matrix algebra, Linear independence, Linear transformations, Determinants, Complex numbers, Eigenvalues, Eigenvectors, Diagonalization, Rotation matrices, Quadratic forms, Least squares. Note: Credit will not be given for both MATH 1503 and MATH 2213 . Prerequisite: A minimum grade of 60% in New Brunswick high school courses: Trigonometry and 3-Space and Advanced Mathematics with introduction to Calculus or its equivalent. MATH 1853 Mathematics for Business I 3 ch (3C) A brief review of pre-calculus math, logarithmic and exponential functions, limits, introduction to derivatives. Linear systems, matrices, systems of linear inequalities, difference equations, arithmetic and geometric sequences, annuities and instalment buying. Applications to Business and Economics will be emphasized throughout the course. Note: Credit will not be given for both MATH 1833 and MATH 1853. Prerequisite(s): New Brunswick Advanced Math 120 or MATH1863 or its equivalent. MATH 1863 Precalculus Mathematics 3 ch (3C 1T) A review of high school Mathematics topics, particularly those covered in the New Brunswick Advanced Math 120 course. Topics include: elementary set theory, manipulation of algebraic expressions, equations and inequalities, analytic geometry, linear and quadratic functions, polynomial and rational functions, exponential and logarithm functions, trigonometric functions, inverse trigonometric functions, analytic trigonometry. Note: This course is designed to serve as preparation for Math 1003 and Math 1853 . It carries no 2012-2013 Calendar Proof credit for certain programs. Please consult with a faculty advisor. MATH 2003 Intermediate Mathematics I 3 ch (3C 1T) Analytic geometry and vectors, differential calculus of several variables including partial derivatives, max-min, multiple integrals, parametric equations and polar coordinates, surface area. Note: Credit will be given for courses in only one of the sequences MATH2003/ 2013 or MATH2503 / 2513 . Prerequisite: A grade of C or higher in MATH1013 . MATH 2013 Intermediate Mathematics II 3 ch (3C 1T) Infinite series and power series, line and surface integrals. Theorems of Green and Stokes, the divergence theorem, differential equations. See note following MATH 2003. Prerequisite: A grade of C or higher in MATH 2003 . MATH 2203 Discrete Mathematics 3 ch (3C) Logic, methods of proof, mathematical induction, elementary set theory, functions and relations. This course is designed for students desiring a good grounding in mathematics. Theorems and proofs are an important part of the course. NOTE: Credit will not be given for both MATH 2203 and CS 1303 . Students majoring in Mathematics or Statistics must choose MATH 2203. Prerequisites: Math 1013 . MATH 2213 Linear Algebra I 3 ch (3C) Linear equations, matrix algebra, determinants, vector spaces, basis, row and column spaces, linear transformations and matrix representations, scalar products, orthogonal projection, least squares, eigenvectors and diagonalization, quadratic forms, singular value decomposition. The course will include use of mathematical software. Credit will not be given for both MATH 2213 and MATH 1503 . Prerequisites: MATH 1013 or equivalent. MATH 2513 Multivariate Calculus for Engineers 4 ch (4C) Functions of several variables, partial derivatives, multiple integrals, vector functions, Green’s and Stoke’s Theorems. See the note following MATH 2003. Prerequisite: A grade of C or higher in Math 1013 ; and Math 1503 or 2213 . MATH 2523 Differential Equations and Series 3 ch (4C) First order differential equations, higher order linear differential equations, infinite series, power series, series solution of differential equations about ordinary points and singular points, Gamma and Beta functions, Bessel function and Legendre polynomials. Prerequisite: A grade of C or higher in Math 1013 . MATH 2633 Fundamental Principles of Elementary School Mathematics 3 ch (3C 1T) This course is primarily intended for individuals interested in elementary and middle school teaching, and is open to students registered in concurrent B.Ed. program. The focus is on the mathematical content of K-8 Atlantic Canada Mathematics Curriculum, and extensions beyond the classroom to show the how and the why behind school mathematics. Topics include problem solving, number concepts, number and relationship operations, patterns and relations, shape and space, as well as data management and probability. This course may be taken by others with the approval of the student’s department Chair or Dean. Prerequisite: Successful completion of at least one year of a university program. MATH 2853 Mathematics for Business II 3 ch (3C) Derivatives, marginal analysis, optimization problems with applications in business, antiderivative, definite integrals and applications, techniques of integration, simple differential 2012-2013 Calendar Proof equations, functions of several variables, partial derivatives, unconstrained and constrained optimization, Lagrange multipliers. Applications to Business and Economics will be emphasized throughout the course. Note: Credit will be given for only one of MATH 1001MATH 1003 , MATH 1823 or MATH 2853 . Prerequisite: MATH 1853 . MATH 2903 Financial Mathematics I 3 ch (3C) Simple, compound, continuously compound interest, future value, series of payments, sinking funds, amortization, installments. Major assets type. Valuation of fixed interest securities, effects of tax, ordinary shares, bonds. Deterministic models for term structure dynamics. Prerequisite: MATH 1003or MATH 1853 . MATH 2913 Financial Mathematics II 3 ch (3C) Derivatives: cash-and-carry markets, price-discovery markets, expiration date, forwards and futures, options, swaps. The algebraic no-arbitrage concept. Asset prices, returns and payoffs, portfolio. Lattice models, payouts and foreign currencies. Prerequisites: MATH 1013 and MATH 2903 . MATH 3073 Partial Differential Equations 3 ch (3C) Methods of solution for first order equations. Classification of second order equations. Characteristics, analytic and numerical methods of solution for hyperbolic, elliptic and parabolic equations. Prerequisite: MATH 2003 and MATH 2013 ; or MATH 2513 and MATH 2523 , or equivalent. MATH 3093 Elementary Number Theory 3 ch (3C) Primes, unique factorization, congruences, Diophantine equations, basic number theoretic functions.Recommended for Education Students or prospective Mathematics teachers. MATH 3213 Linear Algebra II 3 ch (3C) Vector spaces and subspaces, independent and spanning sets, dimension, linear operators, determinants, inner product spaces, canonical forms. Prerequisites:Either MATH 1503 and MATH 1013 or MATH 2213 . MATH 3243 Complex Analysis 3 ch (3C) Complex analytic functions, contour integrals and Cauchy’s Theorem; Taylor’s, Laurent’s series and Liouville’s Theorem; residue calculus. Prerequisite:MATH 2003 and MATH 2013 , or MATH 2513 and MATH 2523 ; or equivalent. MATH 3303 Operations Research I 3 ch (3C) Linear programming models, simplex method, duality theory, post-optimality analysis, network simplex method and special cases, introduction to interior point methods. Credit will not be granted for both MATH 3303 and BA 3623 . Prerequisite: MATH 2213 . MATH 3343 Networks and Graphs 3 ch (3C) Graphs, Euler paths, tournaments, factors, spanning trees, applications; electric networks and Kirchhoff’s laws, matroids; kernels, Grundy function and application to game theory; Menger’s theorem, flows in networks, flow algorithms. Prerequisites: MATH 2213 or 1503 . MATH 3503 Differential Equations for Engineers 3 ch (3C 1T) Nonhomogeneous differential equations, undetermined coefficients, variation of parameters, systems of 1st and 2nd order ordinary differential equations, Laplace transforms, Fourier series, partial differential equations with constant coefficients, boundary value problems. Prerequisite: MATH 1503 or 2213 (C grade minimum). Corequisite: MATH 2513 or MATH 2012-2013 Calendar Proof 2003 . MATH 3633 Fundamental Principles of School Mathematics 3 ch (3C) This course is primarily intended for individuals interested in school teaching. The focus is on the mathematical content of the K-12 Atlantic Canada Mathematics Curriculum with extensions beyond the classroom, to show the how and why behind school mathematics. Topics include mathematical language; real numbers and other mathematical structure; Euclidean geometry; functions; mathematical connections; problem solving. Intended for students registered in concurrent BEd programs, but may be taken for credit by others with the approval of the student’s department Chair or Dean. Prerequisite: NB Advanced Math (120), or equivalent and successful completion of at least one year of a university program. MATH 3713 Analysis I 3 ch (3C) The real number system. Elementary set theory. Metric spaces. Sequences and series. Continuity. Prerequisites:One of MATH 2103 or MATH 2523 , 2203; and either MATH 1503 or MATH 2213 . MATH 3733 Abstract Algebra 3 ch (3C) An introduction to the elementary theory of groups. Rings and Fields. Applications to number theory. Prerequisite: MATH 2203 and either MATH 1503 orMATH 2213 . MATH 3753 Applications of Mathematical Models 3 ch (3C) Provides an overview of mathematical modeling strategies for particular applications. Introduces students in a variety of disciplines to mathematical modeling based problem solving. General concepts such as stochastic vs. deterministic modeling are discussed and case studies of specific applications are presented. Case studies may include models of survival, models of cognition, models of population growth and financial models. Students develop case studies in the areas of their major or their own expertise. Prerequisites: one of STAT 3093 , PSYC 3913 , MATH 2013 , MATH 2513 , MATH 2523 ; or permission of the instructor. MATH 3903 Financial Mathematics III 3 ch (3C) Calculus in stochastic environment: random functions, derivative, chain rule, integral, integration by parts, partial derivatives. Pricing forwards and options. Ito’s lemma and financial applications. Hull-White, Artzner-Heath, and Brennan-Schwartz models. Martingales, pricing methodology, and risk-neutral probability. Prerequisites: MATH 1503 or MATH 2213 and MATH 2913 . MATH 4703 Topics in Mathematics 3 ch (3C) Selected topics at an advanced level. Content varies from year to year. Topic of course will be entered on student’s transcript. Prerequisite: Consent of instructor. MATH 4903 Financial Mathematics IV 3 ch (3C) Forming risk-free portfolios: the Black-Scholes partial differential equation; constant dividend case, exotic options, drift adjustment, equivalent martingale measures. Cox-RossRubinstein, Merton and Vasicek’s models. Stochastic optimization: Hamilton-Jacobi-Bellman equation, application to American options. Prerequisites: MATH 3903 and STAT 3093 . MATH 4993 Project in Mathematics 3 ch Research project in the Mathematical Sciences carried out by the student under the supervision of a member of the Department. The student will submit a written report and make an oral presentation. Prerequisite: Normally 75% of total credits required in the program. 2012-2013 Calendar Proof