Mathematics and Statistics
Degrees and Certificates
Classes
MAT 1000 : Mathematical Communities
Understanding the role of creative thinking, problem solving, and collaboration in mathematics; exploration of research and careers in the mathematical sciences; building community with fellow mathematics majors.
Credits
1MAT 1210 : Mathematical Concepts
Topics selected from logic, number theory, finance, set theory, geometry, applied linear algebra, calculus. Not open to students who have completed MAT 1505.
Credits
3MAT 1220 : Discrete Math Social Sci
Discrete mathematics for the Liberal Arts student: voting methods, weighted voting, fair division, apportionment, circuits, network, trees, directed graphs, planning and scheduling, linear programming, growth and symmetry. Not open to students who have completed MAT 1505.
Credits
3MAT 1280 : Mathematics of Fairness
Examining fairness in our personal lives and in society: Voting systems and power indices, strategic political positioning spatial models, fair division, congressional district apportionment, game theory, the GINI index of economic inequality, gerrymandering.
Credits
3MAT 1290 : Topics in Core Mathematics
Course in an area of pure or applied mathematics or statistics. May be repeated for credit if areas of topical focus are different. Designed specifically to satisfy the core requirement in mathematics and statistics, for students in the humanities and social sciences.
Credits
3MAT 1312 : Biocalculus
Discrete and continuous dynamics of biological systems: discrete dynamical systems, sequences, functions, discrete and continuous limits, the derivative, the integral, methods and applications of differentiation and integration, Taylor polynomials, modeling with differential equations, Euler's method, applications to Biology.
Credits
4MAT 1314 : Modeling for the Life Sciences
Mathematical and statistical modeling in the Life Sciences. Topics selected from: dynamical systems, diffusion, Markov, Bayesian, connectionist, and information theory models, applied to epidemiology, ecology, neuroscience and neuron signaling, cell and molecular biology, genetics, physiology, psychology, and other areas. Pre-requisites MAT 1312 or Equivalent
Credits
3Prerequisites
MAT 1310 or MAT 1312 or MAT 1320 or MAT 1400 or MAT 1500
MAT 1320 : Calculus I for Liberal Arts
Calculus for Liberal Arts students: polynomial, rational and transcendental functions, the derivative, numerical and graphical introduction to integration.
Credits
3MAT 1325 : Calculus II for Liberal Arts
Techniques of differentiation and integration, applications and further developments of calculus.
Credits
3Prerequisites
(MAT 1320 :D- or MAT 1500 :D-)
MAT 1400 : Business Calculus
Functions, limits, and basic definitions of differential and integral calculus. Techniques of differentiation and integration. The Fundamental Theorem of Calculus. Applications in various areas of business and economics.
Credits
4MAT 1500 : Calculus I
Limits, transcendental functions (logarithms, exponential functions, inverse trigonometric functions), differentiation (definition, tangent lines, rates of change, techniques, implicit differentiation, related rates), applications of differentiation (graphing, optimization), indeterminate forms and L'Hopital's Rule. Use of a computer algebra system, eg. MAPLE.
Credits
4MAT 1505 : Calculus II
Integration (indefinite, definite), applications of integration (area, volume, applications to physics and economics, etc.), methods of integration, approximate integration (trapezoidal and Simpson's rules), improper integrals, differential equations, infinite sequences and series. Continued use of a computer algebra system.
Credits
4Prerequisites
MAT 1500 :D-
MAT 2500 : Calculus III
Parametric equations; polar, cylindrical, and spherical coordinates; vectors and the geometry of space; vector functions (derivatives, integrals, curvature, etc.); partial derivatives; optimization; multiple integration and its applications; vector calculus (line integrals, vector analysis). Continued use of a computer algebra system.
Credits
4Prerequisites
MAT 1505 :D-
MAT 2600 : Foundation of Math I
Topics selected from natural numbers, mathematical induction, irrational and transcendental real numbers, complex numbers, Fundamental Theorem of Algebra, infinite cardinals, symbolic logic, functions and relations, iterated functions, mathematical chaos.
Credits
3Prerequisites
MAT 1500 :D-
MAT 2705 : Diff Equation with Linear Alg
First order and linear second order differential equations, matrices and linear equation systems, eigenvalues and eigenvectors, and linear systems of differential equations.
Credits
4Prerequisites
MAT 1505 :D-
MAT 3100 : Applied Linear Algebra
Vectors, matrices, transpose and inverse of a matrix, systems of linear equations, the four fundamental subspaces, eigenvalues and eigenvectors, symmetric matrices, matrix factorizations, applications such as information retrieval, ranking web pages, graphs and networks, least squares, and data compression.
Credits
3Prerequisites
MAT 1312 or MAT 1320 or MAT 1400 or MAT 1500
MAT 3300 : Advanced Calculus
Real numbers, sequences, convergence, supremum and infimum, completeness of the reals, continuous functions, Intermediate Value Theorem, differentiable functions, Mean Value Theorem, Riemann integral, Fundamental Theorem of Calculus, Taylor's Theorem.
Credits
3Prerequisites
MAT 2500 :D- and (MAT 2600 :D- or HON 4151 :D-)
MAT 3305 : Topics in Analysis
Advanced topics selected from real analysis, complex analysis, or higher analysis.
Credits
3Prerequisites
MAT 3300 :D-
MAT 3400 : Linear Algebra
Vector spaces, linear transformations, basis and dimension, orthogonal transformations, least squares, eigenvalues and eigenvectors, similarity, diagonalization, symmetric, applications.
Credits
3Prerequisites
MAT 2705 :D-
MAT 3500 : Modern Algebra I
Topics selected from groups and subgroups, cyclic groups, permutation groups, isomorphisms, direct products, cosets and Lagrange's Theorem, normal subgroups and factor groups, group homomorphisms, the Fundamental Theorem of Finite Abelian Groups, rings, fields.
Credits
3Prerequisites
MAT 2600 :D- and MAT 2705 :D-
MAT 3930 : History of Mathematics
Development of mathematics from ancient times to the birth of calculus in the seventeenth century.
Credits
3Prerequisites
MAT 1505 :D- and MAT 2600 :D-
MAT 4110 : Combinatorics
Induction, permutations and combinations, general counting methods, generating functions, recurrence relations, principle of inclusion-exclusion, graph theory, trees, planarity, crossing numbers, Hamiltonian cycles, Eulerian tours.
Credits
3Prerequisites
MAT 1505 :D-
MAT 4270 : Numerical Analysis
Numerical and computational aspects of root-finding methods, interpolation and polynomial approximation, numerical differentiation and integration, approximation theory.
Credits
3Prerequisites
MAT 1505 :D-
MAT 4550 : Math of Financial Derivatives
Basic tools of financial markets; options; asset price random walks; estimation of parameters; arbitrage put-call parity; Black-Scholes Model; implied volatility; portfolio-optimization; hedging.
Credits
3Prerequisites
MAT 2705 :D-
MAT 4600 : Deterministic Oper Res
Deterministic methods: mathematical optimization, linear programming, formulation and solution techniques, duality, integer linear programming, transportation problem, assignment problem, network flows, dynamic programming.
Credits
3Prerequisites
MAT 2705 :D-
MAT 5110 : Topics in Geometry
Topics selected from affine, hyperbolic, spherical, elliptic, Euclidean or projective geometry.
Credits
3Prerequisites
MAT 2600 :D-
MAT 5200 : Theory of Numbers
Congruences, quadratic reciprocity, Diophantine equations; applications.
Credits
3Prerequisites
MAT 2600 :D-
MAT 5400 : Complex Analysis
Algebra of complex numbers, analytic functions, Cauchy- Riemann equation, Laplace equations, conformal mapping, integrals of complex functions, Cauchy's theorem, power series, Taylor's theorem, Laurent's theorem, residues, entire functions.
Credits
3Prerequisites
(MAT 2500 :D- and MAT 2600 :D-)
MAT 5500 : Topology
Topological equivalence, connectedness, compactness, topology of subsets of Rn, manifolds, topological embeddings, topological spaces.
Credits
3Prerequisites
MAT 3300 :Y
MAT 5600 : Differential Geometry
Geometry of curves and surfaces, curvature, first and second fundamental forms, minimal surfaces, use of MAPLE.
Credits
3Prerequisites
MAT 2500 :D-
MAT 5900 : Seminar in Mathematics
Supervised study of selected topics or problems in mathematics, student presentations. May be repeated for credit if content is different.
Credits
3Prerequisites
MAT 3300 :D- or MAT 3500 :D-
MAT 5920 : Topics in Applied Mathematics
Lecture course in an area of applied mathematics. May be repeated for credit if topics are different.
Credits
3MAT 5930 : Topics in Pure Mathematics
Lecture course in an area of pure mathematics. May be repeated for credit if topics are different.
Credits
3MAT 5991 : Independent Study
Reading in a selected branch of mathematics under the direction of a member of the staff. May be repeated for credit.
Credits
1Prerequisites
MAT 1505 :D-
MAT 5992 : Independent Study
Reading in a selected branch of mathematics under the direction of a member of the staff. May be repeated for credit.
Credits
2Prerequisites
MAT 1505 :D-
MAT 5993 : Independent Study
Reading in a selected branch of mathematics under the direction of a member of the staff. May be repeated for credit.
Credits
3Prerequisites
MAT 1505 :D-
MAT 7101 : Grad Studies Internship
Internship in a professional setting related to the course of study in either Mathematics or Applied Statistics.
Credits
1MAT 7290 : Geometry
Topics selected from affine, finite, hyperbolic, spherical, elliptic, Euclidean or projective geometry.
Credits
3MAT 7300 : History of Math
The development of mathematics from ancient times to the birth of calculus in the seventeenth century. Independent work on a topic in the history of mathematics since 1700.
Credits
3MAT 7305 : Technology in Teaching of Math
Applications of technology to topics selected from algebra, geometry, calculus, statistics and programming. Technologies used may include computer algebra systems, e.g., Maple, geometry software, e.g., Sketchpad, and statistics software, e.g., Fathom.
Credits
3MAT 7310 : Topics in the Teaching of Math
Selected topics of interest to teachers of secondary school mathematics.
Credits
3MAT 7600 : Advanced Calculus
Real numbers, completeness, sequences, limits, continuous functions, the derivative, sequences of functions, pointwise and uniform convergence, power series.
Credits
3MAT 7605 : Topics in Analysis
Advanced topics selected from real analysis, complex analysis, or higher analysis. Prerequisite: Determined by instructor.
Credits
3Prerequisites
MAT 7600 :C
MAT 7610 : Complex Analysis
Complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy integral theorem and Cauchy integral formulae, power series, Taylor and Laurent series, singularities, residue theorem, harmonic functions.
Credits
3MAT 7660 : Linear Algebra
Vector spaces, linear transformations, eigenvalues and eigenvectors, invariant subspaces, decomposition theorem, Jordan forms, bilinear forms, selfadjoint operators, functions of operators, differential systems.
Credits
3MAT 7670 : Mathematical Logic
The sentential calculus, truth functions, analytic tableaux, natural deduction, first order logic, models, consistency, completeness. Applications to computer science including the P-NP problem.
Credits
3MAT 7750 : Numerical Analysis I
Error generation and propagation, root finding, approximation of functions by polynomials and cubic splines, direct and iterative solutions of linear systems, operations count, numerical differentiation and integration.
Credits
3MAT 7770 : Number Theory
Divisibility; Euclidean algorithm; prime numbers; Fundamental Theorem of Arithmetic; congruences; arithmetic functions; Diophantine equations, additional topics, which may vary by semester, include cryptography, law of quadratic reciprocity, continued fractions.
Credits
3MAT 7780 : Financial Mathematics
Basic tools of financial markets; annuities; options; asset price random walks; estimation of parameters; Black-Scholes Model; implied volatility; portfolio-engineering; hedging; discrete models.
Credits
3MAT 7790 : Dynamical SysteMS & Chaos
Topics selected from: iteration of real and complex functions, population models, qualitative theory of differential equations, fractals and dimension, topological and metric properties of systems, and applications.