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Course Criteria
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3.00 Credits
While the subject matter varies, the seminar addresses an advanced topic in mathematics. The development of the topic draws on students' previous course work and helps consolidate their earlier learning. Students are active participants, presenting material to one another in both oral and written form, and conducting individual research on related questions. Required of all majors not writing a thesis. Not open to students who have received credit for a mathematics thesis. Not open to first-year students, sophomores, or juniors.
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3.00 Credits
In this senior seminar students examine notions of rigor and proof in mathematics. Through readings of original sources, students trace particularly the evolution of the "epsilon-delta" proofs in calculus. They read excerpts (in translation) from Cauchy, Weierstrass, Dedekind, and others. Students also choose their own readings to present to the class. Prerequisite(s): Mathematics 301. Corequisite(s): Mathematics 309. Open to seniors only. Not open to students who have received credit for Mathematics 457 or 458. Enrollment limited to 10. B. Shulman.
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3.00 Credits
One of the major scientific accomplishments of the last twenty-five years was the discovery of chaos and the recognition that sensitive dependence on initial conditions is exhibited by so many natural and man-made processes. To really understand chaos, one needs to learn the mathematics behind it. This seminar considers mathematical models of real-world processes and studies how these models behave as they demonstrate chaos and its surprising order. Prerequisite(s): Mathematics 301. Corequisite(s): Mathematics 309. Open to seniors only. Not open to students who have received credit for Mathematics 457 or 458. S. Ross.
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3.00 Credits
Game theory provides a mathematical framework for analyzing situations where individuals (or companies, political parties, or nations) are faced with the prospect of maximizing their own well-being, dependent on the decisions of others. How can we decide on the best strategy How can we mathematically model such abstract notions as fairness and rationality After an introduction to the basics of game theoretic methods, students independently explore its applications to anthropology, warfare, economics, politics, philosophy, biology, and the NFL draft. Prerequisite(s): Mathematics 206 and one of the following: Mathematics s21, 301, or 309. Open to seniors only. Not open to students who have received credit for Mathematics 457, 458, or s45J. Enrollment limited to 10. B. Shulman.
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3.00 Credits
An elliptic curve is defined as the set of points of a cubic polynomial in two variables. Interestingly, one can add any two points on the curve to get another point on the curve. In this way, the points form a group. These groups are used in various areas of mathematics, including cryptography, primality testing, and the proof of Fermat's last theorem. After an introduction to the basics, each student studies various aspects of elliptic curves, drawing from previous knowledge in abstract algebra, analysis, geometry, and number theory. Prerequisite(s): Mathematics 301 and 309. Open to seniors only. Not open to students who have received credit for Mathematics 457 or 458. Enrollment limited to 10. Staff.
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3.00 Credits
How can the rent of a house with differently-sized rooms be divided among a group of people so that each person feels that he or she got the best deal How can we prove that at this very moment there are two diametrically opposite points on Earth's surface that have the same temperature and the same air pressure After an introduction to the required basics of topology, geometry, and combinatorics, students independently explore these and related questions using the Borsuk-Ulam theorem, the Brouwer fixed point theorem, and their discrete versions. Prerequisite(s): Mathematics 301 and 309. Open to seniors only. Not open to students who have received credit for Mathematics 457 and 458. Enrollment limited to 10. P. Jayawant.
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3.00 Credits
Prior to entrance into Mathematics 457and/or 458, students must submit a proposal for the work they intend to undertake toward completion of a thesis. Open to all majors upon approval of the proposal. Required of candidates for honors. Students register for Mathematics 457 in the fall semester and Mathematics 458 in the winter semester. [W3] Normally offered every year. Staff.
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3.00 Credits
Prior to entrance into Mathematics 457and/or 458, students must submit a proposal for the work they intend to undertake toward completion of a thesis. Open to all majors upon approval of the proposal. Required of candidates for honors. Students register for Mathematics 457 in the fall semester and Mathematics 458 in the winter semester. [W3] Normally offered every year. Staff.
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3.00 Credits
Prior to entrance into Mathematics 457 and/or 458, students must submit a proposal for the work they intend to undertake toward completion of a thesis. Open to all majors upon approval of the proposal. Required of candidates for honors. Students register for Mathematics 457 in the fall semester and Mathematics 458 in the winter semester. [W3] Normally offered every year. Staff.
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5.00 Credits
An intensive development of the important concepts and methods of abstract mathematics. Students work individually, in groups, and with the instructors to prove theorems and solve problems. Students meet for up to five hours daily to explore such topics as proof techniques, logic, set theory, equivalence relations, functions, and algebraic structures. The course provides exposure to what it means to be a mathematician. Prerequisite(s): one semester of college mathematics. Required of all majors. Enrollment limited to 30. Normally offered every year. P. Wong, Staff.
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