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Courses
Study of practical arithmetic and geometry, data gathering and analysis, introductory probability and statistics, size and bias in sampling, hypothesis testing, confidence intervals and their use in statistical analysis, linear relationships, interpolation and extrapolation, correlation, linear and exponential growth with practical applications. The course is primarily intended to fulfill the first part of the quantitative reasoning requirement (QR1). Prerequisite: placement by department or permission of instructor. The Department
Note: Courses numbered MS104, MA215 or MC215, 302, 306, 316, and MA102 through MA382 have as a prerequisite QR1 or permission of the department.
MA 102. MATHEMATICS IN CONTEXT 3
A set of courses exploring interesting questions from a variety of disciplines with the aid of mathematics. (Fufills QR2 requirement.) Courses including the following are offered periodically depending on faculty availability. A student may take more than one of these courses for credit.
A. Statistical Controversies. It is often said that one can prove anything using statistics. Indeed, the reading of any newspaper or news magazine presents one with bold statements about important topics (economic, political, and health issues, etc.) based on statistical studies, together with strong opposition to those statements—in a phrase, statistical controversies. This course aims to study many such controversies to try to understand how they arise, what statistics lie behind them, and how at least some of them might be avoided by proceeding with greater care. Intended for students with little or no experience with statistics. (Fufills QR2 requirement.)
B. Modeling Epidemics. This course several mathematical techniques for modeling epidemics, including differential equations and statistical methods. (Fufills QR2 requirement.)
D. Mathematics in Context: Mathematical Models for Business and Economics—Efficient Planning. What is the best way to allocate scarce resources? In the business world, linear programming is often used to answer this question. Phone companies, oil refineries, airlines, and many other businesses use linear programming to schedule transportation networks, plan portfolios, control inventories, and maximize profits. Since its invention in the 1940s, linear programming has become increasingly important, and according to some estimates, well over $100 million in human and computer time is spent yearly in the formulation and solution of linear programming problems. In this course, the student will be introduced to linear programming problems and their solution, related topics such as sensitivity analysis and integer programming, and various other mathematical models useful in business and economics, such as Leontief economic models, basic probability theory, and Markov chains. (Fufills QR2 requirement.)
MS 104. INTRODUCTION TO STATISTICS 4
An introduction to fundamental concepts in statistical reasoning. Students will consider contexts, both historical and modern, in which statistical approaches arose and methodologies developed. Topics considered will include organization and analysis of data, the drawing of inferences from these data, and the careful presentation of these inferences. Examples will be drawn from a variety of disciplines. (Fulfills QR2 requirement.) The Department
MS 104E. INTRODUCTION TO STATISTICS 4
An introduction to fundamental concepts in statistical reasoning. Students will consider contexts, both historical and modern, in which statistical approaches arose and methodologies developed. Topics considered will include organization and analysis of data, the drawing of inferences from these data, and the careful presentation of these inferences. Examples will be drawn primarily from Environmental Studies. (Fulfills QR2 requirement.) The Department
MA 107. CONCEPTS OF MATHEMATICS 3
An introductory course for liberal arts and education majors or anyone seeking a general, nontechnical overview of mathematics. Topics covered include set theory, review of number systems, geometry concepts, basic concerns of probability and statistics, and introductory number theory. (Fulfills QR2 requirement.) The Department
MA 108. CALCULUS WITH ALGEBRA I 3
An introduction to derivatives, integrals, and their applications. Primarily for students who are not adequately prepared for MA111, this course (together with MA109) covers the same material as MA111 but integrates the material requisite to calculus with the calculus itself. Note that MA108 alone can not be used as a substitute for MA111. Successful completion of MA108 and MA109 is equivalent to completion of MA111. Prerequisite: Permission of instructor. The Department
MA 109. CALCULUS WITH ALGEBRA II 3
A continuation of MA108. A study of exponential, logarithmic, and trigonometric functions and their applications in differential and integral calculus. Successful completion of MA108 and MA109 is equivalent to completion of MA111. (Fulfills QR2 requirement.) Prerequisite: MA108. The Department
MA 111. CALCULUS I 4
Derivatives, integrals and their applications. Techniques of differentiation. Integration and differentiation of exponential, logarithmic and trigonometric functions. Prerequisite: high school preparation including trigonometry or consent of department. (Fulfills QR2 requirement.) The Department
MA 111W. CALCULUS I 4
Derivatives, integrals and their applications. Techniques of differentiation. Integration and differentiation of exponential, logarithmic and trigonometric functions. Prerequisite: high school preparation including trigonometry or consent of department. (Fulfills QR2 requirement; meets expository writing requirement for students who placed at EN105 level or who have completed EN103.) The Department
MA 113. CALCULUS II 4
Inverse trigonometric functions and hyperbolic functions. Systematic study of integration. Series and Taylor series. Polar coordinates. Indeterminate forms, L'Hôpital's rule and improper integrals. (Fulfills QR2 requirement.) Prerequisite: MA111, or both MA108 and 109, or consent of department. The Department
MA 113W. CALCULUS II 4
Inverse trigonometric functions and hyperbolic functions. Systematic study of integration. Series and Taylor series. Polar coordinates. Indeterminate forms, L'Hôpital's rule and improper integrals. (Fulfills QR2 requirement; meets expository writing requirement for students who placed at EN105 level or who have completed EN103.) Prerequisite: MA111, or both MA108 and 109, or consent of department. The Department
MA 125, 126. PROBLEM SOLVING IN MATHEMATICS 1, 1
Introductory level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics. During fall semesters, students will have an opportunity to compete in the annual William Lowell Putnam Mathematical Competition. Prerequisite: QR1. Must be taken S/U. May be repeated for credit. The Department
MA 200. LINEAR ALGEBRA 4
Vector spaces, matrices and linear transformations, determinants, solution of linear equations. Prerequisite: high school preparation including trigonometry or consent of department. Offered fall semester. (Fulfills QR2 requirement.) The Department
MA 202. CALCULUS III 4
Multivariable calculus. Prerequisites: MA113 and 200. Offered spring semester. The Department
MA 204. PROBABILITY AND STATISTICS 3
Elementary probability, discrete and continuous random variables, theory of expectation, analysis of distribution functions. (Fulfills QR2 requirement.) Prerequisite: MA111, or both MA108 and 109 or consent of department. Spring 2007 and alternate years. The Department
MA 214. THEORY OF NUMBERS 3
Topics in classical and modern number theory including congruences, Diophantine equations, quadratic residues. (Fulfills QR2 requirement.) Prerequisite: MA111, or both MA108 and 109, or MA200 or consent of department. Spring 2006 and alternate years. The Department
MC 215. MATHEMATICAL REASONING AND DISCRETE STRUCTURES 4
An introduction to mathematical reasoning in the context of studying discrete structures fundamental to both mathematics and computer science. Topics include elementary logic and sets, methods of proof including mathematical induction, algorithms and their analysis, functions and relations, elementary combinatorics, discrete probability, and graph theory. (Fulfills QR2 requirement.) Prerequisites: QR1, and CS106 or MA113, or permission of the instructor. The Department
MA 225, 226. PROBLEM SOLVING IN MATHEMATICS 1,1
Intermediate level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics. During fall semesters, students will have an opportunity to compete in the annual William Lowell Putnam Mathematical Competition. Prerequisite: QR2. Must be taken S/U. May be repeated for credit. The Department
MA 270. DIFFERENTIAL EQUATIONS 4
An introduction to the theory and applications of differential equations. Prerequisite: MA113 and 200. Offered spring semester. The Department
MA 276. SELECTED TOPICS IN MATHEMATICS 3
Topics that complement the established lower level course offerings in mathematics will be selected. Emphasis will be on the nature of mathematical thought. May be repeated for credit. Offered on sufficient demand. The Department
MC 302. GRAPH THEORY 3
An introduction to the theory and applications of graphs. Topics may include graphs and digraphs, connectivity, trees, Euler and Hamiltonian cycles, and graph embeddings. Prerequisite: MC115 or MC215 or MA200 or permission of instructor. Fall 2007 and alternate years. The Department
MA 303. ADVANCED CALCULUS 4
Rigorous treatment of foundational issues in analysis. Topics may include set theory, the real number system, sequences, series, limits and continuity, theory of differentiation and integration, and elementary notions of topology. Prerequisite: MA113 and MA215 or MC215 or consent of the department. Offered fall semester. The Department
MC 306. THEORY OF COMPUTATION 3
A study of the major theoretical models of computation. Topics include automata, nondeterminism, regular and context-free languages, Turing machines, unsolvability, and computational complexity. Prerequisite: MC115 or MC215 and CS106, or permission of instructor. Beginning in fall 2005, MC306 will have CS210 as a prerequisite. The Department
MA 309. ELEMENTS OF MODERN GEOMETRY 4
Study of various topics in modern geometry, with emphasis on the axiomatic method. Fall 2006 and alternate years. Prerequisite: MA113 and MA215 or MC215 or consent of instructor. The Department
MA 310. HISTORY OF MATHEMATICS 3
Study of the development of mathematical ideas. Prerequisite: MA113 and MA215 or MC215 or permission of the instructor. Offered on sufficient demand. The Department
MA 311. DIFFERENTIAL GEOMETRY 3
An introduction to differential geometry in a classical setting: the study of n-surfaces, embedded in Euclidean space. Offered on sufficient demand. Prerequisite: MA200, 202, MA215 or MC215, or consent of the department. MA270 recommended. The Department
MA 313. INTRODUCTION TO TOPOLOGY 3
Selected topics in topology such as metric spaces, point set topology of Euclidean spaces, introduction to algebraic topology. Prerequisite: MA113 and MA215 or MC215 or consent of the department. Spring 2007 and alternate years. The Department
MC 316. NUMERICAL ALGORITHMS 3
An introduction to using computation to obtain approximate solutions to mathematical problems. A variety of algorithms are studied, as are the limitations of using computational methods. Topics include algorithms for solving equations, systems, and differential equations; approximating functions and integrals; curve fitting; round-off errors and convergence of algorithms. Prerequisites: MA111 (or both MA108 and 109), CS106, and MA200. Offered on sufficient demand. The Department
MA 319. ABSTRACT ALGEBRA I 4
Survey of algebraic structures; groups, rings, fields, vector spaces, and linear transformations. Prerequisite: MA200 and MA215 or MC215 or consent of the department. Offered fall semester. The Department
MA 320. ABSTRACT ALGEBRA II 3
Selected topics in advanced algebra. Prerequisite: MA319 or consent of department. Spring 2006 and alternate years. The Department
MA 323. REAL ANALYSIS 3
Selected topics in real analysis. Prerequisite: MA303 or consent of department. Offered alternate years. The Department
MA 324. COMPLEX ANALYSIS 3
Analytic functions, complex integration, complex sequences and series, and conformal mapping. Prerequisite: MA303 or consent of department. Offered alternate years. The Department
MA 325, 326. PROBLEM SOLVING IN MATHEMATICS 1,1
Advanced level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics. During fall semesters, students will have an opportunity to compete in the annual William Lowell Putnam Mathematical Competition. Prerequisite: QR2. Must be taken S/U. May be repeated for credit. The Department
MA 371, 372. INDEPENDENT STUDY 3, 3
Special study in mathematics outside the regular department offerings. Prerequisite: consent of department. The Department
MA 376. SEMINAR 3
Research, discussion, and presentation of selected topics at an advanced level, to provide a capstone experience for the mathematics major; primarily intended for seniors. Prerequisites: MA303 and 319 or consent of the department. This course may be repeated for credit with permission of the department. The Department
MA 381, 382. SENIOR THESIS 3, 3
Optional for mathematics majors. Recommended for those working toward professional careers or graduate study in mathematics, and required for those seeking to satisfy the criteria for departmental honors. The Department
MA 399. INTERNSHIP IN MATHEMATICS 3 or 6
Professional experience at an advanced level for juniors and seniors with substantial academic experience in mathematics. With faculty sponsorship and departmental approval, students may extend their educational experience in pure or applied mathematics. This course may not be used to satisfy the requirements of any major or minor in the department. Prerequisites: MA200, two additional courses in mathematics at the 200 level or above, and permission of the department. Not for liberal arts credit.
