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 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.

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 and an introduction to algebraic functions, exponential and logarithmic functions, and trigonometric functions.

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 matrices 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.

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 instead.

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.

Single-variable calculus has two main aspects: 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 an introduction to integration. The central ideas are explored from the symbolic, graphical, numerical, and physical model points of view.

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

This course provides 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.

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.

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 graphical, and the numerical 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.

This course is a study of the basic concepts of linear algebra and their applications. 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.

In this class, students and faculty discuss problems that cut across the boundaries of the standard courses, and they 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.

This course covers the fundamentals of point-set topology in a way that also serves to introduce the fundamentals of theoretical mathematics, with a particular focus on writing clear and rigorous mathematical proofs. Building on calculus and high school geometry, the course explores standard topics in point-set topology, including basic properties of topological spaces, open sets, continuous functions, topological equivalence, connectedness, compactness, and metric spaces. These are then used to prove fundamental theorems in point-set topology, including a specific case of Brouwer's fixed point theorem. This course also introduces mathematical logic and standard mathematical proof techniques such as direct proofs, proof by contradiction, and mathematical induction, and develops strategies and methods for problem solving and proof writing. The power of mathematical abstraction is emphasized throughout the course, and the course features illustrative examples of how to develop and apply such abstraction. Students will be given opportunities to practice what they have learned and communicate their mathematical findings effectively. After completing this course, students will have a deeper understanding of the mathematics they had previously encountered and will be better prepared to take other courses in theoretical mathematics. This course is a prerequisite for all other courses in the department that focus on theoretical mathematics.

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.

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.

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.

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.

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.

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.

Building on the foundation of point-set topology, this course introduces more advanced topics in topology such as metric spaces, quotient spaces, covering spaces, homotopy, the fundamental group, mathematical knots, and manifolds.

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.

This course covers advanced methods in applied statistics, beyond those of MATH 260. The analyses will be conducted using R, so students entering the course should already have a working knowledge of R. Topics may include generalized linear models, Bayesian statistics, time series analysis, categorical data analysis, and/or statistical graphics.

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, sampling distributions, laws of large numbers, and the central limit theorem. The course emphasizes modeling real-world phenomena throughout.

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 is usually the case in applied statistics.

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.

This course begins as a review and continuation of MATH 290. 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.

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.

This course is 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.

This course provides a rigorous study of the theory behind 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. The focus is on functions of one variable.

This course continues the rigorous study of the theory behind calculus, focusing on scalar- and vector-valued functions of several variables. Additional topics may include differential geometry of curves and surfaces or vector calculus.

This course presents a rigorous study of abstract algebra, with an emphasis on writing proofs. 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 also be covered.

This course continues the rigorous study of abstract algebra, with an emphasis on writing proofs. It continues where MATH 490 leaves off and may include topics such as extension fields and Galois theory.

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, which consists of the student's faculty supervisor and two other faculty members. This committee is involved in the final evaluation of the project. The results of the project are presented in a public seminar and/or written in a publishable form.

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, which consists of the student's faculty supervisor and two other faculty members. This committee is involved in the final evaluation of the project. The results of the project are presented in a public seminar and/or written in a publishable form.

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.

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.

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.