# 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

**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

**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

**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

**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)

**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 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