Mathematics (MATH)           1

MATHEMATICS (MATH)MATH 100Introduction to the ProfessionIntroduces the student to the scope of mathematics as a profession,develops a sense of mathematical curiosity and problem solvingskills, identifies and reinforces the student's career choices, andprovides a mechanism for regular academic advising. Providesintegration with other first-year courses. Introduces applicationsof mathematics to areas such as engineering, physics, computerscience, and finance. Emphasis is placed on the development ofteamwork skills.Lecture: 3 Lab: 0 Credits: 3Satisfies: Communications (C)

MATH 119Geometry for ArchitectsBasic Euclidean and analytic geometry in two and three dimensions;trigonometry. Equations of lines, circles and conic sections;resolution of triangles; polar coordinates. Equations of planes, lines,quadratic surfaces. Applications. This course does not count towardany mathematics requirements in business, computer science,engineering, mathematics, or natural science degree programs.Lecture: 3 Lab: 1 Credits: 3Satisfies: Communications (C)

MATH 122Introduction to CalculusBasic concepts of calculus of a single variable; limits, continuity,derivatives, and integrals. Applications. This course does not counttoward any mathematics requirements in business, computerscience, engineering, mathematics, or natural science degreeprograms.Prerequisite(s): MATH 119 or MATH 148 or IIT MathematicsPlacement score of 122Lecture: 3 Lab: 1 Credits: 3

MATH 130Thinking MathematicallyThis course allows students to discover, explore, and apply modernmathematical ideas. Emphasis is placed on using sound reasoningskills, visualizing mathematical concepts, and communicatingmathematical ideas effectively. Classroom discussion andgroup work on challenging problems are central to the course.Topics from probability, statistics, logic, number theory, graphtheory, combinatorics, chaos theory, the concept of infinity, andgeometry may be included. This course does not count towardany mathematics requirements in business, computer science,engineering, mathematics, or natural science degree programs.Lecture: 3 Lab: 0 Credits: 3Satisfies: Communications (C)

MATH 148Preparation for CalculusReview of algebra and analytic geometry. Functions, limits,derivatives. Trigonometry, trigonometric functions and theirderivatives. Inverse functions, inverse trigonometric functions andtheir derivatives. Exponential and logarithmic functions. This coursedoes not count toward any mathematics requirements in business,computer science, engineering, mathematics, or natural sciencedegree programs.Lecture: 4 Lab: 0 Credits: 4

MATH 151Calculus IAnalytic geometry. Functions and their graphs. Limits andcontinuity. Derivatives of algebraic and trigonometric functions.Applications of the derivative. Introduction to integrals and theirapplications.Prerequisite(s): IIT Mathematics Placement score of 151 or MATH145 with min. grade of C or MATH 148 with min. grade of CLecture: 4 Lab: 1 Credits: 5Satisfies: Communications (C)

MATH 152Calculus IITranscendental functions and their calculus. Integration techniques.Applications of the integral. Indeterminate forms and improperintegrals. Polar coordinates. Numerical series and power seriesexpansions.Prerequisite(s): MATH 149 with min. grade of C or MATH 151 withmin. grade of CLecture: 4 Lab: 1 Credits: 5Satisfies: Communications (C)

MATH 180Fundamentals of Discrete MathematicsBasic counting techniques, discrete probability, graph theory,algorithm complexity, logic and proofs, and other fundamentaldiscrete topics. Required for students in the Bachelor of InformationTechnology and Management degree. This course does not counttoward any mathematics requirements in computer science,engineering, mathematics, or natural science degree programs.Lecture: 3 Lab: 0 Credits: 3

MATH 225Introductory StatisticsAn introduction to statistics; data collection, description,visualization and analysis; basic probability; statistical reasoningand inference including hypothesis tests and confidence intervals: t-tests, chi-squared tests, ANOVA, correlation and regression.Lecture: 3 Lab: 0 Credits: 3Satisfies: Communications (C)

2        Mathematics (MATH)

MATH 230Introduction to Discrete MathSets, statements, and elementary symbolic logic; relations anddigraphs; functions and sequences; mathematical induction; basiccounting techniques and recurrence. Credit will not be granted forboth CS 330 and MATH 230.Lecture: 3 Lab: 0 Credits: 3Satisfies: Communications (C)

MATH 251Multivariate and Vector CalculusAnalytic geometry in three-dimensional space. Partial derivatives.Multiple integrals. Vector analysis. Applications.Prerequisite(s): MATH 152Lecture: 4 Lab: 0 Credits: 4

MATH 252Introduction to Differential EquationsLinear differential equations of order one. Linear differentialequations of higher order. Series solutions of linear DE. Laplacetransforms and their use in solving linear DE. Introduction tomatrices. Systems of linear differential equations.Prerequisite(s): MATH 152Lecture: 4 Lab: 0 Credits: 4

MATH 300Perspectives in AnalysisThe course is focused on selected topics related to fundamentalconcepts and methods of classic analysis and their applicationswith emphasis on various problem-solving strategies, visualization,mathematical modeling, and interrelation of different areas ofmathematics.Prerequisite(s): MATH 252 and MATH 251Lecture: 3 Lab: 0 Credits: 3

MATH 332Elementary Linear AlgebraSystems of linear equations; matrix algebra, inverses, determinants,eigenvalues, and eigenvectors, diagonalization; vector spaces, basis,dimension, rank and nullity; inner product spaces, orthonormalbases; quadratic forms.Prerequisite(s): MATH 251*, An asterisk (*) designates a coursewhich may be taken concurrently.Lecture: 3 Lab: 0 Credits: 3

MATH 333Matrix Algebra and Complex VariablesVectors and matrices; matrix operations, transpose, rank, inverse;determinants; solution of linear systems; eigenvalues andeigenvectors. The complex plane; analytic functions; contourintegrals; Laurent series expansions; singularities and residues.Prerequisite(s): MATH 251Lecture: 3 Lab: 0 Credits: 3

MATH 350Introduction to Computational MathematicsStudy and design of mathematical models for the numericalsolution of scientific problems. This includes numerical methodsfor the solution on linear and nonlinear systems, basic data fittingproblems, and ordinary differential equations. Robustness, accuracy,and speed of convergence of algorithms will be investigatedincluding the basics of computer arithmetic and round-off errors.Same as MMAE 350.Prerequisite(s): (CS 104 or CS 105 or CS 115) and MATH 251 andMATH 252*, An asterisk (*) designates a course which may be takenconcurrently.Lecture: 3 Lab: 0 Credits: 3Satisfies: Communications (C)

MATH 374Probability and Statistics for Electrical and Computer EngineersThis course focuses on the introductory treatment of probabilitytheory including: axioms of probability, discrete and continuousrandom variables, random vectors, marginal, joint, conditional andcumulative probability distributions, moment generating functions,expectations, and correlations. Also covered are sums of randomvariables, central limit theorem, sample means, and parameterestimation. Furthermore, random processes and random signalsare covered. Examples and applications are drawn from problemsof importance to electrical and computer engineers. Credit onlygranted for one of MATH 374, MATH 474, and MATH 475.Prerequisite(s): MATH 251Lecture: 3 Lab: 0 Credits: 3

MATH 380Introduction to Mathematical ModelingThis course provides an introduction to problem-driven (as opposedto method-driven) applications of mathematics with a focuson design and analysis of models using tools from all parts ofmathematics.Prerequisite(s): (CS 104 or CS 105 or CS 115) and MATH 251 andMATH 252* and MATH 332, An asterisk (*) designates a coursewhich may be taken concurrently.Lecture: 3 Lab: 0 Credits: 3Satisfies: Communications (C)

MATH 400Real AnalysisReal numbers, continuous functions; differentiation and Riemannintegration. Functions defined by series.Prerequisite(s): MATH 251Lecture: 3 Lab: 0 Credits: 3

MATH 402Complex AnalysisAnalytic functions, conformal mapping, contour integration, seriesexpansions, singularities and residues, and applications. Intendedas a first course in the subject for students in the physical sciencesand engineering.Prerequisite(s): MATH 251Lecture: 3 Lab: 0 Credits: 3

Mathematics (MATH)           3

MATH 405Introduction to Iteration and ChaosFunctional iteration and orbits, periodic points and Sharkovsky'scycle theorem, chaos and dynamical systems of dimensions oneand two. Julia sets and fractals, physical implications.Prerequisite(s): (MATH 251 and MATH 252 and MATH 332) or(MATH 252 and MATH 333 and MATH 251)Lecture: 3 Lab: 0 Credits: 3

MATH 410Number TheoryDivisibility, congruencies, distribution of prime numbers, functionsof number theory, diophantine equations, applications to encryptionmethods.Prerequisite(s): MATH 230Lecture: 3 Lab: 0 Credits: 3

MATH 420GeometryThe course is focused on selected topics related to fundamentalideas and methods of Euclidean geometry, non-Euclidean geometry,and differential geometry in two and three dimensions and theirapplications with emphasis on various problem-solving strategies,geometric proof, visualization, and interrelation of different areas ofmathematics. Permission of the instructor is required.Lecture: 3 Lab: 0 Credits: 3

MATH 425Statistical MethodsConcepts and methods of gathering, describing and analyzing dataincluding basic statistical reasoning, basic probability, sampling,hypothesis testing, confidence intervals, correlation, regression,forecasting, and nonparametric statistics. No knowledge of calculusis assumed. This course is useful for students in education or thesocial sciences. This course does not count for graduation in anymathematics programs. Credit not given for both MATH 425 andMATH 476.Lecture: 3 Lab: 0 Credits: 3

MATH 426Statistical Tools for EngineersDescriptive statistics and graphs, probability distributions, randomsampling, independence, significance tests, design of experiments,regression, time-series analysis, statistical process control,introduction to multivariate analysis. Same as CHE 426. Credit notgiven for both Math 426 and CHE 426.Lecture: 3 Lab: 0 Credits: 3

MATH 430Applied AlgebraIntroduction to groups, homomorphisms, group actions, rings,field theory. Applications, including constructions with ruler andcompass, solvability by radicals, error correcting codes.Prerequisite(s): MATH 230 or MATH 332*, An asterisk (*) designatesa course which may be taken concurrently.Lecture: 3 Lab: 0 Credits: 3Satisfies: Communications (C)

MATH 431Computational Algebraic GeometrySystems of polynomial equations and ideals in polynomial rings;solution sets of systems of equations and algebraic varietiesin affine n-space; effective manipulation of ideals and varieties,algorithms for basic algebraic computations; Groebner bases;applications. Credit may not be granted for both MATH 431 andMATH 530.Prerequisite(s): MATH 332 and MATH 230Lecture: 3 Lab: 0 Credits: 3Satisfies: Communications (C)

MATH 435Linear OptimizationIntroduction to both theoretical and algorithmic aspects of linearoptimization: geometry of linear programs, simplex method,anticycling, duality theory and dual simplex method, sensitivityanalysis, large scale optimization via Dantzig-Wolfe decompositionand Benders decomposition, interior point methods, network flowproblems, integer programming. Credit may not be granted for bothMATH 435 and MATH 535.Prerequisite(s): MATH 332Lecture: 3 Lab: 0 Credits: 3

MATH 446Introduction to Time SeriesThis course introduces the basic time series analysis andforecasting methods. Topics include stationary processes, ARMAmodels, spectral analysis, model and forecasting using ARMAmodels, nonstationary and seasonal time series models, multivariatetime series, state-space models, and forecasting techniques.Prerequisite(s): MATH 475 with min. grade of C or ECE 511 with min.grade of CLecture: 3 Lab: 0 Credits: 3

MATH 453CombinatoricsPermutations and combinations; pigeonhole principle; inclusion-exclusion principle; recurrence relations and generating functions;enumeration under group action.Prerequisite(s): MATH 230Lecture: 3 Lab: 0 Credits: 3

MATH 454Graph Theory and ApplicationsDirected and undirected graphs; paths, cycles, trees, Eulerian cycles,matchings and coverings, connectivity, Menger's Theorem, networkflow, coloring, planarity, with applications to the sciences (computer,life, physical, social) and engineering.Prerequisite(s): (MATH 230 and MATH 251) or (MATH 252 andMATH 230)Lecture: 3 Lab: 0 Credits: 3Satisfies: Communications (C)

MATH 461Fourier Series and Boundary-Value ProblemsFourier series and integrals. The Laplace, heat, and wave equations:Solutions by separation of variables. D'Alembert's solution of thewave equation. Boundary-value problems.Prerequisite(s): MATH 251 and MATH 252Lecture: 3 Lab: 0 Credits: 3

4        Mathematics (MATH)

MATH 474Probability and StatisticsElementary probability theory including discrete and continuousdistributions, sampling, estimation, confidence intervals, hypothesistesting, and linear regression. Credit not granted for both MATH 474and MATH 475.Prerequisite(s): MATH 251Lecture: 3 Lab: 0 Credits: 3

MATH 475ProbabilityElementary probability theory; combinatorics; random variables;discrete and continuous distributions; joint distributions andmoments; transformations and convolution; basic theorems;simulation. Credit not granted for both MATH 474 and MATH 475.Prerequisite(s): MATH 251Lecture: 3 Lab: 0 Credits: 3

MATH 476StatisticsEstimation theory; hypothesis tests; confidence intervals; goodness-of-fit tests; correlation and linear regression; analysis of variance;nonparametric methods.Prerequisite(s): MATH 475Lecture: 3 Lab: 0 Credits: 3Satisfies: Communications (C)

MATH 477Numerical Linear AlgebraFundamentals of matrix theory; least squares problems; computerarithmetic; conditioning and stability; direct and iterative methodsfor linear systems; eigenvalue problems. Credit may not be grantedfor both MATH 477 and MATH 577.Prerequisite(s): MATH 350 or MMAE 350Lecture: 3 Lab: 0 Credits: 3

MATH 478Numerical Methods for Differential EquationsPolynomial interpolation; numerical integration; numerical solutionof initial value problems for ordinary differential equations bysingle and multi-step methods, Runge-Kutta, Predictor-Corrector;numerical solution of boundary value problems for ordinarydifferential equations by shooting method, finite differences andspectral methods. Credit may not be granted for both MATH 478 andMATH 578.Prerequisite(s): MATH 350 or MMAE 350Lecture: 3 Lab: 0 Credits: 3

MATH 481Introduction to Stochastic ProcessesThis is an introductory, undergraduate course in stochasticprocesses. Its purpose is to introduce students to a range ofstochastic processes which are used as modeling tools in diversefields of applications, especially in risk management applicationsfor finance and insurance. The course covers basic classes ofstochastic processes: Markov chains and martingales in discretetime; Brownian motion; and Poisson process. It also presents someaspects of stochastic calculus.Prerequisite(s): (MATH 332 and MATH 475) or (MATH 475 andMATH 333)Lecture: 3 Lab: 0 Credits: 3

MATH 483Design and Analysis of ExperimentsReview of elementary probability and statistics; analysis of variancefor design of experiments; estimation of parameters; confidenceintervals for various linear combinations of the parameters;selection of sample sizes; various plots of residuals; block designs;Latin squares; one, two, and 2^k factorial designs; nested and crossfactor designs; regression; nonparametric techniques.Prerequisite(s): MATH 476Lecture: 3 Lab: 0 Credits: 3

MATH 484RegressionThis course introduces the basic statistical regression model anddesign of experiments concepts. Topics include simple linearregression, multiple linear regression, least square estimates ofparameters; hypothesis testing and confidence intervals in linearregression, testing of models, data analysis and appropriateness ofmodels, generalized linear models, design and analysis of single-factor experiments.Prerequisite(s): MATH 474 with min. grade of C or (MATH 476 withmin. grade of C and MATH 475 with min. grade of C)Lecture: 3 Lab: 0 Credits: 3Satisfies: Communications (C)

MATH 485Introduction to Mathematical FinanceThis is an introductory course in mathematical finance. Technicaldifficulty of the subject is kept at a minimum while the majorideas and concepts underlying modern mathematical financeand financial engineering are explained and illustrated. Thecourse covers the binomial model for stock prices and touches oncontinuous time models and the Black-Scholes formula.Prerequisite(s): MATH 475Lecture: 3 Lab: 0 Credits: 3

MATH 486Mathematical Modeling IThe course provides a systematic approach to modelingapplications from areas such as physics and chemistry, engineering,biology, and business (operations research). The mathematicalmodels lead to discrete or continuous processes that may bedeterministic or stochastic. Dimensional analysis and scaling areintroduced to prepare a model for study. Analytic and computationaltools from a broad range of applied mathematics will be used toobtain information about the models. The mathematical resultswill be compared to physical data to assess the usefulness ofthe models. Credit may not be granted for both MATH 486 andMATH 522.Prerequisite(s): MATH 251 and MATH 332 and MATH 252Lecture: 3 Lab: 0 Credits: 3Satisfies: Communications (C)

MATH 487Mathematical Modeling IIThe formulation of mathematical models, solution of mathematicalequations, interpretation of results. Selected topics from queuingtheory and financial derivatives.Prerequisite(s): MATH 252Lecture: 3 Lab: 0 Credits: 3

Mathematics (MATH)           5

MATH 488Ordinary Differential Equations and Dynamical SystemsBoundary-value problems and Sturm-Liouville theory; linear systemtheory via eigenvalues and eigenvectors; Floquet theory; nonlinearsystems: critical points, linearization, stability concepts, indextheory, phase portrait analysis, limit cycles, and stable and unstablemanifolds; bifurcation; and chaotic dynamics.Prerequisite(s): MATH 252 and MATH 251Lecture: 3 Lab: 0 Credits: 3

MATH 489Partial Differential EquationsFirst-order equations, characteristics. Classification of second-orderequations. Laplace's equation; potential theory. Green's function,maximum principles. The wave equation: characteristics, generalsolution. The heat equation: use of integral transforms.Prerequisite(s): MATH 252Lecture: 3 Lab: 0 Credits: 3

MATH 491Reading and ResearchIndependent reading and research. **Instructor permissionrequired.**Credit: VariableSatisfies: Communications (C)

MATH 497Special ProblemsSpecial problems.Credit: VariableSatisfies: Communications (C)