MATHEMATICS (MATH)

MATH 401 - ALGEBRA FOR TEACHERS

The conceptual foundations for elementary and middle school algebra will be covered through an investigation of the fundamentals of algebraic modeling. Course topics will include; problem solving, real numbers and mathematical operations, algebraic notation, solving equations, patterns, formulas, graphing linear equations, solving systems of equations, direct and inverse variation, quadratic and exponential functions, and the application of functions. Although emphasis will be on mathematical content and concepts, pedagogy consistent with the NCTM Standards for Teaching Mathematics and problem-based learning will be modeled throughout the course.

Credits: 3

Prerequisites: MATH 115

Course Notes: or Illinois Teaching Certificate.

MATH 407 - CHAOS AND FRACTALS

Introduction to discrete and continuous dynamical systems; stability; chaotic behavior; fractals and fractal measures.

Credits: 3

Course Notes: MATH 233 and MATH 300 required/MATH307 recommended

MATH 409 - DATA MINING

Methods of knowledge discovery in massive data, i.e. the study of computer-assisted process of digging through and analyzing enormous data sets and then extracting the "˜meaning' of the data by applying mathematical methods. The methods that we study in this course are designed to predict behaviors and future trends based on existing data. Topics include classifications techniques, clusterization techniques, association rule discovery techniques, techniques for improving data quality.

Credits: 3

Course Notes: Math/ASCS 300 with a min grade of C-, and (Math 217 or Econ 234 or Math 347, with a min grade of C-).

MATH 410 - FORMAL LANGUAGES & AUTOMATA

Finite automata and regular languages; push-down automata and context-free languages. Turing machines, linear-bounded automata, and context sensitive languages. See also Cst 410.

Credits: 3

Course Notes: CST 280

MATH 416 - HISTORY OF MATHEMATICS

Evolution of mathematical ideas; major developments; problem solving, algorithms, and theoretical framework.

Credits: 3

Course Notes: MATH 231

MATH 417 - GEOMETRY

Comparative study of modern postulates, invariants, and implications of Euclidean, projective, and non-Euclidean geometries.

Credits: 3

Course Notes: MATH 231 or MATH 245 or MATH 290 required with a min grade, of C-.

MATH 418 - NUMBER THEORY

Study of integers. Division and Euclidean algorithms, prime numbers, unique factorization; Diophantine equations; congruences; Fermat's and Euler's theorems; quadratic reciprocity.

Credits: 3

Course Notes: MATH 231 or MATH 245 or MATH 290 required

MATH 420 - INTRODUCTION TO ABSTRACT ALGEBRA

Elementary properties of groups, rings, integral domains, and fields; symmetry; factorization of integers and polynomials; construction of quotient field of an integral domain.

Credits: 3

Course Notes: MATH 300 required.

MATH 423 - COOPERATION AND COMPETITION

Study of the ways in which strategic interactions among autonomous agents produce outcomes with respect to the preferences (or utilities) of those agents. This course covers game-theoretic foundations of cooperative and non-cooperative behavior of independent agents. The course emphasizes applications drawn from artificial intelligence, decision theory, economics, psychology, business management and finance.

Credits: 3

Course Notes: ACSC 300 with a min grade of C- or MATH 300, with a min grade of C- or ACSC 246 with a min, grade of C- or MATH 246 with a min grade of C- and, (MATH 245 with a min grade of C- or MATH 290 with a, min grade of C- or MATH 217 with, a min grade of C- or MATH 23

MATH 428 - LINEAR PROGRAMMING & OPTIM

Models of optimization with linear constraints and objectives; simplex method and related algorithms; duality and sensitivity; transportation and assignment problems; games and network flows. See also Cst 428.

Credits: 3

Course Notes: MATH 122

MATH 430 - NUMERICAL ANALYSIS

Solution of equations by iteration; interpolation; numerical differentiation and integration; numerical solutions to linear systems. Computer use course. See also Cst 330.

Credits: 3

Course Notes: MATH 232 and MATH 300

MATH 432 - OPERATIONS RESEARCH

Stochastic methods in operations research. Queuing theory; Markov processes; decision analysis; simulation; stochastic dynamic programming.

Credits: 3

Course Notes: Math 231, Math 217 or Math 347.

MATH 435 - TOPICS IIN APPLIED MATHEMATICS

Linear eigenvalue and boundary value problems; Fourier series and integrals; Laplace transforms.

Credits: 3

Course Notes: MATH 300 and MATH 307

MATH 445 - COMBINATORICS

Permutations and combinations; identities involving binomial coefficients; inclusion-exclusion principle; recurrence relations; generating functions; introduction to theory of graphs.

Credits: 3

Course Notes: MATH 232 and (MATH 245 or MATH 290) all with a C- or higher, required.

MATH 446 - STOCHASTIC PROCESSES

Poisson and renewal processes. Markov chains with applications to queuing theory, inventory control, and population growth.

Credits: 3

Prerequisites: ACSC 347 or MATH 347 or MATH 447

MATH 447 - ADVANCED PROBABILITY

Probability models; random variables; probability distributions; expectation and moment generating functions of random variables; multivariate distributions.

Credits: 3

Course Notes: MATH 347

MATH 448 - PROBABILITY AND STATISTICS II

Continuation of Math 447. Distributions of functions of random variables, sampling distributions; Central Limit Theorem; point estimators and confidence intervals; hypothesis testing; linear models.

Credits: 3

Course Notes: Math 347 or ACSC 347 with min grade C-.

MATH 449 - REGRESSION & TIME SERIES

Simple and multiple linear regression models; time series analysis; applications to forecasting. Use of a statistical computer package; no previous experience with computers required.

Credits: 3

Prerequisites: MATH 448

Course Notes: ( MATH 231 with a min grade of C- and ( MATH 217, with a min grade of C- or ECON 234, with a min grade of C- ) ) or ACSC 348 with a, min grade of C- or MATH 348 with a min grade of C-.

MATH 450 - BOOLEAN ALG & SWITCH THEORY

Logic gates and Boolean algebras. Minimization of switching functions, and Karnaugh maps. Introduction to logic circuits, flip-flops, counters and registers. Digital arithmetic.

Credits: 3

Course Notes: MATH 245 or MATH 290 required.

MATH 455 - FUNCTIONS OF A COMPLEX VAR

Elementary functions of a complex variable, complex differentiation and integration, Cauchy-Goursat theorem, Taylor and Laurent series, singularities and residues, conformal mapping.

Credits: 3

Course Notes: MATH 233 and (MATH 245 or MATH 290)

MATH 457 - ANOVA & EXPERIMENTAL DESIGN

One-way analysis of variance (ANOVA), multiple comparison methods, basic experimental designs, analysis of covariance (ANCOVA), factorial treatment structures, split plots, confounding and fractional replication in 2<sup>n</sup> factorial systems.

Credits: 3

Prerequisites: MATH 217 or MATH 238 or ACSC 348 or MATH 348 or MATH 448 or ECON 234 or PSYC 407 or MGMT 403

MATH 458 - THEORY OF INTEGRATION

The Lebesgue integral and its relation to the Riemann integral, convergence theorems, elements of measure theory.

Credits: 3

Prerequisites: MATH 300 and MATH 352

Course Notes: MATH 300 and MATH 352 required.

MATH 469 - ACTUARIAL MATHEMATICS I

Survival distributions and life tables; life insurance; life annuities.

Credits: 3

Course Notes: (ACSC 347 with a min grade of C- or MATH 347 with, a min grade of C- ) and ( ACSC 367 with, min grade of C- or MATH 367 with a min, grade of C- or concurrent)

MATH 470 - ACTUARIAL MATHEMATICS II

Benefit premiums; benefit reserves; multiple life functions; multiple decrement models.

Credits: 3

Prerequisites: MATH 469

Course Notes: or Math 369 or Acsc 369 with a min grade C-.

MATH 471 - TOPOLOGY

Set theory and metric spaces; topological spaces and continuity; separation, compactness, and connectedness.

Credits: 3

Course Notes: MATH 300 and MATH 352

MATH 475 - DERIVATIVES MARKETS

We will cover binomial option pricing, the Black-Scholes Formula and equation, market-making and delta hedging, exotic options, the lognormal distribution, Monte Carlo valuation, Brownian motion and Itobparity and other option relationships, volatility, interest rate models.

Credits: 3

Course Notes: ACSC/MATH 269, ACSC/MATH 367, FIN 311, or consent of Instructor.

MATH 476 - LOSS MODELS

Actuarial models; classifying and creating distributions; frequency and severity with coverage modifications; construction of empirical models; estimation for complete data; estimation for modified data; parameter estimation; interpolation and smoothing; simulation.

Credits: 3

Prerequisites: MATH 448 (may be taken concurrently)

Course Notes: or ACSC 348 or MATH 348.

MATH 477 - SURVIVAL MODELS

Survival data, survival functions, hazard functions, life tables, comparing two groups of survival data, parametric models of survival data, and sample size for survival studies.

Credits: 3

Prerequisites: ACSC 348 (may be taken concurrently) or MATH 348 (may be taken concurrently) or MATH 448 (may be taken concurrently)

Course Notes: or concurrent

MATH 478 - TOPICS IN ACTUARIAL MATH

Course content varies. Topics in actuarial models and actuarial modeling. May be repeated for credit for up to six semester hours.

Credits: 3

Course Notes: Consent of instructor.

MATH 480 - ACTUARIAL SCIENCE SEMINAR

Applications of mathematical and financial models to actuarial problems and practice. Topics vary and may include risk management and insurance, corporate finance, price theory, actuarial models, loss models, simulation, and survival models.

Credits: 3

Prerequisites: MATH 448 (may be taken concurrently)

Course Notes: or Math 348 or Acsc 348. Preparation for Exam FM (Chgo), and Exam P (Sch).

MATH 480FM - ACTUARIAL SCIENCE SEMINAR

Preparation for the Society of Actuaries Exam FM and the Casualty Actuarial Society Exam 2.

Credits: 3

Course Notes: Should have ACSC 367 or MATH 367 both with a min grade, of C-. Preparation for Exam FM.

MATH 480P - ACTUARIAL SCI SEM: EXAM P/1

Preparation for the Society of Actuaries Exam P and the Casualty Actuarial Society Exam 1.

Credits: 3

Prerequisites: MATH 448 (may be taken concurrently)

Course Notes: Preparation for Exam P., ACSC 347 with a min grade of C- or concurrent or, MATH 347 with a min grade of C-

MATH 485 - FUNCTIONAL ANALYSIS

Credits: 3

Course Notes: MATH 300 and MATH 352

MATH 488 - SPECIAL TOPICS

Course content varies. May be repeated for up to nine semester hours. This topics course may not be cross-listed with undergraduate coursework.

Credits: 1-3

Course Notes: Prerequisites vary by topics.

MATH 489 - SPECIAL TOPICS

Course content varies. May be repeated for up to nine semester hours.

Credits: 1,3

MATH 490 - MASTER'S THESIS

Individual projects pursued under an instructor's supervision.

Credits: 3

MATH 495 - INDEPENDENT STUDY

Individual projects pursued under an instructor's supervision.

Credits: 1-6

Course Notes: Consent of instructor