Mathematical Systems

Fall 2017
Winter 2018
Spring 2018
Class Size: 25
Credits per quarter

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Taught by

Brian Walters
mathematics, computer science, improvisational theater

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.

This offering will prepare you for careers and advanced study in:

mathematics, physics, mathematics education, philosophy of mathematics, and history of science


Credits per quarter


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 to discuss their level of readiness for this program.

Online learning:
  • Enhanced Online Learning - This offering requires access to web-based tools, but use of these tools does not displace any face-to-face instruction.

$150 in spring quarter for an overnight program retreat.

Upper division science credit:

Most of the work in this program is designed to be upper-division math. Students who successfully complete the program requirements will earn up to 40 upper-division science credits in real analysis, abstract algebra, set theory, combinatorics, history of math, and other subjects (TBD).

Research Opportunities:

Research opportunities may be available in the spring quarter, depending on student interest.

Class Standing: Junior–Senior
Class Size: 25

Scheduled for: Day

Advertised schedule:

First winter class meeting: Monday, January 8 at 10am (tbd)

Located in: Olympia

May be offered again in: