### MATHEMATICS

**MATH-022**

**Basic Algebra (2)**

**Course Level:** Undergraduate

An introduction to algebra. Includes a review of integer and rational numbers; solving linear equations in one or two variables; word problems; polynomials and rational expressions; radicals; the quadratic formula; and some graphing techniques. Usually offered every term. Note: Intended for students with inadequate preparation for other courses in mathematics. No academic credit is received for this course, nor does it fulfill the mathematics requirement for any degree program. Credit equivalent is listed only for the purpose of determining full-time student status.

**MATH-096**

**Selected Topics: Non-recurring (0)**

**Course Level:** Undergraduate/Graduate

Topics vary by section, may be repeated with different topic.

**MATH-099**

**Course Level:** Graduate

**MATH-150**

**Finite Mathematics (3)**

**Course Level:** Undergraduate

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 every term. Prerequisite: three years of high school mathematics or equivalent. Note: For students who need extra work on mathematical skills. No credit toward mathematics major. Students may not receive credit for more than one course numbered MATH-15x.

**MATH-151**

**Finite Mathematics (3)**

**Course Level:** Undergraduate

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 every term. Prerequisite: three years of high school mathematics or equivalent. Note: No credit toward mathematics major. Students may not receive credit for more than one course numbered MATH-15x.

**MATH-154**

**Great Ideas in Mathematics (4)**

**Course Level:** Undergraduate

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. Prerequisite: three years of high school mathematics or equivalent. Note: No credit toward mathematics major. Students may not receive credit for more than one course numbered MATH-15x.

**MATH-155**

**Elementary Mathematical Models (3)**

**Course Level:** Undergraduate

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 every term. Prerequisite: three years of high school mathematics or equivalent. Note: No credit toward mathematics major. Students may not receive credit for more than one course numbered MATH-15x.

**MATH-160**

**Applied Precalculus (3)**

**Course Level:** Undergraduate

Fundamentals of algebraic, exponential, and logarithmic functions with emphasis on applications to problems in business and economics and the natural sciences. Usually offered every term. Prerequisite: three years of high school mathematics or equivalent. Note: Intended primarily for students planning to take MATH-211 Applied Calculus I. 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

Fundamentals of algebraic, logarithmic, exponential, and trigonometric functions. Usually offered every term. Prerequisite: three years of high school mathematics, or MATH-15x, or permission of department. Note: Intended primarily for students planning to take MATH-221 Calculus I. Students may not receive credit toward a degree for both MATH-160 and MATH-170.

**MATH-196**

**Selected Topics: Non-recurring (1-6)**

**Course Level:** Undergraduate

Topics vary by section, may be repeated for credit with different topic.

**MATH-211**

**Applied Calculus I (4)**

**Course Level:** Undergraduate

Functions, differentiation, and integration. Applications to several areas, especially business. Usually offered every term. Prerequisite: MATH-160 or MATH-170, or four years of high school mathematics. Note: 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

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

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 every term. Prerequisite: MATH-170 or four years of high school mathematics. Note: Students may not receive credit toward a degree for both MATH-221 and MATH-211.

**MATH-222**

**Calculus II (4)**

**Course Level:** Undergraduate

Techniques of integration, calculus of exponential and logarithmic functions, infinite series, power series representations, and analytic geometry. Usually offered every term. Prerequisite: MATH-211 or MATH-221, or permission of department.

**MATH-294**

**Community Service-Learning Project (1)**

**Course Level:** Undergraduate

Grading: Pass/Fail only. Permission: instructor and Center for Community Engagement & Service.

**MATH-296**

**Selected Topics: Non-recurring (1-6)**

**Course Level:** Undergraduate

Topics vary by section, may be repeated for credit with different topic.

**MATH-310**

**Linear Algebra (3)**

**Course Level:** Undergraduate

Vector spaces, systems of linear equations, solutions by matrices, determinants, linear transformations, and algebraic forms. Usually offered every spring and summer. Prerequisite: MATH-222 (may be taken concurrently).

**MATH-313**

**Calculus III (4)**

**Course Level:** Undergraduate

Vectors, functions of several variables, partial differentiation, and multiple integrals. Usually offered every term. Prerequisite: MATH-222.

**MATH-321**

**Differential Equations (3)**

**Course Level:** Undergraduate

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: MATH-310 and MATH-313, both of which may be taken concurrently.

**MATH-345**

**Introduction to Game Theory (3)**

**Course Level:** Undergraduate

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. Meets with ECON-345. Usually offered every 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

Permission: instructor and department chair.

**MATH-391**

**Internship (1-6)**

**Course Level:** Undergraduate

Prerequisite: permission of instructor and department chair.

**MATH-396**

**Selected Topics: Non-recurring (1-6)**

**Course Level:** Undergraduate

Topics vary by section, may be repeated for credit with different topic.

**MATH-401**

**Probability (3)**

**Course Level:** Undergraduate

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

**MATH-403**

**Foundations of Mathematics (3)**

**Course Level:** Undergraduate

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. Meets with MATH-603. Usually offered every term. Prerequisite: MATH-222.

**MATH-404**

**Advanced Calculus of Several Variables (3)**

**Course Level:** Undergraduate

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. Meets with MATH-604. Usually offered alternate springs (odd years). Prerequisite: MATH-310, MATH-313, and MATH-403.

**MATH-405**

**Mathematical Logic (3)**

**Course Level:** Undergraduate

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. Meets with MATH-605. Usually offered alternate falls (even years). Prerequisite: MATH-403.

**MATH-410**

**Geometry (3)**

**Course Level:** Undergraduate

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. Meets with MATH-610. Usually offered alternate falls (even years). Prerequisite: MATH-310.

**MATH-412**

**Introduction to Modern Algebra (3)**

**Course Level:** Undergraduate

An introduction to the study of abstract algebraic structures. Includes groups, subgroup, quotient groups, homomorphisms, rings, ideals, fields, and group actions and Sylow theory. Meets with MATH-612. Usually offered every fall. Prerequisite: MATH-403.

**MATH-413**

**Rings and Fields (3)**

**Course Level:** Undergraduate

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. Meets with MATH-613. Usually offered alternate springs (odd years). Prerequisite: MATH-412.

**MATH-415**

**Number Theory (3)**

**Course Level:** Undergraduate

Divisibility, fundamental theorem of arithmetic, congruences, arithmetic functions, Diophantine equations, quadratic residues, sums of squares, and partitions. Meets with MATH-615. Usually offered alternate falls. Prerequisite: MATH-403.

**MATH-420**

**Introduction to Analysis (3)**

**Course Level:** Undergraduate

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. Meets with MATH-620. Usually offered every fall. Prerequisite: MATH-403.

**MATH-421**

**Measure Theory and Integration (3)**

**Course Level:** Undergraduate

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). Meets with MATH-621. Usually offered alternate springs (even years). Prerequisite: MATH-403 and MATH-420.

**MATH-428**

**Competitive Mathematics (1)**

**Course Level:** Undergraduate

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 every fall. Prerequisite: MATH-222.

**MATH-440**

**Topology (3)**

**Course Level:** Undergraduate

Topological spaces, continuity, compactness, connectedness, and metric spaces. Meets with MATH-640. Usually offered alternate falls (odd years). Prerequisite: MATH-403.

**MATH-450**

**Complex Analysis (3)**

**Course Level:** Undergraduate

Complex functions, Cauchy's theorem and integral formulae, Taylor and Laurent series, residue calculus and contour integration, and conformal mapping. Meets with MATH-650. Usually offered every spring. Prerequisite: MATH-313 and MATH-403.

**MATH-451**

**Partial Differential Equations (3)**

**Course Level:** Undergraduate

Fourier series, orthonormal systems, wave equation, vibrating strings and membranes, heat equation, Laplace's equation, harmonic and Green functions. Meets with MATH-651. Usually offered alternate springs (odd years). Prerequisite: MATH-321.

**MATH-460**

**Tools of Scientific Computing (3)**

**Course Level:** Undergraduate

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. Meets with CSC-460. Usually offered every fall. Prerequisite: CSC-280, MATH-221, and MATH-222.

**MATH-465**

**Numerical Analysis: Basic Problems (3)**

**Course Level:** Undergraduate

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. Meets with 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

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. Meets with MATH-670. Usually offered alternate springs (even years). Prerequisite: MATH-222.

**MATH-480**

**Advanced Topics in Mathematics (3)**

**Course Level:** Undergraduate

Topics vary by section, may be repeated for credit with different topic. Intensive courses in a specialized area of mathematics. Meets with MATH-680.

**MATH-490**

**Independent Study Project in Mathematics (1-6)**

**Course Level:** Undergraduate

Permission: instructor and department chair.

**MATH-491**

**Internship (1-6)**

**Course Level:** Undergraduate

Permission: instructor and department chair.

**MATH-496**

**Selected Topics: Non-recurring (1-6)**

**Course Level:** Undergraduate

Topics vary by section, may be repeated for credit with different topic.

**MATH-565**

**Mathematical Applications of Interest and Derivatives (3)**

**Course Level:** Undergraduate/Graduate

Mathematical study of finance, including theory of interest, arbitrage theorem, random walk models of prices, options, Black-Scholes formula and consequences. Meets with ECON-565. Usually offered alternate falls (even numbered). 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 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. Prerequisite: MATH-310, MATH-313, and MATH-503, or permission of instructor.

**MATH-603**

**Foundations of Mathematics (3)**

**Course Level:** Graduate

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. Meets with MATH-403. Usually offered every term.

**MATH-604**

**Advanced Calculus of Several Variables (3)**

**Course Level:** Graduate

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. Meets with MATH-404. Usually offered alternate springs (odd years). Prerequisite: MATH-603.

**MATH-605**

**Mathematical Logic (3)**

**Course Level:** Graduate

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. Meets with MATH-405. Usually offered alternate falls (even years). Prerequisite: MATH-603.

**MATH-610**

**Geometry (3)**

**Course Level:** Graduate

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. Meets with MATH-410. Usually offered alternate falls (even years).

**MATH-612**

**Introduction to Modern Algebra (3)**

**Course Level:** Graduate

An introduction to the study of abstract algebraic structures. Includes groups, subgroup, quotient groups, homomorphisms, rings, ideals, fields, and group actions and Sylow theory. Meets with MATH-412. Usually offered every fall. Prerequisite: MATH-603.

**MATH-613**

**Rings and Fields (3)**

**Course Level:** Graduate

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. Meets with MATH-413. Usually offered alternate springs (odd years). Prerequisite: MATH-612.

**MATH-615**

**Number Theory (3)**

**Course Level:** Graduate

Divisibility, fundamental theorem of arithmetic, congruences, arithmetic functions, Diophantine equations, quadratic residues, sums of squares, and partitions. Meets with MATH-415. Usually offered alternate falls. Prerequisite: MATH-603.

**MATH-620**

**Introduction to Analysis (3)**

**Course Level:** Graduate

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. Meets with MATH-420. Usually offered every fall. Prerequisite: MATH-603.

**MATH-621**

**Measure Theory and Integration (3)**

**Course Level:** Graduate

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). Meets with MATH-421. Usually offered alternate springs (even years). Prerequisite: MATH-603 and MATH-620.

**MATH-640**

**Topology (3)**

**Course Level:** Graduate

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

**MATH-650**

**Complex Analysis (3)**

**Course Level:** Graduate

Complex functions, Cauchy's theorem and integral formulae, Taylor and Laurent series, residue calculus and contour integration, and conformal mapping. Meets with MATH-450. Usually offered every spring. Prerequisite: MATH-603.

**MATH-651**

**Partial Differential Equations (3)**

**Course Level:** Graduate

Fourier series, orthonormal systems, wave equation, vibrating strings and membranes, heat equation, Laplace's equation, harmonic and Green functions. Meets with MATH-451. Usually offered alternate springs (odd years).

**MATH-665**

**Numerical Analysis: Basic Problems (3)**

**Course Level:** Graduate

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. Meets with MATH-465. Usually offered alternate falls (even years).

**MATH-670**

**History of Mathematics (3)**

**Course Level:** Graduate

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. Meets with MATH-670. Usually offered alternate springs (even years).

**MATH-680**

**Advanced Topics in Mathematics (3)**

**Course Level:** Graduate

Topics vary by section, may be repeated for credit with different topic. Intensive courses in a specialized area of mathematics. Meets with MATH-480.

**MATH-685**

**Practicum in Mathematics Education (3)**

**Course Level:** Graduate

May be repeated for credit but not in the same term. 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 Ph.D. program in mathematics education. Usually offered alternate springs (odd years).

**MATH-690**

**Independent Study Project in Mathematics (1-6)**

**Course Level:** Graduate

Permission: instructor and department chair.

**MATH-691**

**Internship (1-6)**

**Course Level:** Graduate

Permission: instructor and department chair.

**MATH-696**

**Selected Topics: Non-recurring (1-6)**

**Course Level:** Graduate

Topics vary by section, may be repeated for credit with different topic.

**MATH-797**

**Master's Thesis Research (1-6)**

**Course Level:** Graduate

Usually offered every term. Grading: SP/UP only.

**MATH-COMP**

**Course Level:** Undergraduate