FSEM1010-07.FSEM: Heart of Mathematics.F16.Guetter,Arthur

Arthur Guetter

Document Type

Syllabi

School

CLA

Department

MATH

Course Subject

FSEM

Course Number

1010

Course Section

07

Course Title

FSEM: Heart of Mathematics

Academic Term and Year

Fall 2016

Credits

4.00

Area of Study

FSEM

Course Description

This is a course on mathematics, but it will be unlike any mathematics course that you have taken before. If you view mathematics as a set of formulas to apply to a list of problems, you will be disappointed; if you want endless, unmotivated word problems, look elsewhere. In this course, we hope to discover what mathematics really is: a living, creative, powerful, and even artistic project, a subject with connections to other fields of inquiry such as the sciences, history, and philosophy. We will ask a broad range of questions that have immediate applications. How does data encryption work? What do those bar codes on my cereal box mean? How do I know that a particular medicine does what it claims to do? But we will go far beyond this, and view mathematics as a powerful technique of pure thought, more akin to philosophy than physics. We hope to show that the search for answers to such questions has a unique beauty and interest of its own. The emphasis will not be a compilation of facts, but an exploration of connections and patterns. The topics we will study will encompass a broad range of ideas, many of them of recent vintage: prime numbers (there are still many unknown properties), geometry, topology (how can one distinguish a tire inner tube from a balloon?), fractals, probability and statistics, and more. We will also look at the role of mathematics in the modern world: for example, could mathematics offer a better voting system?

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