This course, for students in the humanities, the social sciences, School of Education, and School of Nursing, is an introduction to finite combinatorics and probability, emphasizing applications. Topics include finite sets and partitions, enumeration, probability, expectation, and random variables.

Last Updated: 30-JAN-12

This course is designed to introduce the student to the spirit, beauty, and vitality of mathematics. The emphasis is on development of ideas rather than problem solving skills. Topics vary, but are typically chosen from diverse areas such as geometry, number theory, computation, and graph theory.

Last Updated: 30-JAN-12

MT 100 is a first course in the calculus of one variable intended for biology, computer science, economics, management, and premedical students. It is open to others who are qualified and desire a more rigorous mathematics course at the core level. Topics include a brief review of polynomials and trigonometric, exponential, and logarithmic functions, followed by discussion of limits, derivatives, and applications of differential calculus to real-world problem areas. The course concludes with an introduction to integration.

Last Updated: 25-SEP-12

MT 101 is a second course in the calculus of one variable intended for biology, computer science, economics, management, and premedical students. It is open to others who are qualified and desire a more rigorous mathematics course at the core level. Topics include an overview of integration, basic techniques for integration, a variety of applications of integration, and an introduction to (systems of) differential equations.

Last Updated: 25-SEP-12

MT 102 is a first course in the calculus of one variable intended for Chemistry, Computer Science/B.S., Geology, Geophysics, Mathematics, and Physics majors. It is open to others who are qualified and desire a more rigorous calculus course than MT 100. Topics covered include the algebraic and analytic properties of the real number system, functions, limits, derivatives, and an introduction to integration.

Last Updated: 30-JAN-12

MT 103 is a continuation of MT 102. Topics covered in the course include several algebraic techniques of integration, many applications of integration, and infinite sequences and series.

Last Updated: 30-JAN-12

MT 105 is a second course in the calculus of one variable intended for Chemistry, Computer Science/B.S.,Environmental Geosciences, Geological Sciences, Mathematics, and Physics majors. It is designed for students who have completed either MT 101 or a year of Calculus in high school at either the AB or BC curriculum level, but who are not yet prepared to advance to MT 202 Multivariable Calculus. The course first reviews the primary techniques and interesting applications of integration. The remainder of the course provides an introduction to the topics of infinite sequences and series. Other topics may be introduced as time permits.

Last Updated: 25-SEP-12

Recitation section, corequisite to MT 100. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week. Each section of MT 100 has a specific corequisite recitation, numbered MT 121-MT 135; students should sign up for the recitation that matches the corequisite listed in the section of MT 100 they select.

Last Updated: 30-JAN-12

Recitation section, corequisite to MT 101. Discussion of problem-solving techniques, examples, and homework in a small-class setting. One hour per week. Each section of MT 101 has a specific corequisite recitation, numbered MT 141-MT 145; students should sign up for the recitation that matches the corequisite listed in the section of MT 101 they select.

Last Updated: 31-JAN-12

Last Updated: 17-FEB-12

Last Updated: 17-FEB-12

This course introduces statistics as a liberal arts discipline and applies the principles of statistics to problems of interest to health sciences professionals. Students will gain an understanding of statistical ideas and methods, acquire the ability to deal critically with numerical arguments, and gain an understanding of the impact of statistical ideas on the health sciences, public policy, and other areas of application.

Last Updated: 31-OCT-11

MT 190-191 is a course sequence designed for those who plan to teach mathematics in grades K-8. The emphasis is on building conceptual understanding of the mathematics present in the emerging K-8 curriculum and on deepening content knowledge. Number and number systems through the real number system will be studied; functions and the structure of algebra will be developed. Problem solving and reasoning, applications, and making connections will be featured.

Last Updated: 30-JAN-12

As in MT 190, the course emphasizes building conceptual understanding of the mathematics present in the emerging K-8 curriculum and on deepening the content knowledge. Topics drawn from geometry and measurement, data analysis, statistics, and probability will be developed. Problem solving and reasoning, applications, and making connections will be featured.

Last Updated: 30-JAN-12

Topics in this course include vectors in two and three dimensions, analytic geometry of three dimensions, parametric curves, partial derivatives, the gradient, optimization in several variables, multiple integration with change of variables across different coordinate systems, line integrals, and Green's Theorem.

Last Updated: 31-JAN-12

Last Updated: 31-JAN-12

This course is intended for students with strong preparation and high motivation. Topics covered include matrices, linear equations, determinants, eigenvectors and eigenvalues, vector spaces and linear transformations, inner products, and canonical forms. The course will include significant work with proofs.

Last Updated: 07-DEC-12

This honors course in Linear Algebra is intended for students with strong preparation and high motivation. Topics covered include matrices, linear equations, determinants, eigenvectors and eigenvalues, vector spaces and linear transformations, inner products, and canonical forms. The course will include significant work with proofs.

Last Updated: 11-NOV-13

Last Updated: 30-JAN-12

Last Updated: 17-FEB-12

This course is intended to fill a basic need of all teachers of grades K-9. Geometry now occupies a significant role in the elementary mathematics curriculum. The course will treat content, but ideas for presenting geometry as an activity-based program will also be stressed. Topics to be covered include the geoboard and other key manipulatives, elements of motion and Euclidean geometry, and suggestions for using Logo as a tool to enhance teaching geometry.

Last Updated: 30-JAN-12

MT 305 is required for Geology-Geophysics, Geophysics, and Physics majors. It is also recommended for Chemistry majors. Topics include linear second order differential equations, series solutions of differential equations including Bessel functions and Legendre polynomials, and solutions of the diffusion and wave equations in several dimensions.

Last Updated: 25-SEP-12

This course studies four fundamental algebraic structures: groups, including subgroups, cyclic groups, permutation groups, symmetry groups and Lagrange's Theorem; rings, including sub-rings, integral domains, and unique factorization domains; polynomials, including a discussion of unique factorization and methods for finding roots; and fields, introducing the basic ideas of field extensions and ruler and compass constructions.

Last Updated: 30-JAN-12

This course, with MT 312, studies the basic structures of abstract algebra. Topics include groups, subgroups, factor groups, Lagrange's Theorem, the Sylow Theorems, rings, ideal theory, integral domains, field extensions, and Galois theory.

Last Updated: 30-JAN-12

This course, with MT 311, studies the basic structures of abstract algebra. Topics include groups, subgroups, factor groups, Lagrange's Theorem, the Sylow Theorems, rings, ideal theory, integral domains, field extensions, and Galois theory.

Last Updated: 30-JAN-12

The purpose of this course is to give students the theoretical foundations for the topics taught in MT 102-103. It will cover algebraic and order properties of the real numbers, the least upper bound axiom, limits, continuity, differentiation, the Riemann integral, sequences, and series. Definitions and proofs will be stressed throughout the course.

Last Updated: 30-JAN-12

This course, with MT 322, studies the basic structure of the real numbers. Topics include the least upper bound principle, compactness of closed intervals (the Heine-Borel theorem), sequences, convergence, the Bolzano-Weierstrass theorem, continuous functions, boundedness and intermediate value theorems, uniform continuity, differentiable functions, the mean value theorem, construction of the Riemann integral, the fundamental theorem of calculus, sequences and series of functions, uniform convergence, the Weierstrass approximation theorem, special functions (exponential and trig), and Fourier series.

Last Updated: 30-JAN-12

This course, with MT 321, studies the basic structure of the real numbers. Topics include the least upper bound principle, compactness of closed intervals (the Heine-Borel theorem), sequences, convergence, the Bolzano-Weierstrass theorem, continuous functions, boundedness and intermediate value theorems, uniform continuity, differentiable functions, the mean value theorem, construction of the Riemann integral, the fundamental theorem of calculus, sequences and series of functions, uniform convergence, the Weierstrass approximation theorem, special functions (exponential and trig), and Fourier series.

Last Updated: 30-JAN-12

This course is a junior-senior elective intended primarily for the general student who is interested in seeing applications of mathematics. Among the topics covered will be the following: first order linear equations, higher order linear equations with constant coefficients, linear systems, qualitative analysis of non-linear systems, and an introduction to stability and bifurcations.

Last Updated: 10-JUL-12

This course investigates the classical partial differential equations of applied mathematics (diffusion, Laplace/ Poisson, and wave) and their methods of solution (separation of variables, Fourier series, transforms, Green's functions, and eigenvalue applications). Additional topics will be included as time permits.

Last Updated: 31-OCT-11

Topics include the solution of linear and nonlinear algebraic equations, interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, and approximation theory.

Last Updated: 30-JAN-12

This course provides a general introduction to modern probability theory. Topics include probability spaces, discrete and continuous random variables, joint and conditional distributions, mathematical expectation, the central limit theorem, and the weak law of large numbers. Applications to real data will be stressed, and we will use the computer to explore many concepts.

Last Updated: 30-JAN-12

Topics studied include the following: sampling distributions, parametric point and interval estimation, hypothesis testing, goodness-of-fit, and parametric and nonparametric two-sample analysis. Applications to real data will be stressed, and the computer will be used to explore concepts and analyze data.

Last Updated: 30-JAN-12

Topics covered include divisibility, unique factorization, congruences, number-theoretic functions, primitive roots, diophantine equations, continued fractions, quadratic residues, and the distribution of primes. An attempt will be made to provide historical background for various problems and to provide examples useful in the secondary school curriculum.

Last Updated: 11-NOV-13

This course demonstrates how mathematical theory can be developed and applied to solve problems from management, economics, and the social sciences. Topics studied from linear programming include a general discussion of linear optimization models, the theory and development of the simplex algorithm, degeneracy, duality, sensitivity analysis, and the dual simplex algorithm. Integer programming problems and the transportation and assignment problems are considered, and algorithms are developed for their resolution. Other topics are drawn from game theory, dynamic programming, Markov decision processes (with finite and infinite horizons), network analysis, and non-linear programming.

Last Updated: 30-JAN-12

This course is an introduction to graph theory and combinatorics, with a strong emphasis on creative problem-solving techniques and connections with other branches of mathematics. Topics will center around the following: enumeration, Hamiltonian and Eulerian cycles, extremal graph theory, planarity, matching, colorability, Ramsey theory, hypergraphs, combinatorial geometry, and applications of linear algebra, probability, polynomials, and topology to combinatorics. Prerequisite: MT216 Pre/corequisite MT210

Last Updated: 14-MAR-13

This course surveys the history and foundations of geometry from ancient to modern times. Topics will be selected from among the following: Mesopotamian and Egyptian mathematics, Greek geometry, the axiomatic method, history of the parallel postulate, the Lobachevskian plane, Hilbert's axioms for Euclidean geometry, elliptic and projective geometry, the trigonometric formulas, models, and geometry and the study of physical space.

Last Updated: 30-JAN-12

Last Updated: 30-JAN-12

This course is designed to deepen students' mathematical knowledge through solving, explaining, and extending challenging and interesting problems. Students will work both individually and in groups on problems chosen from polynomials, trigonometry, analytic geometry, pre-calculus, one-variable calculus, probability, and numerical algorithms. The course will emphasize explanations and generalizations rather than formal proofs and abstract properties. Some pedagogical issues, such as composing good problems and expected points of confusion in explaining various topics, will come up, but the primary goal is mathematical insight. The course will be of particular use to future secondary math teachers.

Last Updated: 30-JAN-12

This course gives an introduction to the theory of functions of a complex variable, a fundamental and central area of mathematics. It is intended for mathematics majors and well-prepared science majors. Topics covered include: complex numbers and their properties, analytic functions and the Cauchy-Riemann equations, the logarithm and other elementary functions of a complex variable, integration of complex functions, the Cauchy integral theorem and its consequences, power series representation of analytic functions, and the residue theorem and applications to definite integrals.

Last Updated: 30-JAN-12

This course studies the development of mathematical thought, from ancient times to the twentieth century. Naturally, the subject is much too large for a single semester, so we will concentrate on the major themes and on the contributions of the greatest mathematicians. The emphasis in the course will be on the mathematics. Students will follow the historical arguments and work with the tools and techniques of the period being studied.

Last Updated: 11-NOV-13

Although statistical methods have become the analytical methods of choice in areas as diverse as biomedical and environmental sciences, geophysics, education, psychology, sociology, political science, physics, astronomy, and communications, they are often misunderstood and misused. In this course we will study intermediate statistics from several viewpoints, including classical methods, graphical methods, and modern computer-intensive methods. The multiple approach to learning should give you a deeper understanding and appreciation for the field of statistics. Applications will be emphasized throughout the course. Specific topics include nonparametric, permutation and bootstrap methods; multiple sample analysis; least squares analysis; contingency table analysis.

Last Updated: 10-NOV-13

Last Updated: 31-JAN-12

This is an independent study course, taken under the supervision of a Mathematics Department faculty member. Interested students should see the Assistant Chair for Undergraduates.

Last Updated: 31-JAN-12

Last Updated: 31-OCT-11

Last Updated: 31-OCT-11

Last Updated: 31-OCT-11

Last Updated: 31-OCT-11

Last Updated: 31-OCT-11

Last Updated: 31-OCT-11

Last Updated: 05-JUL-12

Last Updated: 25-SEP-12

Last Updated: 31-OCT-11

Last Updated: 31-OCT-11

This course will present some of the basic theorems about Riemann Surfaces from a modern point of view. Time permitting, topics will include the definition of a Riemann Surface (RS), branched coverings and topological properties of RS's, cohomology, the Riemann-Roch Theorem, the relationship between RSs and algebraic curves over the complex numbers, and uniformization.

Last Updated: 31-OCT-11

Selected topics in the theory of Fuchsian Groups with emphasis on connections to the study of manifolds and orbifolds.

Last Updated: 31-OCT-11

Selected topics in Geometry and Topology.

Last Updated: 31-OCT-11

Last Updated: 31-OCT-11

Last Updated: 31-OCT-11

Last Updated: 31-OCT-11

This is an independent study course, taken under the supervision of a Mathematics Department faculty member. Interested students should see the Director of the Graduate Program.

Last Updated: 31-OCT-11