Mathematical Systems


Fall 2015, Winter 2016 and Spring 2016 quarters

Taught by

linguistics, mathematics

Prerequisites

One year of Calculus.

This program is built around intensive study of several fundamental areas of pure mathematics. Topics are likely to include abstract algebra, real analysis, geometry, and topology.

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. 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 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?

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.

Fields of Study

Preparatory for studies or careers in

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

Location and Schedule

Campus location

Olympia

Schedule

Offered during: Day

Books

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Online Learning

Enhanced Online Learning

More information about online learning.

Upper Division Science Credit

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.

May be offered again in

2017-2018

Registration Information

Credits: 16 (Fall); 16 (Winter); 16 (Spring)

Class standing: Sophomore–Senior

Maximum enrollment: 25

Fall

Course Reference Number not yet available.

Winter

Accepting New Students

Signature Required

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 (hastingr@evergreen.edu) to determine your eligibility.

Course Reference Number not yet available.

Spring

Accepting New Students

Signature Required

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 Number not yet available.

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