Difference between revisions of "Topology"
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| + | ==Course Description== | ||
| + | Often called squishy geometry or rubber sheet geometry, topology is the branch of mathematics dealing with the properties of objects that are conserved when an object is continuously deformed. Students first focus on point set topology through the lens of formal proof. The course covers the fundamental ideas of continuity, connectedness, and compactness. Later, students also learn about algebraic and geometric topology, which includes topics such as knot theory and manifolds. There is a focus on drawing accurate diagrams with concrete steps. Students also present proofs of theorems to the class multiple times and culminate the session with presentations about different applications of topology. Much of the challenge of the class comes from the abstractness of concepts and the struggle to visualize certain objects in 3-space. | ||
| + | ==Class History== | ||
| + | Topology was founded as a class in 19.1 by instructor Jake Pichelmeyer. He was working in the field of topology for his Ph.D and had previously introduced some topological concepts into other courses he taught at CTY. Students enjoyed learning about topology, so he decided to develop a course focused on the subject. | ||
| + | '''LAN.19.1:''' | ||
Manifolds in the fifth dimension. Is somehow a new AI joke? | Manifolds in the fifth dimension. Is somehow a new AI joke? | ||
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| + | [[Category:Courses]] | ||
| + | [[Category: Lancaster]] | ||
Revision as of 15:55, 12 July 2019
| Math Course | |
|---|---|
| Course Code | TOPO |
| Year Opened | 2019 |
| Sites Offered | LAN |
Course Description
Often called squishy geometry or rubber sheet geometry, topology is the branch of mathematics dealing with the properties of objects that are conserved when an object is continuously deformed. Students first focus on point set topology through the lens of formal proof. The course covers the fundamental ideas of continuity, connectedness, and compactness. Later, students also learn about algebraic and geometric topology, which includes topics such as knot theory and manifolds. There is a focus on drawing accurate diagrams with concrete steps. Students also present proofs of theorems to the class multiple times and culminate the session with presentations about different applications of topology. Much of the challenge of the class comes from the abstractness of concepts and the struggle to visualize certain objects in 3-space.
Class History
Topology was founded as a class in 19.1 by instructor Jake Pichelmeyer. He was working in the field of topology for his Ph.D and had previously introduced some topological concepts into other courses he taught at CTY. Students enjoyed learning about topology, so he decided to develop a course focused on the subject.
LAN.19.1: Manifolds in the fifth dimension. Is somehow a new AI joke?
