# Mathematics

NOTE: See the beginning of Section F for abbreviations, course numbers and coding.

Mathematics program description.

MATH1001Calculus for Life Sciences3 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.

Prerequisites: A minimum grade of 60% in New Brunswick high school courses: Pre-calc 12A and Pre-calc 12B, or equivalent. Students must also pass a Placement Test which is administered by the Department of Mathematics and Statistics. See "Note 18 to Admission Chart" in Section B of this Calendar for further details.

MATH1003Introduction to Calculus I3 ch (4C)

Functions and graphs, limits, derivatives of polynominal, log, exponential and trigonometric functions. Curve sketching and extrema of functions.

Prerequisites: A grade of at least 60% in New Brunswick high school courses: Pre-calc 12A and Pre-calc 12B, or equivalent. Students must also pass a Placement Test which is administered by the Department of Mathematics and Statistics. 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.

MATH1013Introduction to Calculus II3 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 or a grade of B or higher in MATH 1001.

MATH1503 Introduction to Linear Algebra3 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. NOTE: Credit will not be given for both MATH 1503 and MATH 2213.

Prerequisites: A minimum grade of 60% in New Brunswick high school courses: Pre-calc 12A and Pre-calc 12B, or equivalent.

MATH1853Mathematics for Business I3 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 installment 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. It carries no credit for certain programs. Please consult with a faculty advisor.

Prerequisites: A minimum grade of 60% in New Brunswick high school courses: Pre-Calc 12A and Pre-calc 12B, or MATH1863 or equivalent.

MATH1863Precalculus Mathematics3 ch (4C)

A review of high school mathematics topics, particularly those covered in the New Brunswick high school curriculum. Topics include: elementary set theory, manipulation of algebraic expressions, equation and inequalities, analytic geometry, linear and quadratic functions, polynomial and rational function, exponential and logarithm functions, trigonometric functions, inverse trigonometric functions, analytic trigonometry. NOTE: This course is designed to serve as preparation for MATH 1001, MATH 1003, and MATH 1853. It carries no credit for certain programs. Please consult with a faculty advisor. MATH 1863 and MATH 0863 are not the same course.

MATH2003Intermediate Mathematics I (O)3 ch (3C 1T)

Analytic geometry and vectors. Parametric curves. Polar, cylindrical and spherical coordinates. Functions of several variables, partial derivatives, applications to max-min. Double and triple integrals. NOTE: Credit will be given for courses in only one of the sequences MATH 2003/MATH 2013 or MATH 2523/MATH 2513.

Prerequisite: MATH 1013.

MATH2013Intermediate Mathematics II3 ch (3C 1T)

Review of first order differential equations. Second order linear O.D.E.s. Infinite series including power series, solutions to O.D.E.s. Line and surface integrals. Theorems of Green and Stokes. Divergence theorem. See note following MATH 2003.

PrerequisiteMATH 2003.

MATH2203Discrete Mathematics (A)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 the foundations of mathematics. Theorems and proofs are an important part of the course. NOTE: Credit will not be given for both MATH 2203 and CS 1303. It is recommended that students majoring in Mathematics or Statistics choose MATH 2203.

Co-requisites: MATH 1013 and MATH 1503.
MATH2213Linear Algebra I3 ch (3C)

This course introduces the basic concepts of linear algebra, mainly in finite dimensional real vector spaces. Systems of linear equations, vector and matrix algebra, bases and dimensions of subspaces, row and column spaces, linear transformations and matrix representations, inner products, determinants, eigenvectors and diagonalization. Applications as time permits. Credit will not be given for both MATH 2213 and MATH 1503.

Prerequisite: MATH 1013 or equivalent.

MATH2513Multivariable Calculus for Engineers4 ch (4C)

Functions of several variables, partial derivatives, multiple integrals, vector functions, Green’s and Stoke’s Theorems. See the note following MATH 2003.

Prerequisites: A grade of C or higher in MATH 1013; and MATH 1503 or MATH 2213.

MATH2523Differential Equations and Series (A)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.

MATH2633Fundamental Principles of Elementary School Mathematics (A)3 ch (3C)

This course is primarily intended for individuals interested in elementary and middle schoolteaching, 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. With the exception of Certificate of Math Education, this course is not available for credit to students who would have 6ch of Level 1000 mathematics in their degree programs.

Prerequisite: Successful completion of at least one year of a university program.

MATH2853Mathematics for Business II3 ch (3C)

Derivatives, marginal analysis, optimization problems with applications in business, anti-derivative, definite integrals and applications, techniques of integration, simple differential 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 1001, MATH 1003, MATH 1823 or MATH 2853.

Prerequisite: MATH 1853.

MATH2903Financial Mathematics I3 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 1003 or MATH 1853.

MATH2913Financial Mathematics II3 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, MATH 2903 and STAT 1793 (or equivalent).

MATH3073Partial Differential Equations (A)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.

Prerequisites: MATH 2013; or both MATH 2513 and MATH 3503, or equivalent.

MATH3093Elementary Number Theory (A) 3 ch (3C)

Primes, unique factorization, congruences, Diophantine equations, basic number theoretic functions. As well as serving mathematics majors, this course will be of particular benefit to prospective mathematics teachers.

Prerequisite: At least 6 credit hours in Math excluding MATH 1863.

MATH3213Linear Algebra II (A) 3 ch (3C)

Vector spaces and subspaces, independent and spanning sets, dimension, linear operators, determinants, inner product spaces, canonical forms.

Prerequisite: MATH 1503 or MATH 2213, or consent or instructor.

MATH3243Complex Analysis (A) 3 ch (3C)

Complex analytic functions, contour integrals and Cauchy’s Theorem; Taylor’s, Laurent’s series and Liouville’s Theorem; residue calculus.

Prerequisites: MATH 2003 and MATH 2013, or MATH 2513 and MATH 2523; or equivalent.

MATH3303Operations Research I3 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.

MATH3343Networks and Graphs (A)3 ch (3C)
Graphs, Euler paths, tournaments, factors, spanning trees, applications; graph colourings, planar graphs; Menger's thereom, flows in networks, flow algorithms.

Prerequisites: (MATH 2213 or MATH 1503) and (MATH 2203 or CS 1303).

MATH3503Differential Equations for Engineers3 ch (4C)

Nonhomogeneous differential equations, undetermined coefficients, variation of parameters, systems of 1st and 2nd order ordinary differential equations, Laplace transforms, Fourier series.

Prerequisite: MATH 1503 or MATH 2213.

CorequisiteMATH 2513 or MATH 2003.
MATH3633Fundamental Principles of School Mathematics (A) 3 ch (3C)

This course is primarily intended for individuals interested in schoolteaching. 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.

Prerequisites: A minimum grade of 60% in New Brunswick high school courses Pre-calc 12A and Pre-calc 12B or equivalent, and successful completion of at least one year of a university program; or MATH 2633.

MATH3713Analysis I (A) 3 ch (3C)

A rigorous introduction to analysis on the real numbers. Sequences, limits, sets, functions, axioms for the real numbers, completeness, continuous and differentiable functions, the Mean Value Thereom.

Prerequisites: MATH 1013 and (MATH 2203 or CS 1303.)

MATH3733Abstract Algebra (A) 3 ch (3C)

An introduction to the elementary theory of groups. Rings and Fields. Applications to number theory.

Prerequisites: MATH 2203 and either MATH 1503 or MATH 2213.

MATH3753Applications of Mathematical Models (O)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.

Prerequisite: One of STAT 3093, PSYC 3913, MATH 2013, MATH 2513, MATH 2523; or permission of the instructor.

MATH3903Financial Mathematics III3 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.

MATH4703Topics in Mathematics (O)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.

MATH4903Financial Mathematics IV3 ch (3C)

Forming risk-free portfolios: the Black-Scholes partial differential equation; constant dividend case, exotic options, drift adjustment, equivalent martingale measures. Cox-Ross-Rubinstein, Merton and Vasicek’s models. Stochastic optimization: Hamilton-Jacobi-Bellman equation, application to American options.

Prerequisites: MATH 3903 and STAT 3093.

MATH4993Project in Mathematics3 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.