Math & Computer Science
Mathematics
The Mathematics curriculum is traditional, although many of the best reform ideas (technology, group projects, writing mathematics, etc.) are being incorporated where appropriate to enhance the traditional topics.
The following list of courses represents current or recent course offerings. See the course catalog for updated information.

52104 EXPLORATIONS IN MATHEMATICSThis course investigates some of the important ideas in mathematics illustrating the scope and spirit of mathematics and emphasizing the role that mathematics plays in society from a historical point of view. Topics include number systems, algebra, geometry and measurement. The course is designed for those seeking EC6 or 48 teacher certification, but the course is suitable for a general audience with a broad spectrum of backgrounds and abilities. This course may not be used for the Mathematics major or minor. (Fall, each year; and Spring, odd years) (NS)

52114 INTRODUCTION TO STATISTICSThis course provides students in the social and biological sciences with the skills necessary to perform elementary statistical analysis. Topics include descriptive measures, probability, sampling theory, random variables, binomial and normal distributions, estimation and hypothesis testing, analysis of variance, regression and correlation. This course may not be used for the Mathematics major or minor. (Each semester) (NS)

52124 ELEMENTARY FUNCTION THEORYThis course investigates relations, functions and general properties of functions. Some of the elementary functions considered are polynomials, rational functions, exponentials, logarithms and trigonometric functions. An objective of this course is to prepare students for Calculus I. This course may not be used for the Mathematics major or minor. (Fall) (NS)

52154 CALCULUS IThis course investigates functions and graphs, derivatives, and applications of differentiation. Exponential, logarithmic and trigonometric functions, integration, and applications of integration. The course includes a laboratory component designed to explore applications and to enhance conceptualization. Prerequisite: Mastery of high schoollevel precalculus (algebra, trigonometry, exponential and logarithmic functions). (Each semester) (NS)

52204 TOPICS IN MATHEMATICSThis course investigates a topic in Mathematics that varies according to the interests of professor. This course may be repeated with a change in the topic. (NS)

52254 CALCULUS IIThis course investigates numerical integration, methods of integration, applications of the definite integral, improper integrals, sequences, series, Taylor’s Formula, Taylor approximation, polar coordinates and introductory differential equations. The course includes a laboratory component designed to explore applications and to enhance conceptualization. Prerequisite: Mathematics 52154. (Each semester) (NS)

52291 PUTNAM POWER HOURThis course is designed to sharpen problem solving abilities. Students will tackle challenging problems from the William Lowell Putnam Competitions of previous years and study some of the published solutions. Students enrolled in this course will be encouraged to compete in the Putnam Competition in early December. This course may be repeated for credit, but may not be counted toward the major or minor, and must be taken P/D/F. Prerequisite: Consent of instructor.

52354 CALCULUS IIIThis is a course in multivariable calculus. Topics include vectors, vector functions, curves, functions of several variables, partial differentiation, multiple integration, applications of partial differentiation, applications of multiple integrals, vector calculus, line integrals, Green’s Theorem, and surface integrals. The course includes a laboratory component designed to explore applications and to enhance conceptualization. Prerequisite: Mathematics 52254. (Each semester) (NS)

52384 DISCRETE MATHEMATICSSee Computer Science 54384. (Fall) (NS)

52404 GEOMETRYThis course investigates various approaches to geometry. Topics may include synthetic geometry, analytic geometry, projective geometry, Euclidean geometry and nonEuclidean geometry. Prerequisite: Permission of instructor. (Fall, even years) (NS)

52414 OPERATIONS RESEARCHSee Computer Science 54414 and Business 30414.

52524 INTRODUCTION TO NUMERICAL ANALYSISThis course investigates the derivations and applications of numerical techniques most frequently used by scientists: interpolation, approximation, numerical differentiation and integration, zeroes of functions and solution of linear systems. It is crosslisted as Computer Science 54524. Prerequisites: Mathematics 52674, and Computer Science 54184, or permission of instructor. (Spring, odd years) (NS)

52574 PROBABILITY AND MATHEMATICAL STATISTICSThis course is a calculusbased, mathematical introduction to the fundamental principles of probability theory and applications. Topics include combinatorial analysis used in computing probabilities, the axioms and properties of probability, conditional probability, independence of events, discrete and continuous random variables, the standard distributions, expected value and variance, joint distributions, distributions of a function of a random variable, and sampling distributions. Also included are theoretical results such as Bayes Theorem, Central Limit Theorem, Law of Large Numbers, the Empirical Rule, Hypothesis Testing and Confidence intervals at least for a single mean and a single proportion . Prerequisite: Mathematics 52254. (Spring) (NS)

52674 LINEAR ALGEBRAThis course is an introduction to the basic structure of proofs, linear equations and matrices, vector spaces, linear mappings, determinants, quadratic forms, vector products and groups of symmetries. Prerequisite: Mathematics 52154 and one approved MAT or CSC course at the 200level or above, or permission of instructor. (Each semester) (NS)

52684 ALGEBRAIC STRUCTURES IThis course investigates the theory of sets, relations, functions, groups and rings. A rigorous approach to learning and writing proofs is emphasized. Prerequisite: Mathematics 52674 or permission of instructor. (Fall) (NS)

52694 ALGEBRAIC STRUCTURES IIThis course investigates rings of polynomials and algebraic field theory. Topics include quotient rings, isomorphism theorems, extension fields and Galois theory. Prerequisite: Mathematics 52684. (Spring, odd years) (NS)

52754 DIFFERENTIAL EQUATIONS IThis course investigates the theory and application of differential equations. Topics include first order differential equations, separable equations, exact equations, linear differential equations of order n>1, homogeneous equations with constant coefficients, nonhomogeneous equations, the method of undetermined coefficients, variation of parameters, power series solutions and an introduction to Laplace transforms. Prerequisite: Mathematics 52354, or permission of instructor. (Spring) (NS)

52764 DIFFERENTIAL EQUATIONS IIThis course investigates further topics in differential equations. Topics include the Laplace transform, linear systems, numerical solutions, nonlinear systems and Fourier Series analysis of partial differential equations with boundary conditions. Prerequisites: Mathematics 52674 and 52754 or permission of instructor. (Fall, odd years) (NS)

52834 COMPLEX ANALYSISThis course investigates the algebra and geometry of complex numbers. Topics include analytic and harmonic functions, series, contour integration, conformal maps and transformations. Prerequisite: Mathematics 52354 or permission of instructor. (Fall, even years) (NS)

52844 SEMINAR IN SPECIAL TOPICSThis course is a limited enrollment seminar in a major area of mathematics not generally covered in other courses. Topics may include but are not limited to advanced analysis, combinatorics, logic and history of mathematics. The course may be repeated for credit as topics vary. Prerequisite: Three courses at the 200 level or above and permission of instructor. (NS)

52854 REAL ANALYSIS IThis course investigates the algebra and topology of the real numbers. Topics include completeness, sequences, limits and continuity, differentiation, the MeanValue Theorem, Taylor’s Theorem and infinite series. May also include sequences and series of functions. A rigorous approach to learning and writing proofs is emphasized. Prerequisite: Mathematics 52674, or permission of instructor. (Fall) (NS)

52864 REAL ANALYSIS IIThis course is a continuation of Real Analysis I. Topics vary but may include the theory of Riemann integration, Lebesgue integration, sequences and series of functions, Fourier analysis, function spaces. Prerequisite: Mathematics 52854 or permission of instructor. (Spring, even years) (NS)

52884 TOPOLOGYThis course is a study of the topology of the line and plane. Topics include limit points, open sets, closed sets, connectedness, compactness, continuous functions and homeomorphisms. Prerequisite: Mathematics 52254. (Fall, odd years) (NS)

52894 SENIOR SEMINAR IN MATHEMATICAL MODELINGThis course will fulfill the capstone requirement in Mathematics. Since it serves as a culmination of the student’s undergraduate mathematical experience, a balance is sought between application and theory. Topics may include optimization methods with sensitivity analysis, numerical and analytic methods, linear and nonlinear differential and difference equations, curve and surface fitting, statistics, and stochastic methods. Topics may vary with the instructor. Applications will be taken from the social and natural sciences. Collaboration and significant class participation are expected. Each student will take the Major Field Test. A major semester project resulting in a written paper and an oral presentation is required from each student; an external presentation may also be required.. Prerequisites: Six courses in the major at the 300 level or above, Computer Science 54184, and permission of instructor. (Fall) (NS) (WA)

52001 SELECTED TOPICSMay be repeated with change in topic.

52002 SELECTED TOPICSMay be repeated with change in topic.

52003 SELECTED TOPICSMay be repeated with change in topic.

52004 SELECTED TOPICSMay be repeated with change in topic.

52301 SELECTED TOPICSMay be repeated with change in topic. Prerequisite: Permission of instructor.

52302 SELECTED TOPICSMay be repeated with change in topic. Prerequisite: Permission of instructor.

52303 SELECTED TOPICSMay be repeated with change in topic. Prerequisite: Permission of instructor.

52304 SELECTED TOPICSMay be repeated with change in topic. Prerequisite: Permission of instructor.

52901 TUTORIAL

52902 TUTORIAL

52903 TUTORIAL

52904 TUTORIAL

52951 INDEPENDENT STUDY

52952 INDEPENDENT STUDY

52953 INDEPENDENT STUDY

52954 INDEPENDENT STUDY

52984 HONORSBy invitation only.