Teaching

The statistical interpretation and treatment of experimental problems; experimental design, analysis of variance, regression and correlation, multiple regression, data screening; illustrative examples and applications.

Differentiation of polynomial, rational, trigonometric, exponential, and logarithmic functions. Definite integrals. Applications and approximations. Introduction to a computer algebra system.

Differentiation of polynomial, rational, trigonometric, exponential, and logarithmic functions. Definite integrals. Applications and approximations. Introduction to a computer algebra system.

Formal grammars; normal forms; relationship between grammars and automata; regular expressions; finite state machines, state minimization; pushdown automata; Turing machines; computability; complexity; introduction to recursive function theory.

An introduction to proofs and axiomatic set theory.

The algebra, geometry and analysis of the complex number plane. Analytic functions, rational functions, exponential functions, line integrals, Cauchy's theorem. The course is oriented toward requirements for work in physics and mathematics.

An introductory course in Game Theory including such topics as non-cooperative finite games 'two person zero-sum [constant-sum] games, n-person games', cooperative finite games, linear programming.

Sensed magnitudes. Cross ratio. Transformation theory.

A course of mathematical thought and effective thinking. An introduction to what mathematics is and what it means to do mathematics. An exploration of some of the great ideas of mathematics including geometry from 1 to 4 dimensions, fractals, certainty about uncertainty and decision making.

An introduction to axiomatic set theory, universal algebra and its applications to group, ring, and field theory including congruences, quotient algebras, and homomorphisms.

Methods and applications of combinatorial mathematics including graph theory 'matchings, chromatic numbers, planar graphs, independence and clique numbers' and related algorithms, combinatorial designs 'block designs, Latin squares, projective geometries', error correcting codes.

A study of computer systems and networking concepts. Topics include computer system components, data representation, logic and arithmetic circuits, operating systems, topologies, network architectures, LANs, WANs, networking protocols, OSI model, TCP/IP, network addressing, network equipment and cabling, wireless networks and emerging technologies.

A review of the major issues of computer security. Classification of security threats; physical security; passwords; encryption; firewalls and routers; security policies; intrusion detection systems; security audits.

An overview of computing science concepts. History of computing. Computer software and hardware. Algorithms and their properties. Control constructs of sequence, selection, and repetition. Basic data types and data representation. Overview of programming languages from assembly to high level languages. Introduction to program translation principles. Students will be required to do some programming.

Techniques of discrete mathematics. Topics include: principles of counting, generating functions, principle of inclusion/exclusion, pigeonhole principle, recurrence relations, graphs and trees.

This course is an elementary introduction to the techniques of linear algebra. Topics include: systems of linear equations, matrices, determinants, vectors, vector spaces and subspaces, eigenvalues and eigenvectors, and linear mappings. Selected applications will be presented. Complex vector spaces will be discussed.

Descriptive statistics, introductory probability theory, discrete and continuous random variables, discrete, continuous and joint probability distributions, point and interval estimation, inferences based on a single sample or on two samples.

Data collection and presentation, descriptive statistics. Probability distributions, sampling distributions and the central limit theorem. Point estimation and hypothesis testing. Correlation and regression analysis. Goodness of fit and contingency table. One- and two-factor 'fixed effects' ANOVA. Sign Test, Wilcoxon Signed-Ranks and Rank-Sums Tests, Kruskal Wallis Test, Rank Correlation and Runs Test. Introduction to spreadsheets and dedicated statistics software.

Bases, linear transformations, change of bases, eigenvalues and eigenspaces, diagonalization, inner product, Gram Schmidt orthogonalization process, orthogonal diagonalization, quadratic form, applications.

Matrix algebra and systems of linear equations. Vector equations of lines and planes. Matrix inverses and invertibility. Euclidean n-spaces, subspaces, and bases. Dot product and orthogonality. Determinants. Introduction to linear transformations, eigenvalues, eigenvectors and to a computer algebra system.]

An introduction to mathematical methods used in the life sciences including combinatorial methods, probability theory and elementary inferential statistics, matrix theory and Markov chains, and dynamic systems.

Develops students' problem-solving abilities along heuristic lines and illustrates the process of Applied Mathematics. Students are encouraged to recognize and formulate problems in mathematical terms, solve the resulting mathematical problem, and interpret the solution in real world terms.

A course in mathematical thought and effective thinking. An introduction to what mathematics is and what it means to do mathematics. An exploration of some of the great ideas of mathematics including numbers from the integers to the reals, from the finite to infinity and beyond, and contortions of space.

An introduction to common operating systems and graphical user interfaces including DOS, the Microsoft Windows family, the MacOS, VMS and UNIX-like operating systems such as Linux, UNIX, BSD, FreeBSD, etc.

A course on software development. Topics include study of the principles, methods, tools, and practices of the professional programmer for software development and maintenance. Functions, data structures, classes and inheritance. Emphasis on solving problems. Requires extensive programming.

A continuation of MAT 401. The Lebesgue Integral, Normed Linear Spaces, Fundamental Theorems of Calculus, and Stieltjes Integrals.

Real analysis, including the real numbers system, metric spaces 'connectedness, completeness, and compactness', and the Riemann and Lebesgue Integrals.

The real number system, elementary topology of R and Rⁿ, limits and continuity, integration, infinite series and uniform convergence.

Analyzing software by interacting with a variety of packages. Topics include statistical software packages, databases, spreadsheets, word processing and other packages, how these packages function, and the differences between the major packages available

An introduction to software development principles through the study of traditional elementary programming, object-oriented programming, debugging, and standard algorithms with their analysis. Problem solving, algorithm design, top-down development, program testing and documentation, advanced data types, data manipulation, sequence selection, loops, parameters, arrays, strings, and files. Discussion of basic algorithms for constructing efficient and robust solutions to problems.

Supervised by a faculty member in the Mathematics Department, the student undertakes an independent study of an approved topic and completes a written thesis. The grade is determined solely by the quality of the thesis and its oral defence. The topic will normally be an extension of material covered in 400-level Mathematics courses successfully taken by the student.

Topics in advanced abstract algebra including group, ring and galois theory and universal algebra.

Topics in advanced probability and statistics including stochastic processes, random walks, and time series analysis.