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Course Criteria
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3.00 Credits
This course takes a rigorous approach to functions of a single real variable to explore many of the subtleties concerning continuous and differentiable functions that are taken for granted in introductory calculus. Much more than simply an advanced treatment of topics from calculus, this course uses beautiful and deep results about topics such as the Cantor set, Fourier series, and continuous functions to motivate the rigorous approach. (Bill Goldbloom Bloch, Tommy Ratliff)
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3.00 Credits
This course is an introduction to the study of abstract algebra. We begin with sets, and operations on those sets, that satisfy just a few basic properties and deduce many more properties, creating an impressive body of knowledge from just these few initial ideas. We use this approach to focus on structures known as groups. Symmetry, permutation groups, isomorphisms and homorphisms, cosets and factor groups will be covered, as well as an introduction to rings, domains and fields. A secondary focus will be developing the student's ability to write rigorous and well-crafted proofs. (Janice Sklensky)
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3.00 Credits
A graph is a mathematical structure consisting of dots and lines. Graphs serve as mathematical models for many real-world applications: for example, scheduling committee meetings, routing of campus tours and assigning students to dorm rooms. In this course, we study both the theory and the utility of graphs. Offered at the discretion of the department. (Rochelle (Shelly) Leibowitz)
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3.00 Credits
A comparison of Euclidean and non-Euclidean geometries with an emphasis on understanding the underlying structures that explain these geometries' fundamental differences. At the instructor's discretion, the geometries of the Euclidean plane and Euclidean manifolds will be compared with spherical and hyperbolic geometries. (Tommy Ratliff)
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3.00 Credits
This course covers mathematical theory of fundamental statistical techniques and applications of the theory. Topics: estimation and associated likelihood statements regarding parameters, hypothesis testing theory and construction, ANOVA, regression, Bayesian and resampling methods for inference. (Michael Kahn)
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3.00 Credits
Divisibility properties of the integers, prime and composite numbers, modular arithmetic, congruence equations, Diophantine equations, the distribution of primes and discussion of some famous unsolved problems. Offered at the discretion of the department. (Rochelle (Shelly) Leibowitz)
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3.00 Credits
Complex numbers first arose naturally during the algorithmic process of finding roots of cubic polynomials. Extending the ideas of calculus to complex numbers continues to bring forth beautiful ideas such as the Mandelbrot Set and powerful applications to quantum mechanics. This course will take primarily the geometric perspective in understanding the many surprising and elegant theorems of complex analysis. Offered at the discretion of the department. (Bill Goldbloom Bloch, Rachelle C. DeCoste)
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3.00 Credits
A study of graph theory and general counting methods such as combinations, permutations, generating functions, recurrence relations, principle of inclusion-exclusion. Offered at the discretion of the department. (Rochelle (Shelly) Leibowitz)
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3.00 Credits
An individual or small-group study in mathematics under the direction of an approved advisor. An individual or small group intensively studies a subfield of mathematics not normally taught. An independent study provides an opportunity to go beyond the usual undergraduate curriculum and deeply explore and engage an area of interest. Students are also expected to assume a greater responsibility, in the form of leading discussions and working examples.
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3.00 Credits
A seminar featuring historical and/or contemporary topics in mathematics. Roundtable discussions, student-led presentations and writing are featured.
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