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Fall 2017, Winter 2018, and Spring 2018 quarters
One year of calculus. In some cases, two quarters of calculus may be sufficient; students with only two quarters of calculus experience should contact the faculty at email@example.com to discuss their level of readiness for this program.
This program is built around intensive study of several fundamental areas of pure mathematics. In fall quarter, we will cover Abstract Algebra I, Set Theory, Combinatorics, and a Seminar on Culture and Practices of Modern Mathematics. In winter quarter, we'll cover Abstract Algebra II, Real Analysis I, Probability Theory, and a Seminar on the History of Mathematics. In spring quarter, we'll cover Abstract Algebra III, Real Analysis II, a Seminar on Mathematical Fiction, and another student-selected mathematical subject.
The work in this advanced-level mathematics program is quite likely to differ from students' previous work in mathematics, including calculus, in a number of ways. We will emphasize the careful understanding of the definitions of mathematical terms and the statements and proofs of the theorems that capture the main conceptual landmarks in the areas we study. Hence, the largest portion of our work will involve the reading and writing of rigorous proofs in axiomatic systems. These skills are valuable not only for continued study of mathematics but also in many areas of thought in which arguments are set forth according to strict criteria for logical deduction. Students will gain experience in articulating their evidence for claims and in expressing their ideas with precise and transparent reasoning.
In addition to work in core areas of advanced mathematics, we will devote seminar time to looking at our studies in a broader historical, philosophical, and cultural context, working toward answers to such critical questions as: Are mathematical systems discovered or created? Do mathematical objects actually exist? How did the current mode of mathematical thinking come to be developed? What is current mathematical practice? What are the connections between mathematics and culture? What are the connections between mathematics and literature?
This program is designed for students who intend to pursue graduate studies or teach in mathematics and the sciences, as well as for those who want to know more about mathematical thinking.
Research opportunities may be available in the spring quarter, depending on student interest.
Fields of Studyliterature mathematics philosophy philosophy of science
mathematics, physics, mathematics education, philosophy of mathematics, and history of science
QuartersFall Open Winter Signature Spring Signature
Location and Schedule
Final Schedule and Room Assignment
First winter class meeting: Monday, January 8 at 10am (tbd)
Online LearningEnhanced Online Learning
$150 in spring quarter for an overnight program retreat.