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Math 170 - Ideas in Mathematics
Dr. Dennis DeTurck
Description:
One of the reasons that Mathematics is so fascinating and formidable is its varifold nature. Mathematics is simultaneously
- a set of powerful tools that are useful for science, engineering, business and social science
- a precise and expressive language
- a way of thinking and reasoning
- a discipline all its own, with a historical development, aesthetic standards, spectacular intellectual achievements and fascinating open problems
In almost all of the mathematics courses that almost everyone takes, only the first aspect of the subject is discussed, and perhaps a tiny bit of the second. And studying tools is not so interesting for most people.
In this course, we will focus mostly on the other aspects of mathematics - the richness of the mathematical language and how to engage in mathematical discourse, the mathematical "modus operandi" of calculation, generalization, abstraction and proof, and mostly we will examine a number of mathematical ideas and results in order to understand and appreciate the nature, power and beauty of the subject.
Some of the mathematical topics we will consider are:
- The idea of number - how this has progressed from counting and measuring to representations of multi-dimensional geometric objects and methods for encoding and encrypting data of all sorts
- The idea of space - from the fundamental ideas of the ancients to exotic modern conceptions of physical and abstract spaces.
- The imperative of proof - what distinguishes mathematics from other sciences is that we can prove that our results are really true. Or can we?
- The idea of motion - from the "classical" study of the motion of projectiles to modern dynamical theories that aim to study chaotic and complex systems.
- The idea of indeterminacy - how this has progressed from simple gaming and betting strategies to become a fundamental part of the modern scientific method.
Throughout, there will be emphasis on the mathematics itself, as well as on the social, historical and cultural roots of the subjects at hand.
Course Schedule:
Wednesdays, September 12 to December 5, 7:00 to 9:00 pm ET.
