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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

1### MAT 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

3### MAT 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

3### MAT 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

3### MAT 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

3### MAT 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

4### MAT 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

3#### Prerequisites

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

3### MAT 1325 : Calculus II for Liberal Arts

Techniques of differentiation and integration, applications and further developments of calculus.

#### Credits

3#### Prerequisites

(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

4### MAT 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

4### MAT 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

4#### Prerequisites

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

4#### Prerequisites

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

3#### Prerequisites

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

4#### Prerequisites

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

3#### Prerequisites

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

3#### Prerequisites

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

3#### Prerequisites

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

3#### Prerequisites

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

3#### Prerequisites

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

3#### Prerequisites

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

3#### Prerequisites

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

3#### Prerequisites

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

3#### Prerequisites

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

3#### Prerequisites

MAT 2705 :D-

### MAT 5110 : Topics in Geometry

Topics selected from affine, hyperbolic, spherical, elliptic, Euclidean or projective geometry.

#### Credits

3#### Prerequisites

MAT 2600 :D-

### MAT 5200 : Theory of Numbers

Congruences, quadratic reciprocity, Diophantine equations; applications.

#### Credits

3#### Prerequisites

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

3#### Prerequisites

(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

3#### Prerequisites

MAT 3300 :Y

### MAT 5600 : Differential Geometry

Geometry of curves and surfaces, curvature, first and second fundamental forms, minimal surfaces, use of MAPLE.

#### Credits

3#### Prerequisites

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

3#### Prerequisites

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

3### MAT 5930 : Topics in Pure Mathematics

Lecture course in an area of pure mathematics. May be repeated for credit if topics are different.

#### Credits

3### MAT 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

1#### Prerequisites

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

2#### Prerequisites

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

3#### Prerequisites

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

1### MAT 7290 : Geometry

Topics selected from affine, finite, hyperbolic, spherical, elliptic, Euclidean or projective geometry.

#### Credits

3### MAT 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

3### MAT 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

3### MAT 7310 : Topics in the Teaching of Math

Selected topics of interest to teachers of secondary school mathematics.

#### Credits

3### MAT 7600 : Advanced Calculus

Real numbers, completeness, sequences, limits, continuous functions, the derivative, sequences of functions, pointwise and uniform convergence, power series.

#### Credits

3### MAT 7605 : Topics in Analysis

Advanced topics selected from real analysis, complex analysis, or higher analysis. Prerequisite: Determined by instructor.

#### Credits

3#### Prerequisites

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

3### MAT 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

3### MAT 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

3### MAT 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

3### MAT 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

3### MAT 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

3### MAT 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.