# Course Descriptions

**105 – Introduction to Finite Mathematics –** The course provides an introduction to several areas of finite mathematics which have numerous applications, particularly in the social sciences. Topics will include mathematics of finance, discrete probability, linear programming, matrices, and linear systems. Three hours.

**106 – Introduction to Optimization –** Optimization is the search for efficient solutions to real-world problems. For example, a designer might seek a lowest-cost construction, or a manufacturer might seek a maximum-profit production schedule. This course introduces the mathematics of optimization. Topics include linear programming and unconstrained nonlinear optimization. Numerical and symbolic methods are applied where appropriate. Three hours.

**107 – Introduction to Mathematical Modeling –** An introduction to techniques for constructing mathematical models of real world phenomena, primarily through the study of discrete dynamical systems. Topics include recurrence relations; stable and unstable equilibria; and systems of linked recurrences. Basic growth patterns will be examined, including linear, power, exponential, and periodic. Applications include financial mathematics, biological systems, and population dynamics. Satisfies CAR – Computing. Three hours.

**111 – Introduction to Statistics –** An introduction to statistical inference and sufficient probability theory for such an introduction. Topics include elementary data analysis, elementary probability, discrete and continuous random variables, distributions (including the normal distribution), correlation and regression, sampling distributions, point and interval estimation, confidence levels, and tests of significance. Students may not receive credit for successful completion of MATH 111 and MATH 113. They may receive a total of seven hours of credit for successful completion of a combination of MATH 111 and BIOL 350, or MATH 113 and BIOL 350. However, the two statistics courses may not be used together to fulfill the collegiate requirement in mathematics. Three hours.

**113 – Introduction to Statistics –** Computer intensive version of MATH 111. Students may not receive credit for successful completion of MATH 111 and MATH 113. They may receive a total of seven hours of credit for successful completion of a combination of MATH 111 and BIOL 350, or MATH 113 and BIOL 350. However, the two statistics courses may not be used together to fulfill the collegiate requirement in mathematics. Satisfies CAR – Computing. Three hours.

**120 – Introductory Logic –** This course serves as an overview of the basic elements of logic and a deeper treatment of logic as a deductive science. Students are expected to analyze statements and arguments in ordinary language and symbolic form, to translate statements and arguments from ordinary language into symbolic form, to use truth tables in the analysis of arguments and the classification of statements, and to use techniques of natural deduction to construct proofs of arguments in propositional and predicate logic. Three hours.

**125 – The Art of Mathematics –** From the geometry of perspective to the elaborate structure of some modern sculptures, mathematical knowledge is frequently used by artists to design their work. Some artists use mathematics as their primary inspiration, creating works that explore mathematical concepts. Mathematicians often use diagrams to illustrate theorems, and frequently talk about the intrinsic beauty of their work. There is a growing interest in using the arts to make mathematical ideas more accessible and compelling. In this course we will create two- and three-dimensional works that both use and illustrate mathematical principles. Mastery of the underlying mathematical concepts will be central to the course. Three hours.

**131 – Calculus I –** This is a course in differential calculus. Topics to be covered will include: functions; limits and continuity; the definition of the derivative; techniques of differentiation; and applications of the derivative. Note: A working knowledge of high school algebra, geometry, and trigonometry is required for this course. Credit will not be awarded for both 131 and 141. Four hours.

**132 – Calculus II –** This course is a continuation of MATH 131. Topics to be covered will include: the Fundamental Theorem of calculus; techniques of integration; applications of the definite integral; and sequences and series. Credit will not be awarded for both 132 and 142. Prerequisite: MATH 131 or 141 or permission of instructor. Four hours.

**141 – Calculus with Mathematica I –** This is a course in differential calculus. Topics to be covered will include: functions; limits and continuity; the definition of the derivative; techniques of differentiation; and applications of the derivative. Note: A working knowledge of high school algebra, geometry, and trigonometry is required for this course. Mathematica will be used as an aid in graphing and exploring functions, and as an aid in computation. Credit will not be awarded for both 131 and 141. Satisfies CAR – Computing. Four hours.

**142 – Calculus with Mathematica II –** This course is a continuation of MATH 141. Topics to be covered will include: the Fundamental Theorem of calculus; techniques of integration; applications of the definite integral; and sequences and series. Technology will be used to explain the definition of the definite integral, to obtain numerical approximations of definite integrals, to examine the graphs of functions, and to check computations of integrals and derivatives. Credit will not be awarded for both 132 and 142. Satisfies CAR – Computing. Prerequisite: MATH 131 or 141 or permission of instructor. Four hours.

**203 – Multivariable Calculus –** This course is a continuation of MATH 132/142. Topics to be covered will include: vectors; vector valued functions; functions of two or more variables; partial derivatives; multiple integrals; vector fields; and Green’s Theorem. We will use Mathematica as an aid in graphing and exploring mathematical problems. Prerequisite: MATH 132 or 142. Satisfies CAR – Computing. Four hours.

**213 – Elementary Linear Algebra –** An introduction to the algebra and geometry of three-dimensional Euclidean space and its extension to n-space. Topics include vector algebra and geometry; systems of linear equations; real vector spaces; matrix algebra; determinants; linear transformations; eigenvalues; and diagonalization. Emphasis will be placed on writing mathematical proofs. Prerequisite: MATH 203 or a minimum grade of C– in MATH 132 or 142. Three hours.

**215 – Mathematics Resources, Opportunities, and Careers Seminar –** This weekly seminar helps students become familiar with the scope of the mathematical sciences. The course is designed to help students plan their academic experience so they can successfully pursue the career of their choice after majoring or minoring in mathematics. Research and internship opportunities will be discussed, as will careers that demand mathematical skills. Standard modes of communicating mathematics, and other strategies for success in higher mathematics courses, will be included. Prerequisite: MATH 131 or 141. One hour.

**220 – Discrete Mathematics –** Boolean algebra and propositional logic with applications. Elements of the theory of directed and undirected graphs. Permutations, combinations, and related combinatorial concepts. The course provides mathematical topics of particular value to students in computer science. Prerequisite: MATH 132 or 142 or CSCI 112. Three hours.

** 270 – Traditional Japanese Mathematics – **This travel course will focus on the geometry that arose during Japan’s 18th century cultural blossoming, despite its self-imposed isolation from the scientific revolution in Europe. The course begins on campus with a study of the techniques, important scholars, and historical context of traditional Japanese mathematics. During the travel portion of the course, students will visit key historical sites in Japan, view mathematical artifacts, and absorb the cultural aesthetics that still seem intimately connected with this country’s traditional geometry. Prerequisites: MATH 132 or 142 and permission of instructor. Offered alternate years. Three hours.

**307 – Differential Equations: A Modeling Perspective –** An introduction to the theory and application of differential equations, including the development of mathematical models of scientific phenomena. Qualitative, numerical, and analytic tools will be used to analyze these models, and technology will also play a significant role. Topics include modeling via differential equations, analytic and numeric techniques, existence and uniqueness of solutions, equilibria, changing variables, systems of equations, phase planes, and qualitative analysis. Prerequisite: MATH 132 or 142. Three hours.

**317 – Number Theory –** An introduction to the theory of numbers. Topics covered will include mathematical induction, the division algorithm, and the fundamental theorem of arithmetic, the Euler phi-function, congruence, Diophantine equations, the Chinese Remainder Theorem, quadratic residues, the Law of Quadratic Reciprocity, and cryptography. Students are expected to learn definitions and theorems in order to solve problems and prove results. Prerequisite: MATH 220. Offered alternate years. Three hours.

**321 – Modern Algebra I –** A study of the basic properties of abstract algebraic structures, including groups, rings, and fields. The course attempts to develop the student’s ability to deal with abstract mathematical ideas and proofs, while providing widely used mathematical language and tools. Prerequisite: MATH 220. MATH 213 is recommended but not required. Three hours.

** 322 – Modern Algebra II – **A continuation of MATH 321. Topics include rings, integral domains, factorization of polynomials, vector spaces and fields. Prerequisite: MATH 321. Offered as needed. Three hours.

**330 – Graph Theory – **This course is an introduction to the theory of graphs. This mathematical theory deals with points and interconnecting lines, and has wide ranging applications to computer science, operations research, and chemistry, among many other disciplines. Course topics include degree sequences, trees, Eulerian and Hamiltonian graphs, matching, factoring, coloring, planar graphs, connectivity, Menger’s Theorem, and networks. Students are expected to prove theorems and understand applications of the material to practical problems. Prerequisite: MATH 220 or permission of the instructor. Three hours.

**350 – Game Theory –** This course is a mathematical introduction to the subject of game theory. Its prime objective is to equip the student with sufficient skills to solve applied mathematical problems, taken principally from the realm of economics. Topics covered will include Zermelo’s algorithm, lotteries, utility functions, bimatrix games, bargaining, cooperative and non-cooperative games, mixed strategies, zero-sum games, and Nash and subgame-perfect equilibriums. Students will be expected to use mathematical definitions, formulae, and techniques to solve game theoretic problems. Prerequisite: MATH 203 or a minimum grade of B- in MATH 132 or 142. Offered alternate years. Three hours.

**353 – Complex Analysis –** An introduction to the calculus of analytic functions. The principal topics are complex arithmetic, elementary functions of a complex variable, analyticity, contour integrals, Cauchy’s theorem and its applications, and power series. Prerequisite: MATH 203. Offered alternate years. Three hours.

**371 – Probability –** An introduction to combinatorial theory, sample spaces, random variables, and mathematical expectation and probability distributions including their properties for both the discrete and continuous cases. Prerequisite: MATH 203 or 220. Offered alternate years. Three hours.

**372 – Statistical Inference –** The theory and practice of statistical inference. Experimental and statistical design, point estimation, regression and correlation, confidence intervals, and significance tests. Mathematical foundations including the Central Limit Theorem. Prerequisite: MATH 203 (or concurrently). Offered alternate years. Three hours.

**381-382 – Special Topics in Mathematics –** Three hours each.

**391-392 – Independent Study –** An independent exploration of a specialized area in mathematics under the guidance of a member of the department. Prerequisites: permission of the instructor, a cumulative GPA of 3.25 or greater, and approval of the curriculum committee. Three hours each.

**415 – Mathematics Seminar –** This course serves to present mathematics and the mathematician in a variety of contexts. Students will read selections from current mathematical literature. Lectures given by students and guest speakers will present mathematical ideas and lead to discussions. Students will gain experience making presentations, expressing mathematical arguments in writing, and critiquing mathematical arguments presented by others. Prerequisites: MATH 220 and senior status. One hour.

**421 – Real Analysis I –** A first course in the theory of functions of real variables. Topics include axiomatic description of the real number system, topology of Euclidean and metric spaces, limits and continuity, and differentiation. Students are expected not only to learn the material presented but also to construct proofs independently. Prerequisite: MATH 220. Three hours.

**422 – Real Analysis II –** A continuation of MATH 421. Topics include sequences and series of functions. Riemann-Stieltjes and Lebesgue integration. Prerequisite: MATH 421. Offered as needed. Three hours.

**435 – Higher Geometry –** The axiomatic method will be used to develop a geometric system. Topics will be chosen from Euclidean geometry, plane hyperbolic geometry, and real projective geometry. This course is of particular value to students who anticipate entering secondary teaching. Prerequisite: MATH 203. Offered alternate years. Three hours.

**442 – Numerical Analysis –** The mathematical foundations of scientific computing. Numerical methods for the approximation of roots of equations, integrals, and solutions of differential equations. Also included are interpolation and error estimation. Prerequisite: MATH 213 or 220. Offered alternate years. Three hours.

**450 – Mathematics Internship -** Students in this course are placed in an appropriate organization (typically a commercial, industrial, government, nonprofit, or research facility) and follow an arranged set of readings relevant to their internship experience. Students will be expected to demonstrate (through a written report upon completion of the internship) an understanding of the mathematics used and of its utility in context. Application required; see Internship Program. Offered as needed. Three hours.

**451 – Topology –** An introduction to point-set topology. Topics will include topological spaces, metric spaces, continuous mappings, and homeomorphisms. Students are expected to learn basic definitions and theorems, and to construct proofs on their own. Prerequisite: MATH 220. Offered alternate years. Three hours.

**470 – History of Mathematics –** A study of the historical development of various branches of mathematics, from antiquity to the 20th century. Topics will include: mathematics in ancient Greece, Islamic mathematics, the development of symbolic algebra, the invention of calculus, and the liberation of algebra and geometry. Students are expected to construct cogent mathematical and historical arguments in essay form. Travel course to Britain. Prerequisites: MATH 203 and ENGL 185. Three hours.

**487-488 – Departmental Honors I and II –** Offered as needed. Three hours each.