Investigation of a variety of mathematical models. Models to be investigated will be chosen from the areas of game theory, network models, voting theory, apportionment methods, fair division, and probability and statistics. We will apply these models in such diverse fields as biology, sociology, political science, history, and psychology. Somers, Staff

Quantitative reasoning skills to interpret and assess numerical arguments, with emphasis on issues relevant for informed and effective citizenship. Topics include creating and interpreting graphs and charts single- and multiple-variable functions; linear, exponential, and logarithmic growth indexes; inductive and deductive reasoning; decision theory; measures of center and spread of data; correlation; probability; expected value; experimental design; sampling and surveys. (F2, I.C) Sevilla, Somers

Beginning calculus with extensive review of algebra and elementary functions. Topics include Cartesian plane, algebraic functions, limits and continuity, introduction to the concept of derivative as a Limit of average rates of change, theorems on differentiation, and the differential. Continued in Mathematics 166. The sequence Mathematics 106-166 is equivalent to Mathematics 170; credit may be earned for 106-166 or 170 but not both. (F2, I.C) Prerequisite: Three years of college preparatory mathematics. Fall. Staff

Introduction to statistical concepts and methods without the use of calculus. Topics include descriptive statistics, elementary probability, discrete and continuous probability distributions, correlation and regression, estimation, and hypothesis testing. Mathematics 107 may not be taken for credit by students who have earned credit for Economics 156. (F2, I.C) Staff

Emphasis on concepts and applications to business and social and natural sciences. Use of graphing calculators. Topics include linear functions, polynomial functions, exponential functions, average rate of change, instantaneous rate of change, the derivative, interpretations of the derivative, rules of differentiation, and applications of the derivative. Includes review of algebra and elementary functions. May not be taken for credit by students who have completed Mathematics 106 or 170. (F2, I.C) Fall. Staff

Provides mathematical background and techniques useful to aspects of artistic design in the plane and in space. Essential mathematical concepts and tools applied to solve design problems. Topics include ratio and proportion, similarity, geometric constructions with Euclidean tools and dynamic geometry software, properties of polygons and polyhedra, isometries and other geometric transformations in the plane and space, symmetry and periodic designs, projections from space onto a plane. (F2, I.C) Spring. Hartshorn

Problem-solving, communication, and reasoning. Topics include estimation, geometry and spatial sense, measurement, statistics and probability, fractions and decimals, patterns and relationships, number systems, number relations, and number theory. Designed for prospective elementary education teachers and is a prerequisite for Education 325. (F2, I.C) Staff

Topics include exponential and trigonometric functions and their derivatives, related rates, extremum problems, curve sketching, antidifferentiation, the definite integral, the fundamental theorem of calculus, area under a curve, and applications to business and economics. The sequence Mathematics 106-166 is equivalent to Mathematics 170; credit may be earned for 106-166 or 170 but not both. (F2, I.C) Prerequisite: Three years of college-preparatory mathematics and Mathematics 106. Spring. Staff

Real numbers and an introduction to analytic geometry. Algebraic functions, trigonometric functions, limits, and continuity. The derivative, theorems on differentiation, applications to related rates and minimamaxima problems, curve-sketching. The differential, the definite integral, the fundamental theorem of calculus, finding area under a curve. May not be taken for credit by students who have earned credit for Mathematics 166. (F2, I.C) Prerequisite: Three years of college-preparatory mathematics, including plane trigonometry. Staff

Applications of the definite integral. Logarithmic and exponential functions, trigonometric and inverse trigonometric functions. Techniques of integration of both algebraic and transcendental functions. Parametric equations and curves given in polar coordinates. Indeterminate forms and improper integrals. Separable differential equations. Introduction to infinite sequences and series. Prerequisite: Mathematics 170 or equivalent sequence 106-166. (F2, I.C) Staff

(Formerly Mathematics 201) Infinite sequences and series. Vectors in the plane and three-space. Parametric equations and space curves. Calculus of functions of more than one variable, including limits, partial derivatives, directional derivatives, multiple integration, and applications. Prerequisite: Mathematics 171. Staff

(Formerly Mathematics 204) Introduction to mathematical techniques to model and analyze decision problems. Linear programming, including sensitivity analysis and duality, network analysis, decision theory, game theory, queuing theory. Prerequisite: Mathematics 171. Spring. Somers, Staff

Elementary mathematical logic and types of mathematical proof, including induction and combinatorial arguments. Set theory, relations, functions, cardinality of sets, algorithm analysis, basic number theory, recurrences, and graphs. Prerequisite: Mathematics 171. Fall. Staff

(Formerly Mathematics 210) Vector spaces and linear transformations, matrices, systems of linear equations and their solutions, determinants, eigenvectors and eigenvalues of a matrix. Applications of linear algebra in various fields. Prerequisite: Mathematics 171. Spring. Sevilla, Staff

Various methods of solution of ordinary differential equations, including first-order techniques and higher-order techniques for linear equations. Additional topics include applications, existence theory, and the Laplace transform. Prerequisite: Mathematics 211. Spring. Schultheis, Staff

Numerical techniques for solving applied mathematical problems. Topics include interpolation and approximation of functions, solution of nonlinear equations, solution of systems of linear equations, and numerical integration, with error analysis and stability. Prerequisite: Mathematics 171 and a course in computer science. Fall, alternate years. Fraboni, Staff

A calculus-based introduction to probability and statistical concepts and methods. Topics include descriptive statistics, probability, discrete and continuous probability distributions, regression analysis, sampling distributions and the central limit theorem, estimation and hypothesis testing. Prerequisite: Mathematics 171. Fall. Shank, Somers

This course gives students an opportunity to explore a special topic in mathematics. For more information about recent offerings, see the special topics page. Spring. Staff

Group theory, including structure and properties: subgroups, cosets, quotient groups, morphisms. Permutation groups, symmetry groups, groups of numbers, functions, and matrices. Brief study of rings, subrings, and ideals, including polynomial rings, integral domains, Euclidean domains, unique factorization domains, and fields. Prerequisite: Mathematics 216 or permission of instructor. Fall. Schultheis, Sevilla

Differential and integral calculus of scalar and vector functions. Differential calculus includes differentials, general chain rule, inverse and implicit function theorems, and vector fields. Integral calculus includes multiple integrals, line integrals, surface integrals, and theorems of Green and Stokes. Prerequisite: Mathematics 211. Fall. Staff

Rigorous study of real-valued functions, metric spaces, sequences, continuity, differentiation, and integration. Prerequisite: Mathematics 211 and Mathematics 216 or 220. Spring, alternate years. Fraboni, Staff

Analytic functions, complex integration, application of Cauchy's theorem. Prerequisite: Mathematics 211. Spring, alternate years. Fraboni, Schultheis

Development of statistical concepts and methods. Multivariate probability distributions, point and interval estimation, regression analysis, analysis of variance, chi-square goodness-of-fit and contingency table analysis, and nonparametric tests. Prerequisite: Mathematics 231. Spring. Shank, Somers

Topics in Euclidean two- and three-dimensional geometry from classical (synthetic), analytic, and transformation points of view. Transformations include isometries, similarities, and inversions. Construction and properties of two- and three-dimensional geometric figures. Brief study of some non-Euclidean geometries. Prerequisite: Mathematics 216 or 220. Writing intensive. Fall, alternate years. Hartshorn, Staff

Writing-intensive topics course, theme to be chosen by instructor. Writing assignments cover types of writing for mathematics and related fields: historical articles, expository articles, mathematical reviews, descriptions of problems, techniques or solutions, grant- or report-writing, and research results. Staff