The following courses, numbered 0900-6999 are offered for undergraduate credit. Courses numbered 7000-9999, which are offered for graduate credit only, may be found in the graduate bulletin. Courses in the following list numbered 5000-6999 may be taken for graduate credit unless specifically restricted to undergraduate students by individual course limitations. 

NOTE: A minimum grade of 'C' ('S' in courses numbered under 1000) is required in every prerequisite course. 

'New' Four-Digit Course Numbers: Beginning with the Winter 1998 term the University will convert the course numbering system from three digits to four digits. In order to make the equivalencies between the two numbering systems clear to students who have experienced both systems, the conversion has been done by simply appending a zero to each three-digit course number (220 becomes 2200, 575 becomes 5750, etc.) --except in cases where the three-digit number ends in 90 to 99, the last digit of the three digit number is preserved as the last digit in the new four-digit number and a nine is inserted as the third digit of the new number. (Thus, in these special x90-x99 cases, 490 becomes 4990, 095 becomes 0995, and 093 becomes 0993, etc.)  

Courses Open Only to Undergraduates 

MAT 0991. Basic Concepts in Mathematics. Cr. 3 

Satisfies Math Competency

Prereq: ENG 1020; failure in mathematics proficiency test. Offered for S and U grades only. No degree credit. Introduction to the study of algebra, geometry, probability and statistics.  (T) 

MAT 0993 Beginning Algebra. Cr. 3 

Offered for S, M and U grades only. No degree credit. Review of arithmetic: fractions, decimals, percent, roots, absolute value; algebra: exponents, scientific notation, polynomials, factoring, rational expressions, solving and graphing linear equations, slope; geometry: basic objects and terminology. (T) 

MAT 0995 Intermediate Algebra. Cr. 3 

Prereq: one of the following within the previous two semesters:  satisfactory score on placement exam or MAT 0993.  Offered for S, M and U grades only. No degree credit. Exponents and radicals, solving polynomial and other types of equations and inequalities, graphs and systems of linear equations, introduction to functions, elementary geometry. (T) 

MAT 1050 Algebra with Trigonometry Cr. 5-7 

Prereq: one of the following within the previous two semesters:  satisfactory score on placement exam or MAT 0993.  When elected for 5 credits, only 2 credits apply toward degree.  When elected for 7 credits, only 3 credits apply toward degree.  Algebra:  properties of the Real Number System, solving equations and inequalities, lines, introduction to functions and graphing, exponents and logarithms.  Geometry and Trigonometry:  basic concepts, introduction to the trigonometric functions, solving triangles.  The 7 credit version (called MAT 1050 PREP) includes problem-solving and elements of Pre calculus and Calculus.  PREP is strongly recommended for Engineering, Math, Math Ed. and Science majors.  (T)

MAT 1800 Elementary Functions Cr.4 

Prereq: one of the following within the previous two semesters:  satisfactory score on placement exam or MAT 1050 or MAT 0995.  The properties and graphs of polynomials, rational functions, trigonometric functions, exponentials and logarithms. (T) 

MAT 1860. Discrete Mathematics for Computer Science I. Cr. 4 

Prereq: MAT 1800. Logic, sets, induction, relations, functions, sequences, matrices, combinatorics, applications to computer science. (T)

MAT 1870. Discrete Mathematics for Computer Science II. Cr. 4 

Prereq: MAT l860 or consent of instructor. Analysis of algorithms, recurrence relations, combinatorics, graphs, Boolean algebra, application to computer science. (T) 

MAT 1990. Pre-calculus Workshop. Cr. 2 

Coreq: Designated section of MAT 1800. Offered for S and U grades only. Open only to students in Emerging Scholars Program. Students work cooperatively in groups to solve very difficult and challenging problems based on pre-calculus; both computational and theoretical mathematics. Learning through discovery rather than by lecture. (F,W) 

MAT 2010. Calculus I. Cr. 4 

Prereq: satisfactory score on qualifying exam or MAT 1800 within the previous two semesters. Concept and interpretation of the derivative and integral, differentiation of rational and transcendental functions; the definite integral; area under a curve; the indefinite integral. (T) 

MAT 2020. Calculus II. Cr. 4 

Prereq: MAT 2010. Review:  Definition of the definite integral and the Fundamental Theorem of Calculus;  techniques of integration: substitution, parts, use of tables; approximation integration;  improper integrals;  applications of integration: area, volume, arc length of curves given in polar coordinates and parametrically, and others selected from the Sciences and Social Sciences;  intro. to differential equations:  basic concepts, some solving techniques and applications;  approximating functions:  linear approximations and the differential, Newton's method, sequences and series, convergence tests, power series, Taylor series.   (T) 

MAT 2030. Calculus III. Cr. 4 

Prereq: MAT 2020. This is a course in multivariable Calculus with applications.  Vectors and vector functions in two and three dimensions;  functions of several variables;  differentiation:  partial derivatives, directional derivatives, the gradient;  integration: double and triple integrals, cylindrical and spherical coordinates;  vector calculus: vector fields, line integrals, Green's Theorem, curl and divergence, Stoke's Theorem. (T)

MAT 2110. Calculus Workshop I. Cr. 2 

Coreq: designated sections of MAT 2010. Offered for S and U grades only. Open only to students in Emerging Scholars Program. Students work cooperatively in groups to solve very difficult and challenging problems based on MAT 2010. Computational and theoretical mathematics, taught through discovery rather than by lecture. (F, W) 

MAT 2120. Calculus Workshop II. Cr. 2 

Coreq: designated sections of MAT 2020. Offered for S and U grades only. Open only to students in Emerging Scholars Program. Students work cooperatively in groups to solve very difficult and challenging problems based on MAT 2020. Computational and theoretical mathematics, taught through discovery rather than by lecture. (F, W) 

MAT 2150. Differential Equations and Matrix Algebra. Cr. 4

Prereq: MAT 2030 or equiv.  Differential equations and applications:  basic operations of matrices from linear algebra.  (T)

MAT 2210. (MAT 6150) Elementary Probability and Statistics. Cr. 4 

Prereq: MAT 2010. No credit after MAT 5700. Counting techniques, discrete sample spaces and probability, random variables, mean and variance, joint distributions, the binomial and normal distributions, the central limit theorem, estimation and hypothesis testing. (T)

MAT 2250. Elementary Linear Algebra. Cr. 3 

Prereq: MAT 2020. Topics include: systems of linear equations, matrices, vector spaces, inner products, linear transformations and eigenvalues. Applications presented. (T) 

MAT 2350. Elementary Differential Equations. Cr. 3 

Prereq: MAT 2030 or equiv. Topics include: first order equations, higher order linear equations, Laplace transforms, linear systems. Applications presented throughout the course. (T)

MAT 2860. (MAT 6130) Discrete Mathematics. Cr. 4 

Prereq: MAT 2020. No credit after MAT 1870. Foundations of mathematics: logic, sets, functions, sequences. Algorithms. The integers. Matrices. Mathematical reasoning: methods of proof, induction, recursive definitions. Combinatorics. Relations: recurrence relations, equivalence relations, orderings. Graph theory and trees. Boolean algebra. Applications to computer science. (Y) 

MAT 3310. Actuarial Mathematics. Cr. 1 

Prereq: MAT 2030 and 2250. Problem solving course based on material covered on first Actuarial Exam. Subjects include: differential and integral calculus, multivariate calculus, elementary linear algebra. (Y) 

MAT 4010. Introduction to Abstract Mathematics and Proof Writing. Cr. 3

Prereq:  MAT 2250 or 2860 or consent of instructor.   Introduction to logic (negation, conditional statements, quantifiers), sets, functions and equivalence relations.  Structure of standard proofs and proof writing in number theory, topology and algebra.  (F, W) 

MAT 4990. Directed Study: Honors Program. Cr. 1-4(Max. 8) 

Prereq: admission to Honors Program by Mathematics Honors Committee. (I) 

Courses Open to Undergraduates and Graduates 

MAT 5030. Statistical Computing and Data Analysis. Cr. 3

Prereq:  Mat 2210 or equiv., 2250 or equiv.  Computational aspect of statistics for advanced undergraduate and beginning graduate students.  Computation of various statistical quantities by use of known statistical packages such as SAS, SPSS or BMD and the interpretation of their output.  (B)

MAT 5070. Advanced Calculus. Cr.4 

Prereq: MAT 2030, and 2250 or 2350. The Real Numbers; limits; continuity; sequences and series of functions; uniform convergence; power series; Fourier series; basic properties and topology of Euclidean n-space; transformations, the Jacobian; implicit and inverse function theorems; improper integrals and functions defined by improper integrals; Lagrange multipliers. (T) 

MAT 5100. Numerical Methods. Cr.3 

Prereq: MAT 2030, 2250 and CSC 1020 or familiarity with a programming language. Topics include: numerical errors, solutions of nonlinear equations, interpolation, approximation, numerical integration and differentiation, and matrices and systems of linear equations. (Y) 

MAT 5220. Partial Differential Equations & Boundary Value Problems. Cr. 4

Prereq MAT 5070. Boundary value problems of mathematical physics; Sturm-Liouville problems; eigenvalues and eigenfunctions; Green's functions; variational principles; the Rayleigh-Ritz method. (B) 

MAT 5230. Complex Variables and Applications. Cr. 4 

Prereq: MAT 5070. No credit after MAT 6600. Cauchy-Riemann equations; elementary functions; mappings by elementary functions; the Cauchy integral formula; Morera's theorem; Taylor series; Laurent series; residues and poles; conformal mappings; the Schwarz-Christoffel transformations; potential theory; Fourier and Laplace transforms and applications in differential and integral equations. (B)

MAT 5280. Methods of Differential Equations. Cr. 3 

Prereq: MAT 2350. Linear nth order differential equations; linear systems of differential equations (constant and periodic coefficients); oscillation and comparison theorems for second order differential equations; boundary value problems, stability theory (Liapunov's direct method and frequency domain stability criteria); asymptotic solutions; autonomous non-linear systems; classification of singularities. (B) 

MAT 5350. (PHI 5350) Logical Systems I. Cr. 4 

Prereq: PHI 1850 or PHI 1860 or MAT 5600 or MAT 5420 or consent of instructor. Metaresults concerning formal systems of sentential and first-order logics; soundness, completeness; independence of axioms, introduction to recursive functions; formalization of elementary arithmetic; discussion of Godel's incompleteness theorem and Church's Theorem. (B) 

MAT 5390. (PHI 5390) Logical Systems II. Cr.4 

Prereq: PHI 5350 or MAT 5350 or consent of instructor. Detailed proofs of Godel's incompleteness results, Tarski's Theorem, and Church's Theorem; formal axiomatic treatment of set theory and selected applications. (B) 

MAT 5400. Elementary Theory of Numbers. Cr. 3 

Prereq: MAT 2030 and 2250. Unique factorization theorem; order of magnitude of arithmetic functions; congruences, quadratic residues, law of reciprocity; continued fractions; elements of geometry of numbers; second pearl of number theory. (Y) 

MAT 5410. Applied Linear Algebra. Cr. 4 

Prereq: MAT 2030 and 2250, or consent of instructor. Gaussian elimination, vector spaces, orthogonality, least squares approximation, Householder orthonormalization, definite and semidefinite matrices, Rayleigh's quotient. Applications such as differential equations, Markov processes, linear programming, networks, game theory. (B) 

MAT 5420. Algebra I. Cr. 4 

Prereq: MAT 2030 and 2250. Abstract concepts: sets, mappings, equivalence relations, induction, general methods of proof. Group theory: groups, subgroups, cyclic groups, direct products, cosets, Lagrange's Theorem, quotient groups, homomorphisms, permutation groups. Rings and fields (basic definitions) and vector spaces: basis, dimension, linear transformations. (T) 

MAT 5430. Algebra II. Cr. 4 

Prereq: MAT 5420. Group theory continued: Sylow Theorems, finite abelian groups. Ring Theory: rings, integral domains, fields of quotients, homomorphisms, ideals, quotient rings, P.I.D.s, U.F.D.s, polynomial rings. Advanced topics in linear algebra: canonical forms. Field theory: extensions, spitting fields, finite fields, geometric constructions. (T) 

MAT 5520. Introduction to Topology. Cr. 3 

Prereq: MAT 2030, and 2250 or 2350. No credit toward graduate degree in mathematics or statistics. An introduction to topology, mostly through an intuitive approach. Topics chosen from among: topological equivalence and topological properties, complexes, Euler characteristic, connectedness, compactness, continuity, Brower's Fixed Point Theorem. vector fields, Hairy Ball Theorem. n-dimensional spaces, classification of surfaces, cut and paste techniques, the Mobius band, orientability, the Fundamental group. (Y) 

MAT 5530. Elementary Differential Geometry and its Applications. Cr. 3 

Prereq: MAT 2030 and 2250. Introduction to the differential geometry of curves and surfaces in three-dimensional spaces. together with selected applications, such as computational geometry, mathematical elements of computer graphics, as chosen by instructor. (I) 

MAT 5600. Introduction to Analysis I. Cr. 4 

Prereq: MAT 5070 or consent of instructor. Completeness, convergence, compactness and continuity in the context of Euclidean spaces; applications to differential and integral calculus. (T) 

MAT 5610. Introduction to Analysis II. Cr. 3 

Prereq: MAT 5600. Point-wise and uniform convergence of sequences and series of functions; power series; introduction to analytic functions; Fourier series; possible additional topics. (T) 

MAT 5700. Introduction to Probability Theory. Cr. 4 

Prereq: MAT 2030, 2250 or 2350, Only two credits after MAT 2210 or MAT 6150. Probability spaces, combinatorial analysis; independence; discrete and continuous random variables; expectations; normal, Poisson and binomial distribution; joint, marginal and conditional distribution functions; law of large numbers; central limit theorems. (T) 

MAT 5710. Introduction to Stochastic Processes. Cr. 3 

Prereq: MAT 5700 or consent of instructor. Non-measure theoretic introduction to the theory of stochastic processes and its applications, with emphasis on Markov processes and stationary processes with both discrete and continuous parameters. (B) 

MAT 5770. Mathematical Models In Operations Research. Cr. 3 

Prereq: MAT 2030, 2250, and 2210 or 5700 or consent of instructor. Mathematical models (deterministic and/or, probabilistic) applied to dynamic programming; games; queues and inventories. (B) 

MAT 5800. Introduction to Mathematical Statistics. Cr. 4

Prereq:  MAT 5700.  A one semester course for senior undergraduate and master's degree students.  Introduction to basic mathematical theory of statistics.  (Y)

MAT 5830. Applied Time Series. Cr. 3 

Prereq: college courses in statistics and calculus, or consent of instructor. Time series models; statistical analysis in the time domain and examples; statistical analysis in the frequency domain and examples.  (B)

MAT 5870. Methods of Optimization Cr. 3 

Prereq: MAT 2350. Introduction to basic mathematical theory and computational methods of optimization. Optimality conditions in various optimization problems and numerical methods of optimization (Y) 

MAT 5890. Special Topics In Mathematics. Cr. 3-4 (Max. 12) 

Prereq: MAT 2030, and 2250 or 2350. Material currently of interest to students and faculty. Topics to be announced in Schedule of Classes. (I) 

MAT 5990. Directed Study. Cr. 1-4 (Max. 8) 

Prereq: written consent of adviser and chairperson (and of graduate officer for graduate students). Undergraduates who elect this course must be mathematics majors of honors caliber. Content will vary to satisfy needs of individual student. (T) 

MAT 5993.  Writing Intensive Course in Mathematics. Cr. 0 

Prereq: junior standing, satisfactory completion of English Proficiency Examination, consent of instructor, MAT 2030 and 2250; coreq: 5420.  Offered for S and U grades only. No degree credit. Required for all majors. Disciplinary writing assignments under the direction of a faculty member. Must be selected in conjunction with a course designated as a corequisite. See section listing in Schedule of Classes for corequisites available each term. Satisfies the University General Education Writing-Intensive Course in the Major requirement. (T) 

MAT 6130. Topics In Mathematics for High School Teachers I. (MAT 2860). Cr. 4 

Prereq: MAT 2020. No credit after MAT 1870. Foundations of mathematics: logic, sets, functions, sequences. Algorithms. The integers. Matrices. Mathematical reasoning: methods of proof, induction, recursive definitions. Combinatorics. Relations: recurrence relations, equivalence relations, orderings. Graph theory and trees. Boolean algebra. Applications to computer science. (Y) 

MAT 6140. Topics In Mathematics for High School Teachers II. Cr. 3 

Prereq: MAT 2030, and 2250 or 2350. Axiomatic geometry: logic, methods of proof, models; Hilbert's axioms; the Parallel Postulate; 'Neutral,' Euclidean and non-Euclidean geometries; Hyperbolic geometry; Poincare models. (Y) 

MAT 6150. Topics in Mathematics for High School Teachers III. (MAT 2210). Cr. 4 

Prereq: written consent of chairperson of mathematics education. No credit after MAT 5700. Counting techniques, discrete sample spaces and probability, random variables, mean and variance, joint distributions, the binomial and normal distributions, central limit theorem, estimation and hypothesis testing. (T) 

MAT 6400. Graph Theory. Cr. 4 

Prereq: MAT 5420 or consent of instructor. Basic concepts of graphs and directed graphs; trees; cycles and circuits; connectivity; traversibility; planarity; colorability. Further topics from among factorization, line-graph, coverings and independence, graphs and matrices, automorphism groups, enumeration, Ramsey theory, hypergraphs, packing theory, network flows. (B) 

MAT 6410. Combinatorics. Cr. 4 

Prereq: MAT 5420 or consent of instructor. Enumeration: the classical theory, principle of inclusion and exclusion, generating functions, the Moebius function; combinatorial designs including Latin squares, difference sets, projective geometries, Hadamard matrices, construction problems; transversal theory; Ramsey's theorem; coding theory, partial orders; lattices. (B) 

MAT 6500. Topology 1. Cr. 4 

Prereq: MAT 5610 or consent of instructor. Topological spaces and continuous functions; connectedness; compactness; product and quotient spaces; metric spaces; Urysohn's lemma; Tietze extension theorem; homotopy; covering spaces and path lifting; the fundamental group and examples; Brouwer fixed point theorem and applications. (Y) 

MAT 6600. Complex Analysis. Cr. 2 or 4 

Prereq: MAT 5610 or consent of instructor. Offered for two credits only if student has taken MAT 5230. Complex differentiation; elementary functions; Cauchy's integral theorem; power series; Laurent expansions; singularities; residue theorem; entire and meromorphic functions; Reimann mapping theorem. (Y) 

MAT 6830. Design of Experiments. Cr. 3 

Prereq: MAT 5820. Randomized blocks; Latin and Graeco-Latin squares; factorial designs; confounding; split plot; fractional replication; balanced incomplete blocks. (I)

MAT 6840.  Linear Statistical Models. Cr. 3

Prereq:  MAT 5820 or equiv.  Introduction to theory of linear statistical models; for advanced undergraduate or beginning graduate students.  (B)

Service Courses

MAT 1110. Mathematics for Elementary Teachers I. Cr. 3 

Prereq:  one of the following within the previous two semesters :  satisfactory score on the qualifying exam or MAT 1050 or MAT 0995. No degree credit in Colleges of Science and Liberal Arts . Open only to students in teacher preparation curricula. Whole numbers, integers, geometry. (T) 

MAT 1120. Mathematics for Elementary Teachers II. Cr. 3 

Prereq: MAT 1110. No degree credit in Colleges of Science and Liberal Arts. Open only to students in teacher preparation curricula. Rational numbers, geometry, probability, statistics, number theory. (T) 

MAT 1500. Finite Mathematics for the Social and Management Sciences. Cr. 3 

Prereq: one of the following within the previous two semesters:  satisfactory score on the placement exam or MAT 1050 or MAT 0995.   Only one degree credit after MAT 1800. Finite mathematical methods for model building in the social and management sciences. Polynomial, exponential, and logarithmic functions, matrices, and linear programming. (T) 

MAT 3430. Applied Differential and Integral Calculus. (E T 3430). Cr. 4 

Prereq: MAT 1800. No degree credit in Colleges of Science and Liberal Arts. Limits, derivatives, applications of derivatives, definite integrals and their applications, and trigonometric functions. (T)

MAT 3450. Applied Calculus and Differential Equations. (E T 3450). Cr. 4 

Prereq: MAT 3430. No degree credit in Colleges of Science and Liberal Arts. Continuation of MAT 3430, including logarithmic and exponential functions, first and second order ordinary differential equations, vectors, polar coordinates, Laplace transforms, Taylor series, and Fourier series. (T) 

MAT 5160. Mathematics for Elementary School Teachers I. (MAE 5050). Cr.3 

Prereq:  one of the following within previous two semesters:  satisfactory score on qualifying exam or MAT 1050 or MAT 0995.  No credit toward a major or minor for secondary mathematics teaching. Graduate credit for MAE 5050 only; undergraduate credit for MAT 5160 only. Sets and Venn diagrams; mathematical systems, including group, ring, and field properties; set of real numbers and its common subsets: their properties, algorithms, and applications; number theory, including fundamental theorem of arithmetic; ratio, proportion, and percents; introduction to the complex number system. (Y) 

MAT 5170. Mathematics for Elementary School Teachers II. (MAE 5060). Cr.3 

Prereq: MAT 5160. No credit toward a major or minor for secondary mathematics teaching. Graduate credit for MAE 5060 only; undergraduate credit for MAT 5170 only. Geometry, with emphasis on inductive investigations and conjecturing; measurements of two- and three-dimensional figures; introduction to probability and descriptive statistics; relations and functions; elements of algebra; analytic geometry of the line. (Y)

MAT 5180. Mathematics for Middle/Junior High School Teachers I. (MAE 5100). Cr. 3 

Prereq: MAT 5160 and 5170 or consent of instructor. No credit toward a major or minor for secondary mathematics teaching. Graduate credit for MAE 5100 only; undergraduate credit for MAT 5180 only. Development of Euclidean geometry as a mathematical system; related historical topics; introduction to other geometries; selected topics such as transformations and tessellations. (Y) 

MAT 5190. Mathematics for Middle/Junior High School Teachers II. (MAE 5110). Cr. 3 

Prereq: MAT 5180. No credit toward a major or minor for secondary mathematics teaching. Graduate credit for MAE 5110 only; undergraduate credit for MAT 5190 only. Trigonometry and analytical geometry.  (Y)

STA 1020. Elementary Statistics. (SOC 5280). Cr. 3 

Prereq: one and one-half years high school algebra. Not to be counted as a mathematics course by mathematics majors. Student computer account required. Descriptive statistics, correlation and regression, notions in probability, binomial and normal distributions, testing hypothesis.  (Y)

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