# Mathematical Systems

This program is built around intensive study of several fundamental areas of pure mathematics. In fall quarter we will cover Linear Algebra, Real Analysis 1, Euclidean and non-Euclidean Geometry, and a seminar on the history of mathematics. In winter we will cover Abstract Algebra 1, Real Analysis 2, Topology, and a seminar on the culture and practice of mathematics. In spring we will continue the study of Topology, along with Abstract Algebra 2, and additional math and seminar topics chosen upon consultation with the class.

The work in this advanced-level mathematics program is 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 of logical deduction. You will gain experience in articulating your evidence for claims and in expressing your 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 and philosophical context, working toward answers to critical questions such 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?

The work in the program will include several weekly homework assignments, in-class or take-home exams in each area, seminar reading and writing, and regular student presentations of solutions to homework problems. The 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.

### Registration

** New students accepted in winter and spring with signature.**
Students must demonstrate that they have completed previous coursework in upper-division pure mathematics. This should include at least one quarter of abstract algebra with proofs and another proof-based course in pure math. Email instructor at hastingr@evergreen.edu to determine your eligibility.

One year of Calculus.

#### Course Reference Numbers

#### Signature Required

**New students accepted in winter with signature. ** Students must demonstrate that they have completed previous coursework in upper division pure mathematics. This should include at least one quarter of abstract algebra with proofs, and one quarter of real analysis with proofs. Email instructor (hastingr@evergreen.edu) to determine your eligibility.

#### Course Reference Numbers

#### Signature Required

**New students accepted in spring with signature.** Students must demonstrate that they have completed previous coursework in upper division pure mathematics. This should include at least one quarter each of abstract algebra and real analysis with proofs, and another proof-based course in pure math. Email instructor (hastingr@evergreen.edu) to determine your eligibility.

#### Course Reference Numbers

### Academic details

mathematics, math education, history and philosophy of math, and physical sciences.

Most of the content and credits each quarter will be offered as upper-division science credit. Three to four seminar credits each quarter will not be at the upper-division science level.