**511 - Probability (3) **Probability and independence; discrete and continuous random variables; joint, marginal,
and conditional densities, moment generating functions; laws of large numbers; binomial,
Poisson, gamma, univariate, and bivariate normal distributions.**Prerequisites:** C or higher or concurrent enrollment in MATH 241 or consent of the Undergraduate
Director

**514 - Financial Mathematics I (3) **Probability spaces. Random variables. Mean and variance. Geometric Brownian Motion
and stock price dynamics. Interest rates and present value analysis. Pricing via arbitrage
arguments. Options pricing and the Black-Scholes formula.**Prerequisites:** C or higher or concurrent enrollment in MATH 241 or consent of the Undergraduate
Director

**515 - Financial Mathematics II (3) **Convex sets. Separating Hyperplane Theorem. Fundamental Theorem of Asset Pricing.
Risk and expected return. Minimum variance portfolios. Capital Asset Pricing Model.
Martingales and options pricing. Optimization models and dynamic programming.**Prerequisites:** C or better in MATH 514 or STAT 522 or consent of the Undergraduate Director

**520 - Ordinary Differential Equations (3) **Differential equations of the first order, linear systems of ordinary differential
equations, elementary qualitative properties of nonlinear systems.**Prerequisites:** C or better in MATH 344 or 544; or consent of the Undergraduate Director

**521 - Boundary Value Problems and Partial Differential Equations (3) **Laplace transforms, two-point boundary value problems and Green’s functions, boundary
value problems in partial differential equations, eigenfunction expansions and separation
of variables, transform methods for solving PDE’s, Green’s functions for PDE’s, and
the method of characteristics.**Prerequisites:** C or better in MATH 520 or MATH 241 and 242 or consent of the Undergraduate Director

**522 - Wavelets (3) **Basic principles and methods of Fourier transforms, wavelets, and multiresolution
analysis; applications to differential equations, data compression, and signal and
image processing; development of numerical algorithms. Computer implementation.**Prerequisites:** C or better in MATH 344 or 544 or consent of the Undergraduate Director

**523 - Mathematical Modeling of Population Biology (3) **Applications of differential and difference equations and linear algebra modeling
the dynamics of populations, with emphasis on stability and oscillation. Critical
analysis of current publications with computer simulation of models.**Prerequisites:** C or better in MATH 142, BIOL 301, or MSCI 311 recommended

**524 - Nonlinear Optimization (3) **Descent methods, conjugate direction methods, and Quasi-Newton algorithms for unconstrained
optimization; globally convergent hybrid algorithm; primal, penalty, and barrier methods
for constrained optimization. Computer implementation of algorithms.**Prerequisites:** C or better in MATH 344 or 544 or consent of the Undergraduate Director

**525 - Mathematical Game Theory (3) **Two-person zero-sum games, minimax theorem, utility theory, n-person games, market
games, stability.**Prerequisites:** C or better in MATH 544 or in both MATH 300 and 344, or consent of the Undergraduate
Director

**526 - Numerical Linear Algebra (4) **Matrix algebra, Gauss elimination, iterative methods; overdetermined systems and least
squares; eigenvalues, eigenvectors; numerical software. Computer implementation. Credit
may not be received for both MATH 526 and MATH 544.**Prerequisites:** Concurrent enrollment in or C or better in MATH 142 or consent of the Undergraduate
Director

**527 - Numerical Analysis (3) **Interpolation and approximation of functions; solution of algebraic equations; numerical
differentiation and integration; numerical solutions of ordinary differential equations
and boundary value problems; computer implementation of algorithms.**Prerequisites:** C or better MATH 520 or in both MATH 242 and 344, or consent of the Undergraduate
Director

**531 - Foundations of Geometry (3) **The study of geometry as a logical system based upon postulates and undefined terms.
The fundamental concepts and relations of Euclidean geometry developed rigorously
on the basis of a set of postulates. Some topics from non-Euclidean geometry.

Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director

**532 - Modern Geometry (3) **Projective geometry, theorem of Desargues, conics, transformation theory, affine geometry,
Euclidean geometry, non-Euclidean geometries, and topology.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**533 - Elementary Geometric Topology (3) **Topology of the line, plane, and space, Jordan curve theorem, Brouwer fixed point
theorem, Euler characteristic of polyhedra, orientable and non-orientable surfaces,
classification of surfaces, network topology.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**534 - Elements of General Topology (3) **Elementary properties of sets, functions, spaces, maps, separation axioms, compactness,
completeness, convergence, connectedness, path connectedness, embedding and extension
theorems, metric spaces, and compactification.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**540 - Modern Applied Algebra (3) **Finite structures useful in applied areas. Binary relations, Boolean algebras, applications
to optimization, and realization of finite state machines.**Prerequisites:** MATH 241

**541 - Algebraic Coding Theory (3) **Error-correcting codes, polynomial rings, cyclic codes, finite fields, BCH codes**Prerequisites:** C or better in MATH 544 or in both MATH 300 and 344 or consent of the Undergraduate
Director

**544 - Linear Algebra (3) **Vectors, vector spaces, and subspaces; geometry of finite dimensional Euclidean space;
linear transformations; eigenvalues on theoretical concepts, logic, and meethods.**Prerequisites:** C or better in MATH 300, or consent of the Undergraduate Director

**544L - Linear Algebra Lab (1) **Computer-based applications of linear algebra for mathematics students. Topics include
numerical analysis of matrices, direct and indirect methods for solving linear systems,
and least squares method (regression). Typical applications include theoretical and
practical issues related to discrete Markov’s processes, image compression, and linear
programming.**Prerequisites:** Prereq or coreq: C or better or concurrent enrollment in MATH 544.

**546 - Algebraic Structures I (3) **Permutation groups; abstract groups; introduction to algebraic structures through
study of subgroups, quotient groups, homomorphisms, isomorphisms, direct product;
decompositions; introduction to rings and fields.

**Prerequisites:**C or better in MATH 544 or consent of the Undergraduate Director

**547 - Algebraic Structures II (3) **Rings, ideals, polynomial rings, unique factorization domains; structure of finite
groups; topics from: fields, field extensions, Euclidean constructions, modules over
principal ideal domains (canonical forms).**Prerequisites**: C or higher in MATH 546 or consent of the Undergraduate Director

**548 - Geometry, Algebra, and Algorithms (3)** Polynomials and affine space, Groebner bases, elimination theory, varieties, and
computer algebra systems.**Prerequisites: **Math 300 and Math 544 or consent of the Undergraduate Director.

**550 - Vector Analysis (3) **Vector fields, line and path integrals, orientation and parametrization of lines and
surfaces, change of variables and Jacobians, oriented surface integrals, theorems
of Green, Gauss, and Stokes; introduction to tensor analysis.**Prerequisites:** C or higher in MATH 241 or consent of the Undergraduate Director

**551 - Introduction to Differential Geometry (3) **Parametrized curves, regular curves and surfaces, change of parameters, tangent planes,
the differential of a map, the Gauss map, first and second fundamental forms, vector
fields, geodesics, and the exponential map.

Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director

**552 - Applied Complex Variables (3) **Complex integration, calculus of residues, conformal mapping, Taylor and Laurent Series
expansions, applications.**Prerequisites:** C or better in MATH 241 or consent of the Undergraduate Director

**554 - Analysis I (3) **Least upper bound axiom, the real numbers, compactness, sequences, continuity, uniform
continuity, differentiation, Riemann integral and fundamental theorem of calculus.**Prerequisites:** C or better in MATH 300 and either at least one of 511, 520, 534, 550, or 552, or
consent of the Undergraduate Director

**555 - Analysis II (3) **Riemann-Stieltjes integral, infinite series, sequences and series of functions, uniform
convergence, Weierstrass approximation theorem, selected topics from Fourier series
or Lebesgue integration.**Prerequisites:** C or better in MATH 554 or consent of the Undergraduate Director

**561 - Introduction to Mathematical Logic (3) **Syntax and semantics of formal languages; sentential logic, proofs in first order
logic; Godel’s completeness theorem; compactness theorem and applications; cardinals
and ordinals; the Lowenheim-Skolem-Tarski theorem; Beth’s definability theorem; effectively
computable functions; Godel’s incompleteness theorem; undecidable theories.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**562 - Theory of Computation (3) **Basic theoretical principles of computing as modeled by formal languages and automata;
computability and computational complexity.**Prerequisites:** C or better in CSCE 350 or MATH 344 or 544 or 574 or consent of the Undergraduate
Director

**570 - Discrete Optimization (3) **Discrete mathematical models. Applications to such problems as resource allocation
and transportation. Topics include linear programming, integer programming, network
analysis, and dynamic programming.**Prerequisites:** C or better in MATH 344 or 544, or consent of the Undergraduate Director

**574 - Discrete Mathematics I (3) **Mathematical models; mathematical reasoning; enumeration; induction and recursion;
tree structures; networks and graphs; analysis of algorithms.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**575 - Discrete Mathematics II (3) **A continuation of MATH 574. Inversion formulas; Polya counting; combinatorial designs;
minimax theorems; probabilistic methods; Ramsey theory; other topics.**Prerequisites:** C or better in MATH 574 or consent of the Undergraduate Director

**576 - Combinatorial Game Theory (3) **Winning in certain combinatorial games such as Nim, Hackenbush, and Domineering. Equalities
and inequalities among games, Sprague-Grundy theory of impartial games, games which
are numbers.**Prerequisites:** C or better in MATH 344, 544, or 574, or consent of the Undergraduate Director

**580 - Elementary Number Theory (3) **Divisibility, primes, congruences, quadratic residues, numerical functions. Diophantine
equations.**Prerequisites:** C or better in MATH 300 or consent of the Undergraduate Director

**587 - Introduction to Cryptography (3) **Design of secret codes for secure communication, including encryption and integrity
verification: ciphers, cryptographic hashing, and public key cryptosystems such as
RSA. Mathematical principles underlying encryption. Code-breaking techniques. Cryptographic
protocols.**Prerequisites**: C or better in CSCE 145 or in MATH 241, and in either CSCE 355 or MATH 574, or consent
of the Undergraduate Director

**590 - Undergraduate Seminar (1-3) **A review of literature in specific subject areas involving student presentations.
Content varies and will be announced in the Master Schedule of Classes by suffix and
title. Pass-fail grading. For undergraduate credit only.**Prerequisites:** consent of instructor

**599 - Topics in Mathematics (1-3) **Recent developments in pure and applied mathematics selected to meet current faculty
and student interest.**602 - An Inductive Approach to Geometry (3) **This course is designed for middle-level pre-service mathematics teachers. This course
covers geometric reasoning, Euclidean geometry, congruence, area, volume, similarity,
symmetry, vectors, and transformations. Dynamic software will be utilized to explore
geometry concepts.

**Prerequisites:**C or better in MATH 122 or 141 or equivalent, or consent of the Undergraduate Director

**603 - Inquiry Approach to Algebra (3) **This course introduces basic concepts in number theory and modern algebra that provide
the foundation for middle level arithmetic and algebra. Topics include: algebraic
reasoning, patterns, inductive reasoning, deductive reasoning, arithmetic and algebra
of integers, algebraic systems, algebraic modeling, and axiomatic mathematics. This
course cannot be used for credit towards a major in mathematics.**Prerequisites:** C or better in MATH 122 or 141 or equivalent, or consent of the Undergraduate Director

**650 - AP Calculus for Teachers (3) **A thorough study of the topics to be presented in AP calculus, including limits of
functions, differentiation, integration, infinite series, and applications. (Not intended
for degree programs in mathematics.)**Prerequisites**: current secondary high school teacher certification in mathematics and a C or better
in at least 6 hours of calculus, or consent of the Undergraduate Director

**701I — Foundations of Algebra I. (3)** An introduction to algebraic structures; group theory including subgroups, quotient
groups, homomorphisms, isomorphisms, decomposition; introduction to rings and fields.**Prerequisites**: none

**702I — Foundations of Algebra II. (3) ** Theory of rings including ideals, polynomial rings, and unique factorization domains;
structure of finite groups; fields; modules.**Prerequisites: **MATH 701-I or equivalent

**703I — Foundations of Analysis I. (3)** The real numbers and least upper bound axiom; sequences and limits of sequences;
infinite series; continuity; differentiation; the Riemann integral.**Prerequisites**: MATH 241 or equivalent**704I — Foundations of Analysis II. (3) **Sequences and series of functions; power series, uniform convergence; interchange
of limits; limits and continuity in several variables.

**Prerequisites**: MATH 703-I or equivalent

**712I — Probability and Statistics. (3)**This course will include a study of permutations and combinations; probability and its application to statistical inferences; elementary descriptive statistics of a sample of measurements; the binomial, Poisson, and normal distributions; correlation and regression.

**Prerequisites**:

**Synthetic and analytic projective geometry, homothetic transformations, Euclidean geometry, non-Euclidean geometries, and topology.**

736I — Modern Geometry. (3)

736I — Modern Geometry. (3)

**Prerequisites**: MATH 241 or equivalent

**Properties of analytic functions, complex integration, calculus of residues, Taylor and Laurent series expansions, conformal mappings.**

752I — Complex Variables. (3)

752I — Complex Variables. (3)

**Prerequisites**: MATH 241 or equivalent

**Elementary properties of integers, Diophantine equations, prime numbers, arithmetic functions, congruences, and the quadratic reciprocity law.**

780I — Theory of Numbers. (3)

780I — Theory of Numbers. (3)

**Prerequisites**: MATH 241 or equivalent