Mathematics

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 .

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

Definition of the integral, fundamental theorem of calculus, techniques of integration, improper integrals. Ordinary differential equations. Taylor polynomials and series. 

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 . 

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. 

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 credit for certain programs. Please consult with a faculty advisor. 

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 .

Infinite series and power series, line and surface integrals. Theorems of Green and Stokes, the divergence theorem, differential equations. See note following MATH 2003. 

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. 

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 . 

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

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.

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. 

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 .

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. 

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.

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.

Primes, unique factorization, congruences, Diophantine equations, basic number theoretic functions.Recommended for Education Students or prospective Mathematics teachers.

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

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

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 .

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.

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. 

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.

Selected topics at an advanced level. Content varies from year to year. Topic of course will be entered on student’s transcript.

The real number system. Elementary set theory. Metric spaces. Sequences and series. Continuity.

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

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. 

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. 

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. 

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.