# Mathematical Systems

REVISED

Fall 2013, Winter 2014 and Spring 2014 quarters

Taught by

## Prerequisites

This program is built around intensive study of several fundamental areas of pure mathematics. Covered topics are likely to include abstract algebra, real analysis, set theory, combinatorics and probability.

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 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? What are the connections between mathematics and art? 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.

## Program Details

### Fields of Study

### Preparatory for studies or careers in

### Location and Schedule

#### Campus location

Olympia

#### Schedule

**Offered during:**
Day

### Books

### Online Learning

**Enhanced Online Learning:**Access to web-based tools required, but use of these tools does not displace any face-to-face instruction.

### Required Fees

### Research Possibilities

### Upper Division Science Credit

### May be offered again in

### Revisions

Date | Revision |
---|---|

April 22nd, 2013 | Fall fee has been removed. |