Marie Snipes

The second in a three-semester calculus sequence, this course has two primary foci. The first is integration, including Riemann sums, techniques of integration, and numerical methods and applications of integration. This study leads into the analysis of differential equations by separation of variables, Euler's method and slope fields. The second focus is the notion of convergence, as manifested in improper integrals, and sequences and series, particularly Taylor series. This counts toward the core course requirement for the major. Prerequisite: MATH 111 or AP score of 4 or 5 on Calculus AB exam or an AB sub-score of 4 or 5 on the Calculus BC exam or permission of instructor. Offered every semester.

This course focuses on the study of vector spaces and linear functions between vector spaces. Ideas from linear algebra are useful in many areas of higher-level mathematics. Moreover, linear algebra has many applications to both the natural and social sciences, with examples arising in fields such as computer science, physics, chemistry, biology and economics. In this course, we use a computer software system, such as Maple or Matlab, to investigate important concepts and applications. Topics to be covered include methods for solving linear systems of equations, subspaces, matrices, eigenvalues and eigenvectors, linear transformations, orthogonality and diagonalization. Applications are included throughout the course. This counts toward the core course requirement for the major. Prerequisite: MATH 213. Generally offered three out of four semesters.

This course is a first introduction to real analysis. "Real" refers to the real numbers. Much of our work revolves around the real number system. We start by carefully considering the axioms that describe it. "Analysis" is the branch of mathematics that deals with limiting processes. Thus the concept of distance is also a major theme of the course. In the context of a general metric space (a space in which we can measure distances), we consider open and closed sets, limits of sequences, limits of functions, continuity, completeness, compactness and connectedness. Other topics may be included if time permits. Junior standing is recommended. This counts toward the continuous/analytic (column B) elective requirement for the major. Prerequisite: MATH 213 and 222. Offered every other fall.

This course introduces students to the concepts, techniques and power of mathematical modeling. Both deterministic and probabilistic models are explored, with examples taken from the social, physical and life sciences. Students engage cooperatively and individually in the formulation of mathematical models and in learning mathematical techniques used to investigate those models. This counts toward the computational/modeling/applied (column D) elective requirement for the major. Prerequisite: STAT 106 and MATH 224 or 258, or permission of instructor. Offered every other year.

Topology is an area of mathematics concerned with properties of geometric objects that remain the same when the objects are "continuously deformed." Three of these key properties in topology are compactness, connectedness and continuity; the mathematics associated with these concepts is the focus of the course. Compactness is a general idea helping us to more fully understand the concept of limit, whether of numbers, functions or even geometric objects. For example, the fact that a closed interval (or square, or cube, or n-dimensional ball) is compact is required for basic theorems of calculus. Connectedness is a concept generalizing the intuitive idea that an object is in one piece: The most famous of all the fractals, the Mandelbrot Set, is connected, even though its best computer-graphics representation might make this seem doubtful. Continuous functions are studied in calculus, and the general concept can be thought of as a way by which functions permit us to compare properties of different spaces or as a way of modifying one space so that it has the shape or properties of another. Engineering, chemistry and physics are among the subjects that find topology useful. The course touches on selected topics that are used in applications. This counts toward the continuous/analytic (column B) elective requirement for the major. Prerequisite: MATH 222 or permission of instructor. Generally offered every two to three years.

This course follows MATH 341. Topics include a study differentiation and (Riemann) integration of functions of one variable, sequences and series of functions, power series and their properties, iteration and fixed points. Other topics may be included as time permits. For example: a discussion of Newton's method or other numerical techniques; differentiation and integration of functions of several variables; spaces of continuous functions; the implicit function theorem; and everywhere continuous, nowhere differentiable functions. This counts toward the continuous/analytic (column B) elective requirement for the major. Prerequisite: MATH 341. Offered every other spring.

Individual study is a privilege reserved for students who want to pursue a course of reading or complete a research project on a topic not regularly offered in the curriculum. It is intended to supplement, not take the place of, coursework. Individual study cannot be used to fulfill requirements for the major. To qualify, a student must identify a member of the mathematics department willing to direct the project. The professor, in consultation with the student, creates a tentative syllabus (including a list of readings and/or problems, goals and tasks) and describes in some detail the methods of assessment (e.g., problem sets to be submitted for evaluation biweekly; a 20-page research paper submitted at the course's end, with rough drafts due at given intervals; and so on). The department expects the student to meet regularly with his or her instructor for at least one hour per week. All standard enrollment/registration deadlines for regular college courses apply. Because students must enroll for individual studies by the end of the seventh class day of each semester, they should begin discussion of the proposed individual study by the semester before, so that there is time to devise the proposal and seek departmental approval. Individual study courses may be counted as electives in the mathematics major, subject to consultation with and approval by the Department of Mathematics and Statistics. Permission of instructor and department chair required. No prerequisite.\n\n

This course consists largely of an independent project in which students read several sources to learn about a mathematical topic that complements material studied in other courses, usually an already completed depth sequence. This study culminates in an expository paper and a public or semi-public presentation before an audience consisting of at least several members of the mathematics faculty as well as an outside examiner. Permission of department chair required. Prerequisite: senior standing and the completion of at least one two-semester sequence at the junior-senior level.

This is a basic course in statistics. The topics covered are the nature of statistical reasoning, graphical and descriptive statistical methods, design of experiments, sampling methods, probability, probability distributions, sampling distributions, estimation and statistical inference. Confidence intervals and hypothesis tests for means and proportions are studied in the one- and two-sample settings. The course concludes with inference-regarding correlation, linear regression, chi-square tests for two-way tables and one-way ANOVA. Statistical software is used throughout the course, and students engage in a wide variety of hands-on projects. This counts toward the core course requirement for the major. Students with credit for STAT 116 cannot take STAT 106 for credit. No prerequisite. Offered every semester.