Recommended for students who require preparation for Mathematics 130, for Statistics 242 or for Interdisciplinary Studies 120. Number systems, solutions of equations and inequalities, coordinate systems, graphing, polynomial and rational expressions, exponents, and radicals.  PREREQUISTE(S):A passing score on the Basic Algebra Test and recommendation based on the Mathematics Diagnostic Test.

Student received a sufficient score on Part I of the DePaul Math Diagnostic placement exam.   No credit is earned, but this will meet the MAT 101 prerequisite.

A practical, application-based course directed primarily toward non-math and non-science majors who need a better mathematical background.  The course provides an opportunity to expand mathematical knowledge by exploring various areas of mathematics.  Topics include geometry, number theory, logic, numeration systems, counting methods, set theory and more.

Designed for non-science and non-mathematics majors, this course provides opportunities to expand mathematical experience while exploring a variety of mathematical areas.  Students develop critical thinking skills, such as logical and abstract reasoning, and use powerful mathematical ideas to analyze and solve problems.  Topics include cryptography, problem solving, counting methods, probability, and Game Theory.

Mathematical topics for students interested in business and social sciences, including logic, probability, matrix theory, and linear programming.  Preparation for statistics and computer studies.  PREREQUISITE(S): MAT 101 or placement by the Mathematics Diagnostic Test.

Problem solving, sets, functions, numeration systems, properties of integers and rational numbers and basic number theory.  PREREQUISTE(S):A passing score on the Computational Skills Test and MAT 101, ISP 120 or a sufficient score on the Mathematics Diagnostic Test.

Statistical graphs, measures of central tendency and variation, basic notions of geometry, linear measure, angles, areas of polygons and circles, the Pythagorean theorem, surface area, volume, basic probability, and using algebra as a problem-solving tool.   PREREQUISTE(S): MAT 110.

Students with very little mathematical background and little or no computing background will be given a brief introduction to the use of Microsoft Excel for mathematical purposes. This will be followed by a brief discussion of chance, gambling, and probability. Several popular games (such as lotteries, roulette, craps, and poker) will be considered both from a theoretical point of view and by means of very simple computer simulation. At the end, we will discuss briefly topics from game theory such as zero-sum games and game with cooperation. Prerequisite(s): WRC 104.

Continuation of Math 110-111.  PREREQUISTE(S): MAT 111.

Functions, inverse functions, graphing, linear and quadratic functions, radicals and exponents, exponential and logarithmic functions.  PREREQUISTE(S): MAT 101 or placement by the Mathematics Diagnostic Test.

Student received a sufficient score on Part II of the DePaul Math Diagnostic placement exam.   No credit is earned, but this will meet the MAT 130 prerequisite.

Polynomials, rational functions, basic trigonometry, triangle trigonometry, trigonometric identities and equations.  PREREQUISTE(S): MAT 130 or placement by the Mathematics Diagnostic Test.

Student received a sufficient score on Part III of the DePaul Math Diagnostic placement exam.   No credit is earned, but this will meet the MAT 131 prerequisite.

The logic of compound statements, application to digital logic circuits and computer arithmetic, the logic of predicates and quantified statements, programming logic, elementary number theory and methods of proof, sequences and mathematical induction, algorithms, combinatorial reasoning, the binomial theorem.  PREREQUISITE(S): MAT 130 or placement by the Mathematics Diagnostic Test.

Set theory, functions, order notation, finite-state machines, recursive sequences, recursively defined sets, recursive algorithms, function properties, equivalence relations, graphs, trees.  PREREQUISTE(S): MAT 140.

Limits, continuity, the derivative and rules of differentiation, applications of the derivative, exponential and loganthmic functions, the definite integral and some methods of integration, improper integrals.  PREREQUISTE(S): MAT 130 (or placement by on the Mathematics Diagnostic Test) and MAT 141.

Limits, continuity, the derivative, rules of differentiation, and applications, with precalculus review included for each topic.  The full MAT 147-8-9 sequence will cover all the material of MAT 150-1-2 plus additional precalculus material.  PREREQUISITE(S): MAT 130 or placement by on the Mathematics Diagnostic Test.

Extrema, curve sketching, related rates, definite and indefinite integrals, applications of the integral, exponential and logarithmic functions, with precalculus review included for each topic. PREREQUISTE(S): MAT 147.

Techniques of integration, L'Hopital's rule, improper integrals, Taylor polynomials, series and sequences, first-order differential equations, with precalculus review included for each topic. PREREQUISTE(S): MAT 148.

Limits, continuity, the derivative, rules of differentiation, extrema, curve sketching, related rates and other  applications.  PREREQUISTE(S): MAT 131 or placement by Mathematics Diagnostic Test.

Definite and indefinite integrals, applications of the integral, exponential and logarithmic functions, techniques of integration.  PREREQUISTE(S): MAT 150 or 160.

L'Hopital's rule, improper integrals, Taylor polynomials, series and sequences, first-order differential equations.  PREREQUISITE(S): MAT 151or MAT 161 or MAT 171.

Limits, continuity, the derivative, rules of differentiation, extrema, curve sketching, related rates and other applications.  Course meets for an additional lab session each week in order to cover the material in greater depth. Students considering a math major are advised to take the 160 or 170 sequence.  PREREQUISTE(S): MAT 131 or placement by the Mathematics Diagnostic Test.  5 quarter hours.

Definite and indefinite integrals, applications of the integral, exponential and logarithmic functions, techniques of integration.  Course meets for an additional 1 1/1 hour lab session each week in order to cover the material in greater depth.  PREREQUISTE(S): MAT 160 or 150. 5 quarter hours.

L'Hopital's rule, improper integrals, Taylor polynomials, series and sequences, first-order differential equations.  Course meets for an additional 1 1/2 hour lab session each week in order to cover the material in greater depth.  PREREQUISITE(S): MAT 151 MAT or 161or  MAT 171. 5 quarter hours.

The course will cover the following topics using examples from the sciences:   Functions as models, logarithmic scale graphing, exponential growth and decay, difference equations and limits of sequences, geometric series, functions and limits, trigonometric functions and their limits, continuity, limits at infinity, the derivative, differentiation rules, derivatives of trigonometric and exponential functions,  related rates, derivatives of inverse and logarithm functions.  Course meets for an additional lab session each week during which time students will work on applied mathematics projects based on the topics covered in the course.  Students majoring in the sciences should consult with their major department to decide between the 160 and 170 sequences.  Prerequisites:  MAT 131 or placement by the Mathematics Diagnostic Test.

The course will cover the following topics using examples from the sciences:   Applications of the derivative including approximation and local linearity, differentials, extrema and the Mean Value Theorem, monotonicity and concavity, extrema, inflection points, graphing, L'Hospital's Rule, optimization, and the Newton-Raphson method, antiderivaties, the definite integral, Riemann sums, the Fundamental Theorem of Calculus, area, cumulative change, average value of a function,  and techniques of integration: substitution rule and integration by parts. 
Course meets for an additional lab session each week during which time students will work on applied mathematics projects based on the topics covered in the course. Prerequisite(s):  MAT 150 or MAT 160 or MAT 170.

This course is designed for students in the life sciences and covers some topics from MAT 152, differential equations and an introduction to the Calculus of functions of several variables.  Specific topics are as follows.  Numerical integration, partial fraction expansions, Taylor approximations of a function, differential equations, separation of variables, slope fields, Euler's existence theorem, polygonal approximations to solutions of differential equations, the logistic equation and allometric growth models, equilibiria of differential equations and their stability, applications of stability theory, functions of several variables, partial derivatives, directional derivative and the gradient.
Course meets for an additional lab session each week during which time students will work on applied mathematics projects based on the topics covered in the course. Prerequisite(s):  MAT 151 or MAT 161or MAT 171.

Calculus I Workshop

Calculus II Workshop

Calculus III Workshop

Development Of Mathematics To The  Renaissance

History Of Probability And Statistics

Mathematics And Financial Decisions

Explorations In Mathematics  PREREQUISTE(S): MAT 112 or 113.

An introduction to basic concepts and techniques used in higher is mathematics courses: set theory, equivalence relations, functions, cardinality, techniques of proof in mathematics. The emphasis on problem solving and proof construction by students.  The department recommends that students take this course no later than the spring quarter of the sophomore year.  PREREQUISITE(S): MAT 149, 151, or 161 (or 171).

(Primarily for non-mathematics majors.) Systems of linear equations, matrices and matrix algebra, determinants, applications to linear programming, graph theory, etc.  PREREQUISTE(S): MAT 141 or 151 or 161.

Descriptive statistics, elements of probability, the binomial and normal probability models; large and small sample hypothesis testing, correlation and regression analysis. Use of computer packages.  PREREQUISTE(S): MAT 101 or a sufficient score on the Mathematics Diagnostic Test.  This course does not count toward mathematics major credit.

Vectors in 2-space and 3-space, vector-valued functions, cylindrical and spherical coordinates, multivariable functions, partial differentiation with applications to extrema.  PREREQUISTE(S): MAT 149 or 152 or 162 or consent of instructor.

Multiple integration, line and surface integrals, change of variable in multiple integration, Green's and Stokes' theorems.  PREREQUISTE(S): MAT 260.

Systems of linear equations and matrices; vectors in n-space; vector spaces: linear combinations, linear independence, basis; linear transformations, change of basis, eigenvalues and eigenvectors.  PREREQUISTE(S): MAT 260.

Functions And Graphs For Teachers

Trigonometric Functions And Analytic  Geometry For Teachers

History of mathematics with problem solving. (PREREQUISTE(S):MAT 151 or 161)

Methods of counting and enumeration of mathematical structures. Topics include generating functions, recurrence relations, inclusion relations, and graphical methods.  PREREQUISTE(S): MAT 141 or 215 or consent.

A study of properties of integers: divisibility; Euclid's Algorithm; congruences and modular arithmetic; Euler's Theorem; Diophantine equations; distribution of primes; RSA cryptography.  PREREQUISITE(S): MAT 141 or 215 or consent.

Theories, methods, and materials for teaching and learning mathematics in secondary schools. PREREQUISTE(S): SE 364 or equivalent

The first quarter of a 3-quarter sequence. Topics in the sequence include the integers; abstract groups, rings, and fields; polynomial rings; isomorphism theorems; extension fields; and an introduction to Galois theory.  PREREQUISTE(S): MAT 262 and either 141 or 215.  MAT 303 is highly recommended.

Continuation of 310.  PREREQUISTE(S): MAT 310.

Continuation of 311.  PREREQUISTE(S): MAT 311.

Incidence and separation properties of plane; congruence; parallel postulate; area theory; ruler and compass construction. PREREQUISITE(S): MAT 141 or 215.

Introduction to solid geometry and noneuclidean geometry (hyperbolic and spherical models); other special topics. Prerequisite(s): MAT 320.

Computing with a statistical package. Introduction to data analysis, elementary statistical inference, regression and correlation.  PREREQUISTE(S): MAT 130 or equivalent.  This course does not count toward mathematics major credit.

Advanced features and applications of the statistical package used in 323.  PREREQUISTE(S): MAT 323 or consent of the instructor.

Simple random, stratified, systematic and cluster sampling. Multistage and area sampling. Random-response and capture-release models. PREREQUISTE(S): MAT 353; or either 348 or 323 or BMS 142 and instructor's consent.

Linear models and quadratic forms. Single, two and several-factor experiments, incomplete designs, confounding and fractional factorial experiments. Response surfaces and partially balanced incomplete block designs. PREREQUISTE(S): MAT 353; or either 348 or 323 or BMS 142 and instructor's consent.

Computational and theoretical methods in ordinary diffential equations, complex numbers, systems of equations, phase piane analysis, bifurcations.  Applications to damped, driven osciuators, electronics.

Computational and theoretical methods in ordinary differential equations, complex numbers, systems of equations, phase plane analysis, bifurcations. Applications to damped, driven oscillators, electronics. Lab Fee Winter  COREQUISTE(S): MAT 261.

Real number system, completeness, supremum, and infimum, sequences and their limits, lim inf, lim sup, limits of functions, continuity.   PREREQUISTE(S): Either MAT 149, 152 or 162 and either MAT 141 or 215.

Properties of continuous functions, uniform continuity, sequences of functions, differentiation, integration.   To follow 335 in the Winter Quarter. PREREQUISTE(S): MAT 335.

Complex functions; complex differentiation and integration; series and sequences of complex functions.   Offered in Spring 2001-2002 and in alternate years thereafter. PREREQUISTE(S): MAT 261, and either 141 or 215.

Linear equations, systems with constant coefficients, series solutions, Laplace transforms, and applications. (COREQUISTE(S): MAT 261)

An introduction to point-set topology: metric spaces, topological spaces, continuity, connectedness, and compactness.  PREREQUISTE(S): Either 141 or 215, and either 220 or 262 or consent of instructor.

The SAS programming language. Data exploration, description and presentation. Inference based on continuous and categorical data. Analysis of variance models and regression procedures including logistic regression.  PREREQUISITE(S): One statistics course or consent of instructor.

Multiple regression, correlation, analysis of variance, time series, and sampling. Course content and emphases will vary with students' needs and backgrounds.  PREREQUISITE(S): MAT 348, or 323, or BMS 142, or BMS 157.

Introduction to statistical software (which will be used throughout the course). Descriptive statistics; elementary probability theory; discrete and continuous probability models; principles of statistical inference; Simple linear regression and correlation analysis.  PREREQUISTE(S): MAT 151 or 161 or 171.

A continuation of Mathematics 348. Multiple regression; analysis of frequency data, ANOVA and some experimental designs; nonparametric inference and time series analysis. Use of statistical software.  PREREQUISTE(S): MAT 348.

Exploratory data analysis with emphasis on data expression and reexpression; model building; computer graphical displays such as stem-and-leaf letter value displays; boxplots; resistant lines; data smoothing and transformations. Use of computer software such as MINITAB.  PREREQUISTE(S): MAT 348, or 323, or BMS 142, or BMS 157.

Probability spaces, combinatorial probability methods, discrete and continuous random variables and distributions, moment generating functions, development and applications of the classical discrete and continuous distributions.  PREREQUISTE(S): MAT 261.

Joint probability distributions and correlation; law of large numbers and the central limit theorem; sampling distributions and theory of estimation.  PREREQUISTE(S): MAT 351.

Principles of hypothesis testing; most powerful tests and likelihood ratio tests; linear regression; one-way analysis of variance; categorical data analysis, nonparametric statistics.  PREREQUISTE(S): MAT 352.

The multivariate normal distribution. Hypothesis tests on means and variances including the multivariate linear model. Classification using the linear discriminant function. Principal components and factor analysis.  PREREQUISTE(S): MAT 353 and 262, or consent of instructor.

Discrete Markov chains and random walks, birth and death processes, Poisson processes, queuing systems, and renewal processes.  PREREQUISTE(S): MAT 353.

Simple linear, multiple, polynomial and general regression models. Selection of best regression equation and examination of residuals for homoscedasticity and other diagnostic.  Use of statistical software. PREREQUISTE(S): MAT 353 and either MAT 262 or MAT 220, or instructor's consent.

Inference concerning location and scale parameters, goodness-of-fit tests, association analysis, and tests of randomness using distribution-free procedures. PREREQUISTE(S): MAT 353; or either 348, 323, BMS 142.

Development of the Box-Jenkins methodology for the identification, estimation, and fitting of ARIMA, and transfer-function stochastic models for the purpose of analyzing and forecasting stationary, nonstationary, and seasonal time series data. The course emphasizes practical time-series data analysis using computer packages and includes applications to economic, business, and industrial forecasting.  PREREQUISTE(S): MAT 353; or either 323, 348, BMS 142.

Techniques of computer simulation of the classical univariate and multivariate probability distribution models, and such random processes as random walk, Markov chains, and queues.  PREREQUISTE(S): MAT 353.

The Theory of Interest: Theory and applications of compound interest to annuities, amortization schedules, sinking funds, bonds, and yield rates.  PREREQUISTE(S): MAT 152 or 162.

Basic Contingencies: The theory and applications of contingency mathematics in life and health insurance, annuities, and pensions from both a probabilistic and a deterministic viewpoint. Topics include survival distribution and life tables, life insurance, and life annuities.  PREREQUISTE(S): MAT 361, and either 351 or 348.

Advanced Contingencies:  A continuation of Mathematics 362. Topics include net premiums, net premiums reserves, multiple life functions, multiple decrement models, and valuation theory for pension plans.  PREREQUISTE(S): MAT 362.

Introduction to risk theory and applications. Economics of insurance, individual risk models for short term and single term, collective risk models over an extended period, and applications.  PREREQUISTE(S): MAT 353

Mathematical methods for population analysis and survival models.  PREREQUISTE(S): MAT 353.

Introduction to demography; mortality table construction and methods of population and demographic analysis. PREREQUISTE(S): MAT 353 or instructor's consent.

Credibility Theory (Cross-Listed As MAT 467).  Credibility theory and loss distributions with applications to casulty insurance classification and rate making. PREREQUISTE(S): MAT 362

This course will be required of students in the Financial Mathematics concentration. The main topics will be stochastic calculus and partial differential equations leading up to a derivation of the Black-Scholes option pricing model and its variants, along with discrete methods. This course should also be of interest to students of applied mathematics and physics. There will be opportunity to analyze real option data in conjunction with theory. Possible additional topics would include numerical methods, dividends, options on futures and exotic options.     Prerequisite(s): MAT 338, 355 and FIN 320 or permission of instructor.

Vector spaces, basis and dimension; matrix representation of linear transformations and change of basis; diagonalization of linear operators; inner product spaces; diagonalization of symmetric linear operators, principal-axis theorem, and applications.  PREREQUISTE(S): MAT 262 and either 141 or 215.

Topics in axiomatic set theory, formal logic, and computability theory.  PREREQUISTE(S): MAT 215 or 141.

The course covers the basic principles of discrete and continuous Fourier analysis and some of its applications currently used in scientific modeling. Students will use the computer to implement the computational algorithms developed in the course. Some of the topics covered will include Fourier transforms and their application to signal and image processing, discrete Fourier series, the fast Fourier transform algorithm and applications to digital filtering, and the Radon transforms and its applications to tomography. PREREQUISTE(S): MAT 262 or equivalent.

Modeling of real world problems using mathematical methods. Includes a theory of modeling and a study of specific models, selected from deterministic, stochastic, continuous, and discrete models.  PREREQUISTE(S): MAT 220 or 262, and 348 or 351.

Use of a digital computer for numerical computation. Error analysis, Gaussian elimination and Gauss-Seidel method, solution of non-linear equations, function evaluation, cubic splines, approximation of integrals and derivatives, Monte Carlo methods.  PREREQUISTE(S): MAT 262 or MAT 220; and either 149, 152, 162, or 172; and a programming course

Theory and algorithms for efficient computation, including the Fast Fourier transform, numerical solution of non-linear systems of equations. Minimization of functions of several variables. Sparse systems of equations and corresponding eigenvalue problems.  PREREQUISTE(S): MAT 385.

The Linear Programming problem and its dual; the simplex method; transportation and warehouse problems; computer algorithms and applications to various fields.  PREREQUISTE(S):MAT 262 or 220, and any introductory programming course.

Integer programming; non-linear programming; dynamic programming; queuing theory; game theory.  PREREQUISTE(S): MAT 387 or instructor's consent.

Advanced Topics.  PREREQUISTE(S): MAT 388 or instructor's consent

By arrangement with sponsoring faculty, foreign and domestic tours or residence programs may be combined with lectures, readings, and research assignments. Variable credit.

Consult course schedule for current offerings. Course may be repeated for credit when title and content change. Prerequisite(s): instructor's consent.

Introduction to current theories and practices in college mathematics instruction; helps undergraduate mathematics majors develop a deeper understanding of fundamental mathematical concepts and an awareness of how people learn mathematical ideas, and prepares them to work as consultants in mathematics instruction.  Mathematical tutoring practicum is required. Four credit hour course offered over a two quarter span during the autumn and winter quarters only.  PREREQUISTE(S):Instructor's consent.  See instructor for further information.  This course maybe used to satisfy the junior experiential learning requirement, but it does not count toward mathematics major or minor credit.

Topics vary from year to year.  This course does not count toward the mathematical major or minor credit.

Variable credit.  PREREQUISTE(S):Consent of chair.

Applied Abstract Algebra I

Applied Abstract Algebra II  PREREQUISTE(S): MAT 400.

Parametric and non-parametric statistical inferential methods for the univariate and bivariate situations using SAS.  Specific topics include classical and exploratory graphical & numerical methods of data descriptions; inference about means, medians, and associations including analysis of variance and linear regression.  Data analytic projects are an integral part of the course.  PREREQUISITE(S): One statistic course or consent of instructor.

A continuation of MAT 441. Repeated measures design, association, analysis of covariance, and multivariate relationships.  Diagnostics and model building.  Methods of categorical data analysis.  Logistical regression and log-linear models.  Data analytical projects using SAS are an integral part of the course.  PREREQUISITE(S): MAT 441

A continuation of MAT 442.  The course material generalizes univariate methods of inference to multivariate situations using SAS.  Specific topics include canonical correlation, discriminate analysis, principal component analysis, factor analysis, and multivariate analysis of variance.  Emphasis in the curse is on data analytic projects.  PREREQUISITE(S): MAT 442

The SAS programming language. Data exploration, description and presentation. Inference methods for continuous and categorical data. Analysis of variance models and regression procedures. PREREQUISTE(S): MAT 351 or 451or instructor's consent.

The course covers elements of probability theory; distributions of random variables and linear functions of random variables; moment generating functions; and discrete and continuous probability models.  COREQUISTE(S): MAT 260

A continuation of MAT 451.  More continuous probability model.  Laws of large numbers and the central limit theorem.  Sampling distributions of certain statistics.  An introduction to the theory of estimation and principals of hypothesis testing.  PREREQUISITE(S): MAT 451.

A continuation of MAT 452. More on hypothesis testing, most powerful, uniformly most powerful, and likelihood ratio tests.  Introduction to the analysis of variance; linear regression; categorical data analysis, and nonparametric methods of inference.  PREREQUISITE(S): MAT 452

The multivariate normal distribution. The general linear model. Multivariate regression and analysis of variance; discriminant analysis; principal component and factor analysis; applications and use of statistical software. PREREQUISTE(S): MAT 453.

Discrete Markov chains and random walks, birth and death processes, Poisson process, queuing systems, and renewal processes. PREREQUISTE(S): MAT 453.

Simple linear, multiple, polynomial and general linear regression models. Selection of best regression equation and examination of residuals for homoscedasticity and other diagnostics. Use of statistical software.

Inference concerning location and scale parameters, goodness-of-fit tests, association analysis, and tests of randomness using distribution-free procedures. PREREQUISTE(S): MAT 453 or consent of the instructor.

History; Deming guide to quality; graphical techniques of process control; Schewhart's control charts for means, ranges, standard deviations, individual measurements, and attributes; process capabilities and statistical tolerance; cumulative-sum charts. product liability; acceptance sampling; product and process design; applications and case studies. PREREQUISTE(S): MAT 348 or 451.

Techniques of computer simulation of the classical univariate and multivariate probability models, and such random processes as random walks, Markov chains, and queues. PREREQUISTE(S): MAT 453

One of the following topics: Clinical trials; Reliability and life testing; Categorical data analysis; Meta analysis; Survival Models. PREREQUISTE(S):consent of instructor.

Theory of Interest:  Theory and application of compound interest to annuities, amortization schedules, sinking funds, bonds, and yield rates. PREREQUISTE(S):MAT 152 or MAT 162  or equivalent.

Basic Contingencies: The theory and applications of contingency mathematics in life and health insurance annuities and pensions, from both a probabilistic and a deterministic viewpoint. Topics include survival distribution and life tables, life insurance and life annuities. PREREQUISTE(S): MAT 461.

Advanced Contingencies: A continuation of MAT 462. Topics include net premiums, net premium reserves, multiple life functions, multiple decrement models, and valuation theory for pension plans. PREREQUISTE(S): MAT 462.

Introduction to risk theory and applications. Economics of insurance, individual risk models for short-term and single-term, collective risk models over an extended period, and applications. PREREQUISTE(S): MAT 453.

(Cross-listed as MAT 365)  Mathematical methods for population analysis and survival models.  PREREQUISTE(S): MAT 453.

Introduction to demography, mortauty table construction and methods of population and demographic analysis.  PREREQUISITE(S): MAT 453

Credibility theory and loss distributions with applications to casualty insurance classification and ratemaking. PREREQUISTE(S): MAT 462.

This course will be required of students in the Financial Mathematics concentration. The main topics will be stochastic calculus and partial differential equations leading up to a derivation of the Black-Scholes option pricing model and its variants, along with discrete methods. This course should also be of interest to students of applied mathematics and physics. There will be opportunity to analyze real option data in conjunction with theory. Possible additional topics would include numerical methods, dividends, options on futures and exotic options.     Prerequisite(s): MAT 338, 355 & FIN 320 or permission of instructor.

Vector spaces, basis and dimension; matrix representation of linear transformations and change of basis; diagonalization of linear operators; inner product spaces; diagonalization of symmetric linear operators, principal-axis theorem, and applications.  PREREQUISTE(S): MAT 262 and either 141 or 215.

The course covers the basic principles of discrete and continuous Fourier analysis and some of its applications currently used in scientific modeling. Students will use the computer to implement the computational algorithms developed in the course. Some of the topics covered will include Fourier transforms and their application to signal and image processing, discrete Fourier series, the fast Fourier transform algorithm and applications to digital filtering, and the Radon transforms and its applications to tomography. PREREQUISTE(S): MAT 262 or equivalent.

Modeling of real world problems using mathematical methods. Includes a theory of modeling and a study of specific models, selected from deterministic stochastic, continuous and discrete models. PREREQUISTE(S): MAT 220 or 262 and MAT 451 or 348.

Use of a digital computer for numerical computation. Error analysis, Gaussian elimination and Gauss-Seidel method, solutions of linear and nonlinear equations, function evaluation, cubic splines, approximation of integrals and derivatives, Monte Carlo methods. PREREQUISTE(S): MAT 262 or MAT 220 or equivalent and a programming course.

Theory and algorithms for efficient computation including the Fast Fourier Transform. Numerical solution of nonlinear systems of equations. Minimization of functions of several variables. Sparse systems of equations and eigenvalue problems. PREREQUISTE(S): MAT 485

The linear programming problem and its dual; the simplex method; transportation and warehouse problems; computer algorithms and applications to various fields. PREREQUISTE(S): MAT 220 or MAT 262 or equivalent.

Integer programming; nonlinear programming; dynamic programming. PREREQUISTE(S): MAT 487 or by consent of instructor.

Discrete and continuous-time Markov chain models, Queuing systems, and topics from renewal and reliability theory. PREREQUISTE(S): MAT 453.

Directed and undirected graphs. Bipartite graphs. Hamiltonian cycles and Euler tours. Flows in capacity-constrained networks.

Optimization of sequential decision processes. Markov decision models. Contraction mapping methods. Applications drawn from inventory theory and production control.

The minimax theorem for two-person, zero-sum games. Two-person general-sum games and noncooperative person games; Nash equilibrium.

Development of the Box-Jenkins methodology for the identification, estimation and fitting of ARIMA, and transfer-function stochastic models for the purpose of analyzing and forecasting stationary, non-stationary, and seasonal time series data. The course emphasizes practical  time series data analysis, using computer packages and includes applications to economic, business and industrial forecasting. PREREQUISTE(S): MAT 453 or MAT 348.

Simple random, stratified, systematic and cluster sampling. Multistage and area sampling. Random-response and capture-release models. PREREQUISTE(S): MAT 453 or 348.

Single-factor fixed, random and mixed designs with and without restrictions on randomizations, including randomized block designs, Latin & Graeco-Latin squares.  Factorial and fractional factorial experiments.  Nested and split-plot designs.  Confounding and response surface methodology.  PREREQUISTE(S): MAT 453 or 348.

Offered by arrangement. Approval by department chair required.

Mathematics Software For Teachers

Non-credit. Required of all students who are not registered for regular courses but who occasionally utilize University facilities during completion of course requirements and/or research. $40.00 per quarter.

Introduction to various mathematical software packages for the investigation of significant mathematical ideas. Emphasis will be on the use of software in the high school classroom for the enhancement of students' discovery and understanding of fundamental mathematical concepts.

Logo For Mathematics Teachers

Issues underlying the organization of mathematics curricula. Analysis of existing and proposed patterns of organization. Results of recent research in mathematics education regarding selecting and ordering content.

Theories, methods, materials and techniques for teaching and learning mathematics in secondary, middle, and upper-elementary schools.

Real numbers, exponentials and logarithms trigonometric functions, limits, the derivative and its applications.  Introduction to graphing calculators and some applications to classroom teaching.

Concave and convex functions, optimization, the integral and its applications.  Study of some numerical algorithms and implementation using graphing calculators PREREQUISTE(S): MAT 610.

Methods of integration, first and second order differential equations and Taylor series.  Applications to numerical analysis and approximation with graphing calculators. PREREQUISTE(S): MAT 611.

Axiom systems, types of reasoning used in proofs, Euclidean geometry results with concentration on triangles and circles, introduction to non-Euclidean geometry, and introduction to geometry classroom software.

Explorations In Turtle Geometry  (prereq.: 620) (corequisite: 611)

Geometry, Number Patterns, And The NCTM  Standards

Classical problems and techniques in number theory, algebra and geometry from a historical point of view. Stress on both historical aspects of mathematics and on solutions of concrete problems.

Continuation of MAT 630. Topics include the development of calculus, probability theory, number theory, non-Euclidean geometry, and set theory. PREREQUISTE(S): MAT 630.

Functions of several variables, vectors, dot products and cross products, partial differentiation, directional derivatives,optimization, Lagrange multipliers, multiple integrals, polar spherical coordinates. Use of graphing calculators and computers to illustrate concepts.

Combinatorics, sets, probability, random variables, distribution and density functions, standard probability laws, jointly distributed random variables. Use of computers to illustrate distributions. PREREQUISTE(S): MAT 611.

Central limit theorem, point and interval estimation of parameters, hypothesis testing, least squares and regression. PREREQUISTE(S): MAT 650.

Logic and proof,  number theory, sequences and mathematical induction, sets and functions, cardinality recursion, and introduction to combinatorics.

Number systems, polynomial rings, fields, vector spaces, and groups. This course provides the theoretical foundation for many topics covered in high school mathematics courses. PREREQUISTE(S):MAT 612 and MAT 660 or consent of program director.

Completeness properties of the real number line, limit theorems, the intermediate value theorem, the existence of the definite integral, differential equations, and slope fields. Students will review problems from recent AP Calculus examinations and each topic will be linked to specific problems on the AP exams.

Introduction to current theories and practices in college mathematics instruction; designed to prepare students to work as consultants in mathematics instruction by helping them develop a deeper understanding of fundamental mathematical concepts and an awareness of how people learn mathematical ideas.  Mathematical tutoring practicum is required.  Four-credit hour course offered over a two quarter span during the autumn and winter quarters only. PREREQUISTE(S):Permission of instructor.  See instructo rfo rfurther information.

Diverse topics in mathematical modeling or mathematical appreciation germane to the secondary school classroom. PREREQUISTE(S):consent of instructor.