Explorations in Mathematical Inquiry

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Session: 

  • Session A: July 10 - July 22, 2017
  • Session B: July 24 - August 5, 2017

Time: 

  • 9:30 a.m. - 12 p.m.

Category: 

  • Mathematics

Instructor: 

  • Matthew DeCross
Prerequisite: 
Algebra II or Pre-calculus
Description: 

What exactly does a research mathematician do all day? A popular image of a mathematician is that of a coffee-addicted lone wolf, working late into the night in an isolated office on the next fantastically complicated breakthrough idea that no other living soul will read. We will show this couldn’t be further from the truth: modern math research is collaborative, incremental, and grounded in natural and reasonable questions. Furthermore, many of the most famous mathematicians (and other scientists) are well-known not solely due to their breakthrough work but more importantly for the remarkable clarity and precision with which they communicate their ideas. In this module, students will have the opportunity to play in a mathematical research sandbox, investigating small-scale open-ended scenarios and reviewing one major modern research idea in teams. We will explain how to present the mathematical progress we make by typesetting in LaTeX and Beamer, and emphasize how to use the advantages offered by these tools to improve technical communication.

Via this module, students will:

  • Understand the process of mathematical inquiry as experienced by professional mathematicians.
  • Be exposed to several modern research-level topics in mathematics.
  • Become proficient in distilling relevant and irrelevant information in reviewing the state-of-the-art on a new topic of investigation.
  • Gain technical facility in typesetting mathematical and scientific work in LaTeX and Beamer.
  • Develop techniques for communicating technical concepts more effectively both verbally and in writing

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