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Summer 2022 Pre-College Prog: Models of the Universe PS0101 section 001
Geometric Topology: A Tool for Modeling
Geometric Topology: Unive

Call Number 10687
Day & Time
MTWRF 11:10am-1:00pm
407 Mathematics Building
Day & Time
MTWRF 3:10pm-5:00pm
407 Mathematics Building
Points 0
Grading Mode Ungraded
Approvals Required None
Instructor Joseph Quinn
Method of Instruction In-Person
Course Description Is the universe infinite or finite? What is the curvature and overall shape of the space we live in, and how might we detect this? Many have considered these questions throughout the ages, and while we still don’t know the answers, a field of mathematics called geometric topology has given rise to a relatively new framework for approaching them. In this course, participants learn how models for topological spaces relate to theories on the shape of the physical universe. Philosophical discussions are informed by pencil and paper computations, experiments with common household materials, and interactive online games and modules. We begin by learning from the mistakes of archaic geocentric models so as to build intuition about manifolds — structures that look one way up close but totally different from far away. This sets the stage for a precise definition of dimension, providing the framework for the rest of the course. Students explore notions of curvature, flatness, boundedness, embeddings, and finiteness by constructing models of two-dimensional geometries out of toothpicks, cotton swabs, tape, or whatever works — creativity encouraged! We then apply our findings to the three-dimensional world, with the help of a few video games, such as flying a space ship through hyperbolic space. Finally, we look at the role of fractals in modeling reality, and how they push our notion of dimension to fascinating new horizons. Participants gain, in addition to early exposure to modern content at the intersection of topology and physical cosmology, an appreciation for rigorous mathematical thinking that is motivated not so much by numbers and quantity as by profound questions about the nature of our world.
Web Site Vergil
Subterm 07/19-08/05 (L)
Department Pre-College Programs (SHSP)
Enrollment 10 students (20 max) as of 8:04AM Saturday, July 2, 2022
Subject Pre-College Prog: Models of the Universe
Number PS0101
Section 001
Division School of Professional Studies
Open To Pre-College Programs, Professional Studies
Campus Morningside
Section key 20222COMO0101K001

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SIS update 07/02/22 08:04    web update 07/02/22 17:40