Splash Biography
JACK GALLAHAN, Princeton sophomore studying mathematics.
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Major: Math College/Employer: Princeton Year of Graduation: 2025 |
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Brief Biographical Sketch:
Not Available. Past Classes(Clicking a class title will bring you to the course's section of the corresponding course catalog)M679: Trisection: An Ancient Problem, and the Birth of Modern Mathematics in Splash 2023 (Apr. 22, 2023)
In this course, I will show you how to solve a problem that evaded human minds for well over two thousand years: can any angle be trisected with compass and straight edge? Along the way, I will introduce the beautiful framework of ideas known as "Galois theory" that finally dissolved this problem.
M680: The Brouwer Fixed-Point Theorem: A Journey into Algebraic Topology in Splash 2023 (Apr. 22, 2023)
As L. E. J. Brouwer was stirring his coffee one day, he noticed one point seemed to remain motionless. Indeed, after stirring a cup of coffee, on bit of liquid must be in exactly the same place that it started in. This a result known as the Brouwer Fixed-Point Theorem, which I will prove in this class. Along the way, I will introduce some of the basic ideas of the beautiful subject known as Algebraic Topology, including the concepts of homotopy and the fundamental group.
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