# Courses

**MATH 111. Calculus II (Staff)**

Continuation of MATH 110. A thorough treatment of integral calculus, including the Fundamental Theorem of calculus. Transcendental functions, followed by a study of techniques of integration, polar coordinates, and infinite series. Computer symbolic algebra projects are included. Prerequisite: MATH 110. F, S. (Group II, Quantitative)

**MATH 210. Multivariable Calculus (Nunemacher)**

Vectors and geometry of three-dimensional space, partial derivatives, multiple integrals, and an introduction to vector analysis. Computer symbolic algebra projects are included. Prerequisite: MATH 111. F. (Group II, Quantitative)

**MATH 230. Applied Statistics (Linder)**

Calculus-based introductory course in statistics. Exploratory data analysis, questions of causation, probability, continuous and discrete random variables, distributions of sums of random variables, confidence intervals, significance tests, use and abuse of tests, one and two sample procedures, inferences in linear regression, and analysis of variance. Students may not count graduation credit for both MATH 230 and MATH 105 or both MATH 230 and PYSC 210. Prerequisite: MATH 110. F, S. (Group II, Quantitative)

**MATH 250. Discrete Mathematics (Jackson)**

An introduction to mathematical reasoning and to the kind of mathematics appropriate for the study of properties of (possibly large) finite systems. Topics include proof techniques, mathematical induction, elementary number theory, combinatorics, relations, and graph theory. Applications will be made to the construction of models useful in the social and physical sciences and to the study of algorithms in computer science. Prerequisite: MATH 111 F. (Group II)

**MATH 270. Linear Algebra (Jackson)**

Matrix algebra, finite dimensional vector spaces, linear transformations, determinants, eigenvalues, and applications. Prerequisite: MATH 210 or MATH 250. Recommended: MATH 250. S. (Group II)

**MATH 280. Differential Equations (Schwartz)**

Study of first and second-order equations, numerical methods, and first-order systems. Applications to problems in the physical, life, and social sciences are emphasized. Computer software is used to support the study by providing enhanced symbolic, numerical, and graphing capability. Additional topics include certain prerequisites from linear algebra (as needed), and Laplace transforms. Prerequisite: MATH 111. S. (Group II)

**MATH 310. Mathematical Logic (Nunemacher)**

A study of the foundations of mathematics and logical reasoning. Topics include propositional calculus, predicate calculus, properties of formal systems, completeness and compactness theorems, Godel’s Incompleteness Theorem, and axiomatic set theory. Some attention will be given to related philosophical issues. Prerequisite: MATH 250. Also listed as PHIL 371. (Group II)

**MATH 320. Geometry (Schwartz)**

An introduction to the study of geometry, both ancient and modern. Topics will be chosen from Euclidean, affine, projective, elliptic, and hyperbolic geometries. Some time will be spent on axiomatics and the history of geometry. Tools such as matrices and groups will be developed as they are needed for the study of geometric problems. Prerequisite: MATH 250 or consent of instructor. F. (Group II)

**MATH 330. Complex Variables (Nunemacher)**

A study of analytic functions, power series, complex integration, conformal mapping, and the calculus of residues with applications to physical science. Prerequisite: MATH 210 and one course numbered 250 or above. (Group II)

**MATH 335. Vector Analysis and Geometry (Nunemacher)**

Advanced calculus of functions of more than one variable. Topics include the geometry of Euclidean space, vector fields, line and surface integrals, curvature and differential geometry. Prerequisite: MATH 210. (Group II)

**MATH 340. Analysis I (Schwartz)**

Rigorous development of the topology of the real line, theory of metric spaces, and the foundations of calculus. Attention is given to constructing formal proofs. Prerequisite: MATH 210 and MATH 250. Recommended: MATH 270. F. (Group II)

**MATH 345. Special Topics in Mathematics (Staff)**

A course of varying content reflecting the needs and interests of students. (Group II)

**MATH 350. Probability (Schwartz)**

An introduction to the major topics of probability including sample spaces, conditional probability, discrete and continuous random variables, exception and variance, and limit theorems (law of large numbers, central limit theorem). Time permitting, topics in stochastic processes or statistics are introduced. Prerequisite: MATH 210. F. (Group II)

**MATH 360. Mathematical Statistics (Linder)**

Sampling distributions, derivation of distributions, proof of the Central Limit Theorem, methods of estimation, hypothesis testing, uniformly most powerful tests, estimation in multiple regression, nonparametric methods, experimental design. Prerequisite: MATH 230, and 350. S. (Group II)

**MATH 365. Special Topics in Statistics (Linder)**

A course of varying content reflecting the needs and interests of students. (Group II)

**MATH 370. Abstract Algebra I (Jackson)**

Introduction to the algebraic systems of groups, rings, and fields; with applications. Attention is given to the construction of formal proofs. Prerequisite: MATH 250, MATH 270. F. (Group II)

**MATH 380. Applied Mathematics (Wiebe)**

Selected topics in ordinary and partial differential equations including Sturm-Liouville problems, Fourier series, Laplace transforms, boundary value problems, and special functions of mathematical physics. Prerequisite: MATH 210 and MATH 280. (Group II)

**MATH 385. Numerical Analysis (Nunemacher)**

A survey of numerical mathematics and continuous algorithms. Topics may include number representation, error analysis, finding roots of equations, interpolation, numerical differentiation and integration, solving system of linear equations, and numerical methods for differential equations. Prerequisite: MATH 210, MATH 270, CS 110. (Group II)

**MATH 440. Analysis II (Schwartz)**

An advanced analysis course considering topics such as Lebesque measure and integration, Hilbert and Banach spaces, Fourier series, and topology. Prerequisite: MATH 340. (Group II)

**MATH 470. Abstract Algebra II (Jackson)**

Continuation of MATH 270 and MATH 370. Topics may include further group theory, field and Galois theory, and linear algebra topics such as Jordan normal form. Prerequisite: MATH 370. (Group II)

**MATH 490. Independent Study in Mathematics (Staff)**

Independent study of a topic in advanced mathematics under the guidance of a faculty member. Individually arranged.

**MATH 491. Directed Readings (Staff)**

Reading in advanced mathematics under the guidance of a faculty member. Individually arranged.

**MATH 498. Student Seminar (0.5 unit; Jackson)**

A student-lead discussion of advanced topics of interest to the students and the instructor. Students will complete an independent or group project on the selected topic, write a paper on their findings, and present their results to the class. Intended for junior and senior mathematics majors; other students may be admitted with the consent of the instructor. Grading for the course is S/U. The course may be repeated for credit on a different topic. Prerequisite: MATH 250.

**MATH 499. Seminar (Staff)**

Intensive study of a topic selected by the faculty member in charge with presentations by students. Recent topics have included chaos, stochastic processes, combinatorics, experimental design, number theory, and curves and singularities. S.