are non-credit courses intended for those students who either have a weak background in mathematics or are returning to the subject after some years. The program enables students to master mathematical operations such as those involving whole numbers, fractions, decimals, percents, integers, exponents, linear equations, algebraic and rational expressions, formulas, graphs, systems of linear equations, basic trigonometry, exponents and radicals, and quadratics.

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.

is an introduction to integral calculus, including Riemann sums, techniques of integration and improper integrals. Applications include exponential growth and decay, area between curves and volumes of solids of revolution.

covers topics which include sets, logic, permutations, combinations, and elementary probability.

covers topics which include elementary matrices, linear programming, elementary number theory, mathematical systems and geometry.

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.

is a study of the differential calculus of functions of two variables, an introduction to convergence of infinite sequences and series.

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.

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

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.

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.

are basic concepts of mathematical reasoning, sets and set operations, functions, relations including equivalence relations and partial orders as illustrated through the notions of congruence and divisibility of integers, mathematical induction, principles of counting, permutations, combinations and the Binomial Theorem.

is 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.

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.

is proof techniques, structure of R, sequences, limits, continuity, uniform continuity, differentiation.

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.

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.

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.

is direction fields, equations of first order and first degree, higher order linear equations, variation of parameters, methods of undetermined coefficients, Laplace transforms, systems of differential equations. Applications include vibratory motion, satellite and rocket motion, pursuit problems, population models and chemical kinetics.

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.

is classical Euclidean geometry of the triangle and circle. The inversion transformation, including the theorem of Feuerbach. Elliptic and hyperbolic geometries.

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.

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.

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.

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.

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.

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.

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.

is a course in which, under the guidance of a faculty member, students conduct a scientific study based upon original research or a critical review of extant data in an appropriate area. Normally the project will have a computational component. Students are required to submit a report and give a presentation. This project fulfils the Core requirement for a fourth-year individual project in the area of specialization. This is a Designated Writing Course.