This course provides an introduction to contemporary mathematics and its applications. It may include topics from management science, statistics, social choice, the geometry of size and shape, and mathematics for computer science. These topics are chosen for their basic mathematical importance and for the critical role their application plays in a person's economic, political, and personal life. This course is designed to be accessible even to students with a minimal background in mathematics. This course is not designed to prepare students for further work in mathematics. No credit will be given for MATH 103 if the student has prior credit for another mathematics course that is equivalent to any of our courses numbered Math 110 or higher. Unlike most other introductory mathematics classes, this course is not a requirement for any currently offered major. Therefore, students are advised not to take this class before deciding on a major.

Prerequisites
One year of high school mathematics. No credit will be given for MATH 103 if if the student has prior credit for another mathematics course that is equivalent to any course numbered MATH 110 or higher.
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Mathematical Approaches

This course presents the basic concepts of algebra and trigonometry needed for future courses in mathematics, science, business, or the behavioral and social sciences. It includes a review of elementary algebra, introduction to algebraic functions, exponential and logarithmic functions, and trigonometric functions.

Prerequisites
Three years of high school mathematics. Students who have MATH 110 transfer credit may not take this course

This course provides an introduction to the theory of linear systems and discrete probability with applications from business and the physical and social sciences. The study of linear systems includes a discussion of matrix theory and linear programming. The concepts from linear systems and probability are integrated in the study of Markov Chains and Game Theory. This course contains topics of particular interest to students studying business or business-related topics. It is an excellent choice for such students who are also seeking a minor in mathematics.

Prerequisites
Three years of high school mathematics.
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Mathematical Approaches

This course provides an introduction to statistics, concentrating on statistical concepts and the "why and when" of statistical methodology. The course focuses on learning to ask appropriate questions, collect data effectively, summarize and interpret information, and understand the limitations of statistical inference.

Students with Advanced Placement credit for MATH 160 should consider enrolling in MATH 260.

Prerequisites
Three years of high school mathematics. Students who have MATH 160 transfer credit may not take this course
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Mathematical Approaches

This course takes a problem-solving approach to the concepts and techniques of single variable differential calculus, with an introduction to multivariate topics. Applications are selected primarily from business and the behavioral and social sciences.

Prerequisites
Three years of high school mathematics. Students will not receive credit for MATH 170 if they have already received credit for MATH 180, 181, or 280, without prior permission of the department.
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Mathematical Approaches

There are two main topics in the calculus for functions of one variable: differentiation and integration. This course focuses on differentiation starting with limits and continuity, then introduces the derivative, and applications of the derivative in a variety of contexts. The course concludes with and introduction to integration. The central ideas are explored from the symbolic, graphic, numeric, and physical model points of view.

Prerequisites
MATH 110 or equivalent with C- or higher. Students who have MATH 180 transfer credit may not take this course.
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Mathematical Approaches

This course is a continuation of MATH 180. It focuses on integration and its relation to differentiation. Topics include definite integrals, antiderivatives, the Fundamental Therorems of Calculus, applications of integration, sequences, and series. The central ideas are explored from the symbolic, graphic, numeric, and physical model points of view.

Prerequisites
MATH 180 with a grade of C- or higher, or its equivalent. Students who have MATH 18X Second Qtr Calculus or MATH 18X Calculus II Online transfer credit may not take this course.
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Mathematical Approaches

An introduction to the mathematics underlying computer science. Topics include a review of basic set theory, logic (propositional and predicate), theorem proving techniques, logic as a method for representing information, equivalence relations, induction, combinatorics, and graph theory, and possibly formal languages and automata.

Prerequisites
CSCI 161 with a grade of C- or higher.

This course covers the fundamentals of conducting statistical analyses, with particular emphasis on regression analysis and linear models. Students learn to use sophisticated computer software as a tool to analyze and interpret data.

Prerequisites
MATH 160, MATH 181, PSYC 201, Advanced Placement Statistics, or the equivalent of one of these.
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Mathematical Approaches

This course, a continuation of the calculus sequence that starts with MATH 180 and 181, is an introduction to the study of functions that have several variable inputs and/or outputs. The central ideas involving these functions are explored from the symbolic, the graphic, and the numeric points of view. Visualization and approximation, as well as local linearity continue as key themes in the course. Topics include vectors and the basic analytic geometry of three-space; the differential calculus of scalar-input, vector-output functions; the geometry of curves and surfaces; and the differential and integral calculus of vector-input, scalar-output functions.

Prerequisites
MATH 181 or its equivalent with a grade of C- or higher.
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Mathematical Approaches

This course is a study of the basic concepts of linear algebra, and includes an emphasis of developing techniques for proving theorems. Students will explore systems of linear equations, matrices, vector spaces, bases, dimension, linear transformations, determinants, eigenvalues, change of basis, and matrix representations of linear transformations.

Prerequisites
MATH 181 or its equivalent with a grade of C- or higher. Students with transfer credit for MATH 29X (i.e., MATH 290 online) may not take this course.

In this class students and faculty discuss problems that cut across the boundaries of the standard courses and investigate general strategies of problem solving. Students are encouraged to participate in a national mathematics competition. This class meets one hour a week, is graded only on a pass/fail basis, is a 0 credit course, and may be repeated.

In this class students are given examples of problems from an annual international mathematical modeling contest. The students, in groups and with faculty mentoring, develop approaches to the problems. The students and faculty also discuss winning solutions to the problems. The students are expected to participate in the contest and give a presentation of their solution. The course meets once per week, is graded on a pass/fail basis, is a 0 credit course, and can be repeated.

Prerequisites
MATH 280 and 290 or permission of the instructor. All prerequisite courses must have been completed with a grade of C- or higher.

Ordinary differential equations (ODEs) are first introduced in the calculus sequence. This course provides a deeper look at the theory of ODEs and the use of ODEs in modeling real-world phenomena. The course includes studies of first order ODEs (both linear and nonlinear), second and higher order linear ODEs, and first order systems of ODEs (both linear and nonlinear). Existence and uniqueness of solutions is discussed in each setting. Most topics are viewed from a variety of perspectives including graphical, numerical, and symbolic. Tools and concepts from linear algebra are used throughout the course. Other topics that may be covered include series solutions, difference equations, and dynamical systems.

Prerequisites
MATH 280 and 290 or permission of the instructor. All prerequisite courses must have been completed with a grade of C- or higher. Students with transfer credit for MATH 30X (i.e., MATH 301 online) may not take this course.

This course introduces partial differential equations, how they arise in certain physical situations, and methods of solving them. Topics of study include the heat equation, the wave equation, Laplace's Equation, and Fourier Series with its applications to partial differential equations and boundary value problems. Additional topics may include Green's Functions, the Fourier Transform, the method of characteristics, dispersive waves, and perturbation methods.

Prerequisites
MATH 301 or equivalent with a grade of C- or higher.

Students learn about numerical solutions to linear systems; numerical linear algebra, polynomial approximations (interpolation and extrapolation); numerical differentiation and integration. Students also learn about error analysis and how to select appropriate algorithms for specific problems.

Prerequisites
MATH 280, 290, and CSCI 161 or equivalent. All prerequisite courses must have been completed with a grade of C- or higher.

This course is about how to find the best - or at least good - solutions to large problems frequently arising in business, industrial, or scientific settings. Students learn how to model these problems mathematically, algorithms for finding solutions to them, and the theory behind why the algorithms work. Topics include the simplex method, duality theory, sensitivity analysis, and network models. The focus is on linear models and models with combinatorial structure, but some nonlinear models are considered as well. Optimization software is used frequently.

Prerequisites
MATH 280, 290, and CSCI 161 or equivalent. All prerequisite courses must have been completed with a grade of C- or higher.

This course entails study of the basic principles of combinatorial analysis. Topics include combinations, permutations, inclusion-exclusion, recurrence relations, generating functions, and graph theory. Additional material may be chosen from among the following topics: Latin squares, Hadamard matrices, designs, coding theory, and combinatorial optimization. Satisfies the proof-based requirement in the mathematics major.

Prerequisites
MATH 290 with grade of C- or higher

This course entails the study of the properties of numbers, with emphasis on the positive integers. Topics include divisibility, factorization, congruences, prime numbers, arithmetic functions, quadratic residues, and Diophantine equations. Additional topics may include primitive roots, continued fractions, cryptography, Dirichlet series, binomial coefficients, and Fibonacci numbers. Satisfies the proof-based requirement in the mathematics major.

Prerequisites
MATH 290 with grade of C- or higher

This course covers the basics of point-set topology. The course focuses on what type of structures need to be placed on a set in order to make it a "topological space" and what properties are deduced from these structures. Topics include open and closed sets, continuity, compactness, connectedness, and a selection of topics from metric spaces, manifolds, functions spaces or quotient spaces. Satisfies the proof-based requirement in the mathematics major.

Prerequisites
MATH 290 with grade of C- or higher

This course is an introduction to the application of calculus and linear algebra to the geometry of curves and surfaces. Topics include the geometry of curves, Frenet formulas, tangent planes, normal vectors and orientation, curvature, geodesics, metrics, and isometries. Additional topics may include the Gauss-Bonnet Theorem, minimal surfaces, calculus of variations, and hyperbolic geometry. After completion, students will have the background to begin studying further mathematical and theoretical physics topics such as Riemannian geometry, differential topology, general relativity, and gauge theory. Students will additionally develop their mathematical intuition and ability to use calculations and proofs to verify theorems and solve problems. Satisfies the proof-based requirement in the major contracts and the standard major.

Prerequisites
MATH 280 and 290 or equivalents. All prerequisite courses must have been completed with a grade of C- or higher.

This course covers advanced methods in applied statistics, beyond those of Mathematics 260. The emphasis is on applied aspects of generalized linear models, which provide a framework for analyzing some types of data for which ordinary linear models are not suitable. The analyses will be conducted using R, so students entering the course should already have a working knowledge of R. Topics other than generalized linear models are included as time allows, such as: time series analysis, categorical data analysis, and statistical graphics.

Prerequisites
MATH 260 with a grade of C- or higher, the equivalent, or permission of the instructor.

This course provides an introduction to the standard topics of probability theory, including probability spaces, random variables and expectations, discrete and continuous distributions, generating functions, independence and dependence, special probability models, sampling distributions, laws of large numbers, and the central limit theorem. The course emphasizes modeling real-world phenomena throughout. Satisfies the proof-based requirement in the mathematics major.

Prerequisites
MATH 280 and 290 or equivalents. All prerequisite courses must have been completed with a grade of C- or higher.

This course introduces the theory of linear regression and uses it as a vehicle to investigate the mathematics behind applied statistics. The theory combines probability theory and linear algebra to arrive at commonly used results in statistics. The theory helps students understand the assumptions on which these results are based and decide what to do when these assumptions are not met, as it usually the case in applied statistics. Satisfies the proof-based requirement in the mathematics major.

Prerequisites
MATH 375 or equivalent with a grade of C- or higher.

The calculus of functions with complex numbers as inputs and outputs has surprising depth and richness. The basic theory of these functions is developed in this course. The standard topics of calculus (function, limit, continuity, derivative, integral, series) are explored in this new context of complex numbers leading to some powerful and beautiful results. Applications include using conformal mappings to solve boundary-value problems for Laplace's equation.

Prerequisites
MATH 280 and 290 or permission of the instructor. All prerequisite courses must have been completed with a grade of C- or higher.

This course begins as a review and continuation of MATH 290: Linear Algebra. Topics covered include invariant subspaces, Jordan canonical form, and rational canonical forms of linear transformations. The remainder of the course is split between advanced topics and applications. Advanced topics include decompositions (such as the LU decomposition), principal axis theorem, alternate definitions of the determinant, singular values, and quadratic forms. Applications include topics such as least-squares fit, error-correcting codes, linear programming, physical problems employing eigenvalues, Markov chains, and secret sharing.

Prerequisites
MATH 290 with grade of C- or higher

This course allows students to explore mathematical topics beyond those covered in the standard mathematics curriculum. Some semester-long topics include combinatorics, number theory, numerical analysis, and topology. See the department website for further information on topics to be offered during the next two years, including the prerequisites for each topic. The course may be repeated on a different topic for credit. Prerequisites vary with topic.

A study of the process of mathematical modeling as well as specific deterministic (both discrete and continuous) and stochastic models. Certain mathematical topics such as graph theory are developed as needed.

Prerequisites
MATH 280 and 290; MATH 375 recommended. All prerequisite courses must have been completed with a grade of C- or higher.

This course provides a rigorous study of calculus. The course begins with a study of the real numbers and then moves on to the core topics of limits, continuity, differentiation, integration, and series. In the first semester, the focus is on functions of one variable; in the second semester, the focus is on scalar- and vector-valued functions of several variables. Additional topics may include differential geometry of curves and surfaces or vector calculus.

Prerequisites
MATH 280 and 290 or equivalents. All prerequisite courses must have been completed with a grade of C- or higher.

This course provides a rigorous study of calculus. The course begins with a study of the real numbers and then moves on to the core topics of limits, continuity, differentiation, integration, and series. In the first semester, the focus is on functions of one variable; in the second semester, the focus is on scalar- and vector-valued functions of several variables. Additional topics may include differential geometry of curves and surfaces or vector calculus.

Prerequisites
MATH 280, 290, and 321 or equivalents. All prerequisite courses must have been completed with a grade of C- or higher.

These courses present a rigorous treatment of modern algebra. The writing of proofs is emphasized. Modern applications of abstract algebra to problems in chemistry, art, and computer science show this is a contemporary field in which important contributions are currently being made. Topics include groups, rings, integral domains, field theory, and the study of homomorphisms. Applications such as coding theory, public-key cryptography, crystallographic groups, and frieze groups may be covered. These are proof-based courses.

Prerequisites
MATH 290 with a grade of C- or higher, or permission of instructor.

These courses present a rigorous treatment of modern algebra. The writing of proofs is emphasized. Modern applications of abstract algebra to problems in chemistry, art, and computer science show this is a contemporary field in which important contributions are currently being made. Topics include groups, rings, integral domains, field theory, and the study of homomorphisms. Applications such as coding theory, public-key cryptography, crystallographic groups, and frieze groups may be covered. These are proof-based courses.

Prerequisites
MATH 290 with a grade of C- or higher, or permission of instructor.

A senior thesis allows students to explore areas of mathematics that are new to them, to develop the skill of working independently on a project, and to synthesize and present a substantive work to the academic community. Thesis proposals are normally developed in consultation with the student's research committee. This committee consists of the student's faculty supervisor and two other faculty members. It is involved in the final evaluation of the project. The results are presented in a public seminar or written in a publishable form.

Prerequisites
At least 4 upper-division (300-400 level) courses by the end of the junior year, or completion of the major by the end of the fall term of the senior year. The student should have a GPA of at least 3.5 in all major courses numbered 300 or above.

A senior thesis allows students to explore areas of mathematics that are new to them, to develop the skill of working independently on a project, and to synthesize and present a substantive work to the academic community. Thesis proposals are normally developed in consultation with the student's research committee. This committee consists of the student's faculty supervisor and two other faculty members. It is involved in the final evaluation of the project. The results are presented in a public seminar or written in a publishable form.

Prerequisites
At least 4 upper-division (300-400 level) courses by the end of the junior year, or completion of the major by the end of the fall term of the senior year. The student should have a GPA of at least 3.5 in all major courses numbered 300 or above.

Independent study is available to those students who wish to continue their learning in an area after completing the regularly offered courses in that area.

Prerequisites
Junior or senior class standing and cumulative grade average of 3.0.

Independent study is available to those students who wish to continue their learning in an area after completing the regularly offered courses in that area.

Prerequisites
Junior or senior class standing and cumulative grade average of 3.0.

This scheduled weekly interdisciplinary seminar provides the context to reflect on concrete experiences at an off-campus internship site and to link these experiences to academic study relating to the political, psychological, social, economic and intellectual forces that shape our views on work and its meaning. The aim is to integrate study in the liberal arts with issues and themes surrounding the pursuit of a creative, productive, and satisfying professional life. Students receive 1.0 unit of academic credit for the academic work that augments their concurrent internship fieldwork. This course is not applicable to the Upper-Division Graduation Requirement. Only 1.0 unit may be assigned to an individual internship and no more than 2.0 units of internship credit, or internship credit in combination with co-operative education credit, may be applied to an undergraduate degree.

Prerequisites
Junior or senior standing, 2.5 GPA, ability to complete 120 hours at internship site, approval of the CES internship coordinator, and completion of learning agreement.