# Mathematical Systems

This program is built around intensive study of several fundamental areas of pure mathematics, including Abstract Algebra, Real Analysis, Linear Algebra, Set Theory, and Combinatorics. The program will also include seminars on Practices of Modern Mathematics, History of Mathematics, and Mathematical Fiction. **Students with strong algebra skills can enroll in most parts of this program; for full registration in the program, one year of Calculus is required. ** In fall quarter, students can choose to take any combination of Abstract Algebra I, Real Analysis I, Set Theory, or Prac tices of Modern Mathematics.

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, often in the context of 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? In what sense do mathematical objects actually exist ? What is current mathematical practice? How did the current mode of mathematical thinking come to be developed? What are the connections between mathematics and culture? What are the potential and existing 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 develop a detailed understanding of mathematical thinking at a high level.

This program is currently planned as a hybrid remote/in-person offering. For fall quarter, students should expect a significant amount of class time to occur online via Zoom; we will also have in-person cla s s sessions at least two days per week and are hopeful that we can transition to even more in-person class days . Because the program will be partly remote (online), with information delivered via Zoom and Canvas, students will need access to a computer with a good internet connection for 8-10 hours/week of synchronous online class time.

### Registration

Parts of this program (up to 12 credits in fall, 12 credits in winter, and 8-12 credits in spring) can be taken by students who have strong algebra skills; experience with Discrete Math is helpful but not required. Interested students who haven’t taken Calculus should contact the faculty to discuss their options within this program.

For full registration in the program, students will need to have taken one year of Calculus.

#### Course Reference Numbers

#### Signature Required

Admission will be based upon evaluation of student's previous experience with upper-division mathematics. Interested students should contact the faculty via email before the first day of class or at the Academic Fair.

#### Course Reference Numbers

#### Signature Required

Admission will be based upon evaluation of student's previous experience with upper-division mathematics. Interested students should contact the faculty via email before the first day of class or at the Academic Fair.

### Academic details

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

$150 spring quarter for overnight program retreats.

Most of the content of 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.

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