
Mathematics Courses31310000 Mathematics Fundamentals U LA Basic concepts underlying algebra, functions, exponents, areas, fractions, and percents. Reasoning skills required for these concepts. Word problems. Meets three hours. See also 31318000; credit cannot be earned for both 31310000 and 31318000. Prerequisites: Math placement in group 4. 1 credit. (FS,Y) 31310500 Mathematics for Decision Making NS LA Introduction to probability theory; mathematics of finance; linear programming. Additional topics at the instructor's discretion. Students may not receive credit for both 31310500 and 31310600. Prerequisites: Math placement in group 1, 2, or 3. 3 credits. (FS,Y) 31310600 Mathematics for Decision Making with Technology NS LA 2b Introduction to probability theory; mathematics of finance; linear programming. Additional topics at the instructor's discretion. Appropriate technology is introduced to present some of the topics differently and in more depth than 31310500. Students may not receive credit for both 31310500 and 31310600. Prerequisites: Math placement in group 1, 2, or 3. 4 credits. (FS,Y) 31310700 Fundamentals of Applied Calculus NS LA Introduction to calculus with an emphasis placed on problems in business and economics. Topics include modeling data with polynomial, exponential, and other functions; rates of change and other applications of derivatives; optimization; and the definite integral. Technology, such as graphing calculators, will be used throughout this course. Completion of this course with a grade of C or better will move students in group 3 to group 2. Not open to students who have taken 31310800, 31311100, or 31311200. Prerequisites: Math placement in group 2 or 3. 4 credits. (FS,Y) 31310800 Calculus for Decision Making NS LA 2b Introduction to calculus with an emphasis placed on problems in the social and life sciences. Topics include polynomial, exponential, and logarithmic functions and their derivatives; curve sketching, optimization, and rates of change; the definite integral and area. Further topics may be chosen from applications of differential equations and trigonometric functions. Not open to students who have taken 31310700, 31310801, 31310803, 31311100, or 31311200. Students with group 1 placement who plan to take more than one semester of calculus should instead take 31311100. Prerequisites: Math placement in group 1 or 2. 4 credits. (FS,Y) 31311100 Calculus I NS LA 2b Calculus of functions of one variable. Topics include limits, continuity, derivatives, applications of derivatives (problems of motion, graphing, and optimization), antiderivatives, and an introduction to the definite integral. Functions covered include polynomial, rational, exponential, logarithmic, trigonometric, and piecewisedefined functions. Prerequisites: Math placement in group 1. 4 credits. (FS,Y) 31311200 Calculus II NS LA 2b Continuation of calculus of functions of one variable. Topics include differential equations, including slope fields, numerical solutions, and separation of variables; evaluation of integrals and antiderivatives; applications of integration; improper integrals; series, with an emphasis placed on power series. Prerequisites: 31311100. 4 credits. (FS,Y) 31313100 Power Algebra NS LA 2b College algebra is introduced as motivated by applications. Students make conjectures and predictions about reallife applications and actively participate in constructing simple mathematical models. Focus on mathematical concepts and thinking rather than algebraic manipulations. Provides the skills and knowledge to take a course such as 31310800 Calculus for Decision Making. Upon the recommendation of the instructor, students completing this course move to group 2. Students not receiving the recommendation of the instructor have the option of taking the department exam to move from group 3 to 2. Students may not receive credit for both 31310100 and 31313100. Prerequisites: Math placement in group 3. 4 credits. (FS,Y) 31313200 Dynamic Functions NS LA 2b Using a blend of geometric, numerical, and symbolic approaches, students construct mathematical models to better understand a variety of reallife applications. A graphical and analytic analysis specifically focuses on exponential, logarithmic, and trigonometric function theory, motivated by practical problems. Explores and develops precalculus mathematics while focusing on mathematics as a practical tool. Upon the recommendation of the instructor, students completing this course move to placement in group 1. Students not receiving the recommendation of the instructor have the option of taking the department placement exam to move from group 2 to group 1. Students may not receive credit for both 31310200 and 31313200. Prerequisites: Math placement in group 2. 4 credits. (FS,Y) 31313500 Mathematical Art with Computers LA 2b Focuses on mathematical concepts such as symmetry, crystallographic groups, recursive patterns, spirals, and the golden ratio as they relate to geometric design. The use of computers enables us to explore these topics without an extensive math background. Prerequisites: Math placement in group 3, 2, or 1. 3 credits. (S,Y) 31314400 Business Statistics NS LA Descriptive statistical techniques; introduction to probability; statistical inference including problems of estimation and hypothesis testing; correlation and regression analysis. Technology used in this course may include graphing calculators and statistical software. A student cannot receive credit for this course and 67039000. Not open to students who have completed 31324300, 31324400, 31324402, or 31331600. To obtain mathematical maturity, it is strongly recommended that students complete a calculus course before taking this course. Prerequisites: Math placement in group 1 or 2. 4 credits. (FS,Y) 31315200 Selected Topics: What Is Mathematics? NS LA 2b Cultural approach to selected topics in mathematics. See instructor for current list of topics. Students may not receive credit for both 31315200 and 31325200. Prerequisites: Math placement in group 3, 2, or 1. 3 credits. (FS,Y) 31315500 Basic Statistical Reasoning NS LA 2b Basic concepts involved in statistical reasoning, such as sampling and experimental design, description of data, normal approximation to data, correlation and regression, and probability. Emphasis is placed on understanding the use of statistics rather than on how to do statistical analysis. Not open to students who have taken 31310800, 31311100, 33020700, or 67039000. Prerequisites: Math placement in group 3, 2, or 1; completion of one course in the social or natural sciences. 3 credits. (FS,Y) 31316100 Math and Society NS LA 2b Explores connections between mathematics and the liberal arts. Covers three to six topics chosen for their mathematical and societal component, with comparable emphasis given to each component. Only a high school math background is assumed, but students must have scored in group 2 or 1 on the math placement exam. Actual course content varies with instructor, but examples of topics are exponential growth and world population; symmetry and group theory in art and architecture; fair allocation and equity; binomial models and the death penalty; quantitative communication and the media. Prerequisites: Math placement in group 2 or 1. 3 credits. (FS,Y) 31317600 Mathematical Problem Solving with Technology NS LA Topics include procedural programming: loops, conditionals, procedures, and recursion. These concepts are used in mathematical contexts and applications that involve both problem solving and the use of technology. The application of Gaussian elimination to solving systems of linear equations is one of these applications. Introduces a computer algebra system and a procedural programming language. Use of spreadsheets and programmable graphing calculators may be included. Prerequisites or corequisites: 31311100. 4 credits. (S,Y) 31318000 Mathematics Fundamentals with Computers U LA Meets four hours. Three of the four hours explore the same topics as 31310000 Mathematics Fundamentals: reasoning skills and basic concepts underlying algebra, functions, exponents, areas, fractions, and percents. The fourth hour is a computer lab, where students use the computer to increase their understanding of mathematics. Credit cannot be earned for both 31318000 and 31310000. Prerequisites: Math placement in group 4. 2 credits. (FS,Y) 31319000 Selected Topics in Mathematics NS LA Topics to be determined by instructor and department. May be repeated for credit for selected topics on different subjects. Prerequisites: Appropriate to topics. 14 credits. (IRR) 31319200 Independent Study U LA Reading on selected subjects with frequent, informal discussions with the instructor. Prerequisites: Permission of instructor. 13 credits. (IRR) 31321100 Calculus III NS LA 2b Introduction to vectors and the geometry of vector spaces. Calculus of functions of several variables: partial derivatives, gradients, optimization, double integrals. Prerequisites: 31311100; 31311200. 4 credits. (FS,Y) 31321200 Calculus IV NS LA Multiple integrals and change of variables. Line and surface integrals. Classical theorems of vector calculus. Prerequisites: 31321100. 3 credits. (S,Y) 31324300 Statistics NS LA Descriptive statistical techniques; review of basic probability; random variables and their distributions; statistical inference including problems of estimation and hypothesis testing; and correlation and regression analysis. A student cannot receive credit for this course and 67039000 or 31324400. Not open to students who have taken 31331600. Prerequisites: 31310500 or 31310600 and math placement in group 2, or 31311100 and 31311200. 3 credits. (FS,Y) 31324400 Statistics with Probability NS LA 2b Descriptive statistical techniques; introduction to probability theory including counting methods, expected value, independence, and random variables and their distributions; statistical inference including problems of estimation and hypothesis testing; correlation and regression analysis; introduction to further topics chosen from Chisquare tests, multiple regression, and analysis of variance. Technology used in this course may include graphing calculators and statistical software. A student cannot receive credit for this course and 67039000, 31314400, 31324300, or 31324402. Not open to students who have taken 31331600. Prerequisites: 31310800 or 31311100. 4 credits. (FS,Y) 31325000 ProblemSolving Seminar NS LA Techniques used in the solution of diverse mathematical problems are developed and discussed. Problems will often be drawn from national competitions such as the Putnam exam and the COMAP Modeling Competition, or from problem sections of mathematics journals. The course will be offered for either 0.5 or 1.0 credit ; may be repeated for credit up to a total of 4 credits. Prerequisites: 31311100. Pass/fail only. 0.51.0 credit. (F,S) 31325200 Selected Topics: What Is Mathematics? NS LA 2b Cultural approach to selected topics in mathematics. See instructor for current list of topics. Prerequisites: Math placement in group 2; one college mathematics course or sophomore standing. Students may not receive credit for both 31315200 and 31325200. 3 credits. (F,Y) 31326000 Linear Algebra, Modeling, and Reasoning I NS LA A study of mathematical reasoning including standard methods of proof, such as direct proof, indirect proof, proof by cases, and use of the contrapositive, induction, and quantification. Functions, matrices, and matrix algebra, eigenvalues, and characteristic polynomials are studied theoretically and used to provide tools in applications. Other topics, such as set theory, may be included. Tools developed may include transformation matrices, coding matrices, and incidence matrices. Prerequisites or corequisites: 31311200. 4 credits. (F,Y) 31326100 Linear Algebra, Modeling, and Reasoning II NS LA Topics include equivalence relations, abstract linear algebra, abstract vector spaces, independence, bases, dimension, and linear maps. Analytic, numeric, and geometric solutions of firstorder differential equations are studied. Topics in modeling such as solutions of constant coefficient second order differential equations, homogeneous and nonhomogeneous differential equations, discrete dynamical systems, difference equations, and graph theory. Prerequisites: 31326000. 4 credits. (S,Y) 31328000 Mathematica U LA Introduction to Mathematica  its syntax, structure, and distinctive features. Use of Mathematica as a problemsolving tool for mathematics. Prerequisites: 31311200. 1 credit. (F,Y) 31329000 Selected Topics in Mathematics NS LA Topics to be determined by instructor and department. This course may be repeated for credit when topics vary. Prerequisites: As appropriate to topics. 14 credits. (IRR) 31329100 Sophomore Seminar NS LA Series of discussions presenting an overview of mathematics led by various faculty members. Should be taken by majors in sophomore year. Prerequisites: 31311100; 31311200; 31326000 (may be taken concurrently). Pass/fail only. 1 credit. (S,Y) 31329200 Independent Study U LA Readings on selected subjects with frequent, informal discussions with the instructor. Prerequisites: Permission of instructor. 13 credits. (IRR) 31330300 Abstract Algebra NS LA Introduction to algebraic structures. Study includes concepts from group theory, ring theory, or field theory. Topics may include Abelian groups, cyclic groups, permutation groups, factor groups, ideals, quotient rings, integral domains, isomorphisms, and homomorphisms. Additional topics may be included. Prerequisites: 31326100. 4 credits. (F,Y) 31330500 Introduction to Analysis NS LA Topology of the real line. Continuity, differentiability, and integrability of functions of a real variable. Prerequisites: 31321100; 31326100. 4 credits. (S,Y) 31331600 Probability/Statistics NS LA Specific content varies. Topics may include some of the following: probability systems; random variables, their distributions and expected values; Poisson and the theory of Markov processes; estimation theory (point, interval, and Bayesian inference); hypothesis testing; regression theory; correlation; and time series. Prerequisites: 31321100; 31326100. 4 credits. (F,O) 31334000 Operations Research NS LA Emphasis is placed on mathematics used in applications. Specific content varies. Topics may include some of the following: mathematical modeling such as linear programming, dynamic programming, applied Markov processes, queuing theory;, and game theory; numerical analysis, such as numerical solutions of linear and nonlinear equations, interpolation, numerical differentiation and integration, numerical solutions to differential equations, and functional approximations; simulation such as Monte Carlo methods, continuous models, discrete events, random number generation, and statistical output analysis; applied graph theory; applied statistics; and applied dynamical systems. Prerequisites: 31321100; 31326100. 4 credits. (S,O) 31336200 Modern Geometry NS LA Rigorous development of Euclidean and hyperbolic geometry from both a metric and synthetic point of view. Some topics in transformational geometry are also covered. Prerequisites: 31326100; one course at the level of 31321200 or higher, excluding 31326000. 4 credits. (F,E) 31339000 Selected Topics in Mathematics NS LA Topics to be determined by instructors and department. Fulfills a required mathematics elective. This course may be repeated for credit when topics vary. Prerequisites: 31326100 or equivalent; other prerequisites as appropriate to topics. 14 credits. (IRR) 31339100 Independent Study U LA Reading on selected subjects with frequent, informal discussions with the instructor. This course may be repeated for credit for different studies. Does not fulfill a required mathematics elective. Prerequisites: 31326100 or equivalent. 13 credits. (IRR) 31339200 Independent Study U LA Reading on selected subjects with frequent, informal discussions with the instructor. Fulfills a required mathematics elective. This course may be repeated for credit for different studies. Prerequisites: 31326100, or equivalent. 13 credits. (IRR) 31339500 Selected Topics in Mathematics NS LA Topics to be determined by instructors and department. This course may be repeated for credit for selected topics on different subjects. Does not fulfill a required mathematics elective. Prerequisites: 31326100 or equivalent; other prerequisites as appropriate to topics. 14 credits. (FS,Y) 31339700 Junior Seminar NS LA Students will work with faculty on focused mathematical investigations. Research problems will be presented by faculty teaching 31339810 Research Experience in Mathematics. Students will attend a variety of talks related to mathematics. Weekly problem solving related to research topics. Prerequisites: 31329100. Pass/fail only. 1 credit. (F, Y) 31339810 Research Experience in Mathematics NS LA Students actively participate in mathematical investigation and exposition, working collaboratively on research questions. Review of relevant literature and research methods will be incorporated. Students are required to present their findings both in writing (consistent with the standards of the discipline) and in public presentations. Topics vary by instructor. Prerequisites: 31339700; permission of instructor. 3 credits. (S,Y) 31340100 Selected Topics in Theoretical Continuous Mathematics NS LA Emphasis is on mathematical topics in which the concept of continuity plays a key role. Specific content varies. Topics may include, but are not limited to, the following: topology, such as pointset topology, metric topology, geometric topology, differential topology, and manifold theory; advanced real analysis, such as sequences and series of functions, convergence of functions, integration theory; topology of the real line, function theory; complex analysis such as analytic functions, conformal mappings, elementary functions and power series, complex integration and calculus of residues; advanced differential equations, such as ordinary equations of first and higher orders, singular solutions, total differential equations, and solution by series; fractal geometry; and continuous dynamical systems. Prerequisites: At least one level3 mathematics course; permission of the instructor. 4 credits. (S,E) 31340200 Selected Topics in Theoretical Discrete Mathematics NS LA Emphasis is placed on mathematical topics principally concerned with discrete entities. Specific content varies. Topics may include, but are not limited to, the following: number theory, such as properties of integers, diophantine equations, congruence, and quadratic reciprocity; algebra, such as advanced topics in group, ring, and field theory, automorphisms, and Galois theory; graph theory; discrete dynamical systems; and combinatorics. Prerequisites: 31330300. 4 credits. (S,O) 31344000 Selected Topics in Applied Mathematics NS, LA Emphasis is on mathematics in an applied setting. Topics may include, but are not limited to, the following: stochastic processes, actuarial mathematics, partial differential equations and applied dynamical systems, numerical analysis, and applied statistics. Prerequisites: At least one level3 mathematics course. 4 credits. (F,E) 31348000 Connections in Advanced Mathematics NS LA Study of connections and relationships among various disciplines within mathematics. Specific content varies. Topics may include, but are not limited to, the following: historical development of mathematics and various philosophies of mathematics, cultural similarities and differences in viewpoints and developments in mathematics, crossdiscipline approaches that combine subdisciplines such as probability techniques in number theory and random graph theory, field theory and geometric constructions, and algebraic topology. Prerequisites: At least one level3 course in mathematics or the related discipline; permission of instructor. 4 credits. (S,E) 31349000 Selected Topics in Advanced Mathematics NS LA Topics to be selected by instructor and students. Fulfills a required mathematics elective. This course may be repeated for credit when topics vary. Prerequisites: 31326100 or equivalent; other prerequisites as appropriate to topics. 3 credits. (IRR) 31349100 Independent Study U LA Reading on selected advanced subjects, with frequent, informal discussions with the instructor. Does not fulfill a required mathematics elective. This course may be repeated for credit. Prerequisites: Permission of instructor. 13 credits. 31349200 Independent Study U LA Reading on selected advanced subjects, with frequent, informal discussions with the instructor. Fulfills a required mathematics elective. This course may be repeated for credit. Prerequisites: Permission of instructor. 13 credits. 3134930031349400 Honors Course NS LA Preparation of honors thesis in partial fulfillment of requirement for graduation with honors in mathematics. Prerequisites: Honors standing in mathematics. 12 credits. (IRR) 31349500 Selected Topics in Advanced Mathematics NS LA Topics to be selected by instructor and students. Does not fulfill a required mathematics elective. This course may be repeated for credit when topics vary. Prerequisites: 31326100 or equivalent; other prerequisites as appropriate to topics. 3 credits. 

A. Ozolins, Office of Creative Services, 15. July, 2005 