# MATHEMATICS

## MATH-096 Selected Topics: Non-recurring (0) Course Level: Undergraduate/Graduate

Selected Topics: Non-Recurring (0) Topics vary by section. Repeatable for credit with different topic.

## MATH-099 Course Level: Graduate

## MATH-150 Finite Mathematics (3) Course Level: Undergraduate

Finite Mathematics (3) Review of algebra, sets, linear equations and inequalities, nonlinear inequalities, interest problems, systems of linear equations, functions and graphs, and elementary data analysis. Usually Offered: fall and spring. Restriction: Registration not allowed in both MATH-150, and MATH-151, MATH-154, or MATH-155. Note: Registration eligibility determined by appropriate score on the Mathematics Placement test. For students who need extra work on mathematical skills. No credit toward mathematics major. Students may not receive credit toward a degree for both MATH-150, and MATH-151, MATH-154, or MATH-155.

## MATH-151 Finite Mathematics (3) Course Level: Undergraduate

Finite Mathematics (3) Review of algebra, sets, linear equations and inequalities, nonlinear inequalities, interest problems, systems of linear equations, functions and graphs, and elementary data analysis. Usually Offered: fall, spring, and summer. Restriction: Registration not allowed in both MATH-151, and MATH-150, MATH-154, or MATH-155. Note: Registration eligibility determined by appropriate score on the Mathematics Placement test. No credit toward mathematics major. Students may not receive credit toward a degree for both MATH-151, and MATH-150, MATH-154, or MATH-155.

## MATH-154 Great Ideas in Mathematics (4) Course Level: Undergraduate

Great Ideas in Mathematics (4) This course explores a sample of beautiful branches of modern mathematics, concentrating on conceptual underpinnings rather than technical aspects. Includes study of infinity, number theory, fractals, and modern geometry, among other mathematical ideas. The course focuses on verbal and written communication skills and problem solving. Restriction: Registration not allowed in both MATH-154, and MATH-150, MATH-151, or MATH-155. Note: Registration eligibility determined by appropriate score on the Mathematics Placement test. No credit toward mathematics major. Students may not receive credit toward a degree for both MATH-154, and MATH-150, MATH-151, or MATH-155.

## MATH-155 Elementary Mathematical Models (3) Course Level: Undergraduate

Elementary Mathematical Models (3) Study of mathematical subjects including linear, quadratic, polynomial, rational, exponential, and logarithmic functions, in the context of difference equations models. Emphasizes concepts and applications using numerical, graphical, and theoretical methods. Also includes an introduction to the mathematical subject of chaos. Usually Offered: fall and spring. Restriction: Registration not allowed in both MATH-155, and MATH-150, MATH-151, or MATH-154. Note: Registration eligibility determined by appropriate score on the Mathematics Placement test. No credit toward mathematics major. Students may not receive credit toward a degree for both MATH-155, and MATH-150, MATH-151, or MATH-154.

## MATH-160 Applied Precalculus (3) Course Level: Undergraduate

Applied Precalculus (3) Fundamentals of algebraic, exponential, and logarithmic functions with emphasis on applications to problems in business and economics and the natural sciences. Usually Offered: fall and spring. Restriction: Registration not allowed in both MATH-160 and MATH-170. Note: Registration eligibility determined by appropriate score on the Mathematics Placement test. Intended primarily for students planning to take MATH-211. No credit toward mathematics major. Students may not receive credit toward a degree for both MATH-160 and MATH-170.

## MATH-170 Precalculus Mathematics (3) Course Level: Undergraduate

Precalculus Mathematics (3) Fundamentals of algebraic, logarithmic, exponential, and trigonometric functions. Usually Offered: fall and spring. Restriction: Registration not allowed in both MATH-170 and MATH-160. Note: Registration eligibility determined by appropriate score on the Mathematics Placement test. Intended primarily for students planning to take MATH-221. Students may not receive credit toward a degree for both MATH-170 and MATH-160.

## MATH-196 Selected Topics: Non-recurring (1-6) Course Level: Undergraduate

Selected Topics: Non-Recurring (1-6) Topics vary by section. Repeatable for credit with different topic.

## MATH-211 Applied Calculus I (4) Course Level: Undergraduate

Applied Calculus I (4) Functions, differentiation, and integration. Applications to several areas, especially business. Usually Offered: fall, spring, and summer. Prerequisite: MATH-160 or MATH-170. Restriction: Registration not allowed in both MATH-211 and MATH-221. Note: Registration eligibility may be determined by appropriate score on the Mathematics Placement test. Credit toward a major in the Department of Mathematics and Statistics requires departmental approval. Students may not receive credit toward a degree for both MATH-211 and MATH-221.

## MATH-220 Bridge from Applied Calculus I to Calculus II (1) Course Level: Undergraduate

Bridge from Applied Calculus I to Calculus II (1) This course prepares students who have taken MATH-211 Applied Calculus I to continue on to MATH-222 Calculus II. Material covered includes the study of trigonometric functions, limits and continuity, and the differentiation and integration of a variety of functions, with a focus on mathematical rigor and algebraic proficiency. Grading: Pass/Fail only. Prerequisite: MATH-211 with a grade of B or better.

## MATH-221 Calculus I (4) Course Level: Undergraduate

Calculus I (4) Real numbers; coordinate systems; functions; limits and continuity; differentiation and applications; trigonometric functions; indefinite and definite integration and applications; fundamental theorem of integral calculus. Usually Offered: fall, spring, and summer. Prerequisite: MATH-170. Restriction: Registration not allowed in both MATH-221 and MATH-211. Note: Registration eligibility may be determined by appropriate score on the Mathematics Placement test. Students may not receive credit toward a degree for both MATH-221 and MATH-211.

## MATH-222 Calculus II (4) Course Level: Undergraduate

Calculus II (4) Techniques of integration, calculus of exponential and logarithmic functions, infinite series, power series representations, and analytic geometry. Usually Offered: fall and spring. Prerequisite: MATH-211 or MATH-221. Note: Registration eligibility may be determined by appropriate score on the Mathematics Placement test.

## MATH-294 Community Service-Learning Project (1) Course Level: Undergraduate

Community Service-Learning Project (1) Grading: Pass/Fail only. Permission: instructor and Center for Community Engagement & Service.

## MATH-296 Selected Topics: Non-recurring (1-6) Course Level: Undergraduate

Selected Topics: Non-Recurring (1-6) Topics vary by section. Repeatable for credit with different topic.

## MATH-310 Linear Algebra (3) Course Level: Undergraduate

Linear Algebra (3) Vector spaces, systems of linear equations, solutions by matrices, determinants, linear transformations, and algebraic forms. Usually Offered: fall and spring. Prerequisite/Concurrent: MATH-222.

## MATH-313 Calculus III (4) Course Level: Undergraduate

Calculus III (4) Vectors, functions of several variables, partial differentiation, and multiple integrals. Usually Offered: fall and spring. Prerequisite: MATH-222.

## MATH-321 Differential Equations (3) Course Level: Undergraduate

Differential Equations (3) First order equations, linear equations of higher order, solutions in series, Laplace transforms, numerical methods, and applications to mechanics, electrical circuits, and biology. Usually offered every fall. Prerequisite/Concurrent: MATH-310 and MATH-313.

## MATH-345 Introduction to Game Theory (3) Course Level: Undergraduate

Introduction to Game Theory (3) This course explores applications such as auctions, firm competition, and voting with mathematical analysis. It includes Nash equilibrium, subgame perfect equilibrium, evolutionary stability, repeated games, signaling, mechanism design, uncertainty, and behavioral game theory. Crosslist: ECON-345. Usually Offered: fall. Prerequisite: ECON-200, and MATH-211 or MATH-221. Note: This course does not fulfill the University Mathematics Requirement.

## MATH-390 Independent Reading Course in Mathematics (1-6) Course Level: Undergraduate

Independent Reading Course in Mathematics (1-6) Permission: instructor and department chair.

## MATH-396 Selected Topics: Non-recurring (1-6) Course Level: Undergraduate

Selected Topics: Non-Recurring (1-6) Topics vary by section. Repeatable for credit with different topic.

## MATH-401 Probability (3) Course Level: Undergraduate

Probability (3) Algebra of sets; probability in discrete sample spaces; combinatorial analysis; random variables; binomial, Poisson, normal, and other distributions; and applications. Usually Offered: fall. Prerequisite: MATH-313 (may be taken concurrently).

## MATH-403 Foundations of Mathematics (3) Course Level: Undergraduate

Foundations of Mathematics (3) An introduction to the proof-based methodology of advanced mathematics courses, with emphasis on the fundamentals of logic and set theory (truth-tables and quantifiers, Boolean operations, functions, relations, and cardinality); elementary number theory (mathematical induction and modular arithmetic), and structural properties of the fields of real and complex numbers. Crosslist: MATH-603. Usually Offered: fall and spring. Prerequisite: MATH-222.

## MATH-404 Advanced Calculus of Several Variables (3) Course Level: Undergraduate

Advanced Calculus of Several Variables (3) Vector- functions of several variables, limits and continuity, differentials and tangent plane, implicit and inverse functions, line and surface integrals, gradient, divergent, curl, Stoke's and Green's theorems. Crosslist: MATH-604. Usually Offered: alternate springs (odd years). Prerequisite: MATH-310, MATH-313 and MATH-403

## MATH-405 Mathematical Logic (3) Course Level: Undergraduate

Mathematical Logic (3) The mathematical study of the scope and limits of deductive reasoning with special attention to propositional and first order logic, leading to results concerning completeness, compactness, and the existence of decision procedures for various logical systems, culminating in the incompleteness theorems of Godel. Crosslist: MATH-605. Usually Offered: alternate falls (even years). Prerequisite: MATH-403.

## MATH-410 Geometry (3) Course Level: Undergraduate

Geometry (3) Euclidean and non-Euclidean (spherical, elliptic, and hyperbolic) geometries from axiomatic and analytic points of view. Includes isometrics, transformation groups, symmetry groups, quadratic forms, projective geometry, as well as some historical background. Crosslist: MATH-610. Usually Offered: alternate falls (even years). Prerequisite: MATH-310.

## MATH-412 Introduction to Modern Algebra (3) Course Level: Undergraduate

Introduction to Modern Algebra (3) An introduction to the study of abstract algebraic structures. Includes groups, subgroup, quotient groups, homomorphisms, rings, ideals, fields, and group actions and Sylow theory. Crosslist: MATH-612. Usually Offered: fall. Prerequisite: MATH-403.

## MATH-413 Rings and Fields (3) Course Level: Undergraduate

Rings and Fields (3) An advanced study of rings and fields with a focus on polynomials and their roots. Includes ring theory, factorization, polynomials, field theory, ruler and compass constructions, Galois theory, and solvability of polynomials. Crosslist: MATH-613. Usually Offered: alternate springs (odd years). Prerequisite: MATH-412.

## MATH-415 Number Theory (3) Course Level: Undergraduate

Number Theory (3) Divisibility, fundamental theorem of arithmetic, congruences, arithmetic functions, Diophantine equations, quadratic residues, sums of squares, and partitions. Crosslist: MATH-615. Usually Offered: alternate falls. Prerequisite: MATH-403.

## MATH-420 Introduction to Analysis (3) Course Level: Undergraduate

Introduction to Analysis (3) This course develops the foundations of mathematical analysis by focusing on the real numbers as a complete ordered field, infinite sequences and series, limits and continuity, and key theorems of the differential and integral calculus. Crosslist: MATH-620. Usually Offered: fall. Prerequisite: MATH-403.

## MATH-421 Measure Theory and Integration (3) Course Level: Undergraduate

Measure Theory and Integration (3) This course presents the fundamental concepts and techniques of measure theory. It includes Borel sets, measures, measurable sets and functions, integrals as measures, Lp spaces, modes of convergence, and decomposition and generation of measures (including product measure). Crosslist: MATH-621. Usually Offered: alternate springs (even years). Prerequisite: MATH-403 and MATH-420.

## MATH-428 Competitive Mathematics (1) Course Level: Undergraduate

Competitive Mathematics (1) This course prepares students for competitions in mathematics, in particular the William Lowell Putnam Mathematics Competition. The class studies how to approach problems that may at first appear impossible. Students become familiar with techniques from diverse areas of mathematics to attack these problems. Usually Offered: fall. Prerequisite: MATH-222.

## MATH-440 Topology (3) Course Level: Undergraduate

Topology (3) Topological spaces, continuity, compactness, connectedness, and metric spaces. Crosslist: MATH-640. Usually Offered: alternate falls (odd years). Prerequisite: MATH-403.

## MATH-450 Complex Analysis (3) Course Level: Undergraduate

Complex Analysis (3) Complex functions, Cauchy's theorem and integral formulae, Taylor and Laurent series, residue calculus and contour integration, and conformal mapping. Crosslist: MATH-650. Usually Offered: spring. Prerequisite: MATH-313 and MATH-403.

## MATH-451 Partial Differential Equations (3) Course Level: Undergraduate

Partial Differential Equations (3) Fourier series, orthonormal systems, wave equation, vibrating strings and membranes, heat equation, Laplace's equation, harmonic and Green functions. Crosslist: MATH-651. Usually Offered: alternate springs (odd years). Prerequisite: MATH-321.

## MATH-460 Tools of Scientific Computing (3) Course Level: Undergraduate

Tools of Scientific Computing (3) Designed to teach scientific rigor in the use of computers and/or computational tools. Techniques from mathematics are introduced which lead to efficient algorithm design, algorithm analysis, data classification, data manipulation, and scientific computation. Includes data types, induction, recursion, sorting, searching, summation, optimization, asymptotic analysis, basic number theory, discrete probability, and parallel computing. Crosslist: CSC-460. Usually Offered: fall. Prerequisite: CSC-280, MATH-221, and MATH-222.

## MATH-465 Numerical Analysis: Basic Problems (3) Course Level: Undergraduate

Numerical Analysis: Basic Problems (3) Computer arithmetic and error analysis in computation, matrix decomposition methods in solving systems of linear equations and linear least squares problems, polynomial approximation and polynomial data fitting, iterative algorithms for solving nonlinear equations, and numerical differentiation and integration. Crosslist: MATH-665. Usually Offered: alternate falls (even years). Prerequisite: CSC-280, MATH-222, and MATH-310.

## MATH-470 History of Mathematics (3) Course Level: Undergraduate

History of Mathematics (3) This course surveys aspects of historical development of mathematics from ancient to modern times and examines the ideological, social, and cultural forces which shaped this development. By providing historical continuity, the course interrelates and unifies the major subject areas such as algebra, calculus and analysis, geometry, number theory, probability, set theory, and the foundation of mathematics. Crosslist: MATH-670. Usually Offered: alternate springs (even years). Prerequisite: MATH-222.

## MATH-480 Advanced Topics in Mathematics (3) Course Level: Undergraduate

Advanced Topics in Mathematics (3) Topics vary by section. Intensive courses in a specialized area of mathematics. Crosslist: MATH-680. Repeatable for credit with different topic.

## MATH-490 Independent Study Project in Mathematics (1-6) Course Level: Undergraduate

Independent Study Project in Mathematics (1-6) Permission: instructor and department chair.

## MATH-491 Internship (1-6) Course Level: Undergraduate

Internship (1-6) Permission: instructor and department chair.

## MATH-496 Selected Topics: Non-recurring (1-6) Course Level: Undergraduate

## MATH-565 Mathematical Applications of Interest and Derivatives (3) Course Level: Undergraduate/Graduate

Mathematical Applications of Interest and Derivatives (3) Mathematical study of finance, including theory of interest, arbitrage theorem, random walk models of prices, options, Black-Scholes formula and consequences. Crosslist: ECON-565. Usually Offered: alternate falls (even years). Grading: A-F only. Prerequisite: MATH-221, MATH-222, MATH-313, and STAT-202 or STAT-203.

## MATH-601 Harmonic Analysis (3) Course Level: Graduate

Harmonic Analysis (3) Harmonic analysis on the circle, the real line, and on groups. The main concepts are: periodic functions, Fourier series, Fourier transform and spherical harmonics. The course includes a brief account of the necessary ingredients from the theory of the Lebesgue integral. Usually Offered: alternate springs (even years). Prerequisite: MATH-603.

## MATH-603 Foundations of Mathematics (3) Course Level: Graduate

Foundations of Mathematics (3) An introduction to the proof-based methodology of advanced mathematics courses, with emphasis on the fundamentals of logic and set theory (truth-tables and quantifiers, Boolean operations, functions, relations, and cardinality); elementary number theory (mathematical induction and modular arithmetic), and structural properties of the fields of real and complex numbers. Crosslist: MATH-403. Usually Offered: fall and spring.

## MATH-604 Advanced Calculus of Several Variables (3) Course Level: Graduate

Advanced Calculus of Several Variables (3) Vector-functions of several variables, limits and continuity, differentials and tangent plane, implicit and inverse functions, line and surface integrals, gradient, divergent, curl, Stoke's and Green's theorems. Crosslist: MATH-404. Usually Offered: alternate springs (odd years). Prerequisite: MATH-603.

## MATH-605 Mathematical Logic (3) Course Level: Graduate

Mathematical Logic (3) The mathematical study of the scope and limits of deductive reasoning with special attention to propositional and first order logic, leading to results concerning completeness, compactness, and the existence of decision procedures for various logical systems, culminating in the incompleteness theorems of Godel. Crosslist: MATH-405. Usually Offered: alternate falls (even years). Prerequisite: MATH-603.

## MATH-610 Geometry (3) Course Level: Graduate

Geometry (3) Euclidean and non-Euclidean (spherical, elliptic and hyperbolic) geometries from axiomatic and analytic points of view. Includes isometrics, transformation groups, symmetry groups, quadratic forms, projective geometry, as well as some historical background. Crosslist: MATH-410. Usually Offered: alternate falls (even years).

## MATH-612 Introduction to Modern Algebra (3) Course Level: Graduate

Introduction to Modern Algebra (3) An introduction to the study of abstract algebraic structures. Includes groups, subgroup, quotient groups, homomorphisms, rings, ideals, fields, and group actions and Sylow theory. Crosslist: MATH-412. Usually Offered: fall. Prerequisite: MATH-603.

## MATH-613 Rings and Fields (3) Course Level: Graduate

Rings and Fields (3) An advanced study of rings and fields with a focus on polynomials and their roots. Includes ring theory, factorization, polynomials, field theory, ruler and compass constructions, Galois theory, and solvability of polynomials. Crosslist: MATH-413. Usually Offered: alternate springs (odd years). Prerequisite: MATH-612.

## MATH-615 Number Theory (3) Course Level: Graduate

Number Theory (3) Divisibility, fundamental theorem of arithmetic, congruences, arithmetic functions, Diophantine equations, quadratic residues, sums of squares, and partitions. Crosslist: MATH-415. Usually Offered: alternate falls. Prerequisite: MATH-603.

## MATH-616 Cryptography (3) Course Level: Graduate

Crytography (3) This course introduces fundamental mathematical ideas that are central to cryptography and related fields. The course covers how these ideas have been employed to create algorithms to encrypt information and analyzes the security and efficiency of these algorithms. The approach involves a blend of theoretical analysis and hands-on exploration and implementation. Usually Offered: fall. Grading: A-F only. Prerequisite: MATH-603.

## MATH-620 Introduction to Analysis (3) Course Level: Graduate

Introduction to Analysis (3) This course develops the foundations of mathematical analysis by focusing on the real numbers as a complete ordered field, infinite sequences and series, limits and continuity, and key theorems of the differential and integral calculus. Crosslist: MATH-420. Usually Offered: fall. Prerequisite: MATH-603.

## MATH-621 Measure Theory and Integration (3) Course Level: Graduate

Measure Theory and Integration (3) This course presents the fundamental concepts and techniques of measure theory. It includes Borel sets, measures, measurable sets and functions, integrals as measures, Lp spaces, modes of convergence, and decomposition and generation of measures (including product measure). Crosslist: MATH-421. Usually Offered: alternate springs (even years). Prerequisite: MATH-603 and MATH-620.

## MATH-631 Information Theory (3) Course Level: Graduate

Information Theory (3) The processing, storage, and communication of information, addressing two fundamental questions in the communication and storage of information, namely what are the limits on information compression (the entropy) and what is the best rate of information (the channel capacity). This course develops the mathematical foundations of information theory, including entropy and mutual information, partitioning and equipartitioning, data representation and compression, channel capacity, and dealing with distortion and noise. Usually Offered: fall. Grading: A-F only. Prerequisite: MATH-620.

## MATH-640 Topology (3) Course Level: Graduate

Topology (3) Topological spaces, continuity, compactness, connectedness, and metric spaces. Crosslist: MATH-440. Usually Offered: alternate falls (odd years). Prerequisite: MATH-603.

## MATH-650 Complex Analysis (3) Course Level: Graduate

Topological spaces, continuity, compactness, connectedness, and metric spaces. Crosslist: MATH-440. Usually Offered: alternate falls (odd years). Prerequisite: MATH-603.

## MATH-651 Partial Differential Equations (3) Course Level: Graduate

Partial Differential Equations (3) Fourier series, orthonormal systems, wave equation, vibrating strings and membranes, heat equation, Laplace's equation, harmonic and Green functions. Crosslist: MATH-451. Usually Offered: alternate springs (odd years).

## MATH-660 Tools of Scientific Computing (3) Course Level: Graduate

Tools of Scientific Computing (3) Designed to teach scientific rigor in the use of computers and/or computational tools. Techniques from mathematics are introduced which lead to efficient algorithm design, algorithm analysis, data classification, data manipulation, and scientific computation. Includes data types, induction, recursion, sorting, searching, summation, optimization, asymptotic analysis, basic number theory, discrete probability, and parallel computing. Crosslist: MATH-460 and CSC-460/CSC-660. Usually Offered: fall. Grading: A-F only. Permission: department.

## MATH-665 Numerical Analysis: Basic Problems (3) Course Level: Graduate

Numerical Analysis: Basic Problems (3) Computer arithmetic and error analysis in computation, matrix decomposition methods in solving systems of linear equations and linear least squares problems, polynomial approximation and polynomial data fitting, iterative algorithms for solving nonlinear equations, and numerical differentiation and integration. Crosslist: MATH-465. Usually Offered: alternate falls (even years).

## MATH-670 History of Mathematics (3) Course Level: Graduate

History of Mathematics (3) This course surveys aspects of historical development of mathematics from ancient to modern times and examines the ideological, social, and cultural forces which shaped this development. By providing historical continuity, the course interrelates and unifies the major subject areas such as algebra, calculus and analysis, geometry, number theory, probability, set theory, and the foundation of mathematics. Crosslist: MATH-470. Usually Offered: alternate springs (even years).

## MATH-680 Advanced Topics in Mathematics (3) Course Level: Graduate

Advanced Topics in Mathematics (3) Topics vary by section. Intensive courses in a specialized area of mathematics. Crosslist: MATH-480. Repeatable for credit with different topic.

## MATH-685 Practicum in Mathematics Education (3) Course Level: Graduate

Practicum in Mathematics Education (3) Seminar course in researching, implementing, and writing in publishable form an innovative teaching methodology, educational contribution, or internship in cooperating school system, college, or other organization involving teaching. Required of all students in the PhD program in mathematics education. Usually Offered: alternate springs. Repeatable for credit.

## MATH-690 Independent Study Project in Mathematics (1-6) Course Level: Graduate

Independent Study Project in Mathematics (1-6) Permission: instructor and department chair.

## MATH-691 Internship (1-6) Course Level: Graduate

Internship (1-6) Permission: instructor and department chair.

## MATH-696 Selected Topics: Non-recurring (1-6) Course Level: Graduate

## MATH-797 Master's Thesis Research (1-6) Course Level: Graduate

Master's Thesis Research (1-6) Usually Offered: fall and spring. Grading: SP/UP only.