TOPCS: ADVANCED-RESEARCH

Topics course: In this course students work in small groups on original research projects. Students are expected to attend a brief presentation of projects at the start of the semester. Recent topics include interactions between algebra and graph theory, plant patterns, knot theory, and mathematical modeling. This course is open to all students interested in gaining research experience in mathematics, Prerequisites vary depending on the project, but normally 153 and 211 are required.

DIALOGUES IN MATHEMATICS

In this class we don’t do math as much as we talk about doing math and the culture of mathematics. The class includes lectures by students, faculty and visitors on a wide variety of topics, and opportunities to talk with mathematicians about their lives. This course is especially helpful for those considering graduate school in the mathematical sciences. Prerequisites: MTH 211, MTH 212 and two additional mathematics courses at the 200-level, or permission of the instructor. May be repeated once for credit. This course is graded satisfactory/unsatisfactory only.

COMBINATORICS

Enumeration, including recurrence relations and generating functions. Special attention paid to binomial coefficients, Fibonacci numbers, Catalan numbers and Stirling numbers. Combinatorial designs, including Latin squares, finite projective planes, Hadamard matrices and block designs. Necessary conditions and constructions. Error correcting codes. Applications. Prerequisites: MTH 153 and MTH 211 or permission of the instructor.

MODELING IN THE SCIENCES

Same as MTH 205. This course integrates the use of mathematics and computers for modeling various phenomena drawn from the natural and social sciences. Scientific topics, organized as case studies, span a wide range of systems at all scales, with special emphasis on the life sciences. Mathematical tools include data analysis, discrete and continuous dynamical systems and discrete geometry. This is a project-based course and provides elementary training in programming using Mathematica. Prerequisites: MTH 112 or MTH 114. CSC 111 recommended. Enrollment limited to 20.

MODELING IN THE SCIENCES

Same as CSC 205. This course integrates the use of mathematics and computers for modeling various phenomena drawn from the natural and social sciences. Scientific topics, organized as case studies, span a wide range of systems at all scales, with special emphasis on the life sciences. Mathematical tools include data fitting, discrete and continuous dynamical systems and discrete geometry. The course provides training through programming in Mathematica and/or MATLAB. Prerequisites: MTH 112. CSC 111 recommended. Enrollment limited to 20.

First Nights

We will examine five major musical works from the 17th to the 20th century: Orfeo (Monteverdi), Messiah (Handel), the Ninth Symphony (Beethoven), the Symphonie fantastique (Berlioz), and Le Sacre du printemps (Stravinsky). Using Thomas Kelly's book First Nights, recordings of modern performances, and selected readings, we will study how these works function as pieces of music and what makes them unique.

Human Physiology

A course on the function of human organ systems, at both the cellular and whole tissue level. We will study the mechanisms that regulate a variety of organ systems and learn how these mechanisms respond to the changing needs of the individual. We will discuss how we used animal models to determine the normal function of these systems, practice the math used to model their function, and analyze how the activities of these systems are integrated.
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