Topology

From RealCTY
Jump to: navigation, search
Topology
Math Course
Course CodeTOPO
Year Opened2019
Sites OfferedLAN
Part of a series on
Realcty logo 20060831.png
CTY Courses
Category · Template · CAA Courses
Sites
Baltimore · Carlisle · Lancaster · Los Angeles · Saratoga Springs · Seattle
Humanities
Logic: PoR
International Politics · Law and Politics in US History
Exploring Ethics · Existentialism: On Being Human
Philosophy of Mind
Cognitive Psychology · Linguistics
Dissent
Newton, Darwin, and Einstein
The Art and Science of Filmmaking
Writing
Writing Your World · The Art of Fiction
Fiction and Poetry
Utopias and Dystopias
Persuasion and Propaganda
Math
Individually Paced Mathematics Sequence
Probability and Game Theory
Number Theory · Mathematical Logic
Cryptology · Advanced Cryptology
Topology
Economics
Macroeconomics and the Global Economy
Fundamentals of Microeconomics
Computer Science
Data Structures and Algorithms
Fundamentals of Computer Science
Science
FPHS Biology · FPHS Chemistry · FPHS Physics
Astrophysics
Paleobiology · Genetics · Neuroscience
Investigations in Engineering
Introduction to Biomedical Sciences · Electrical Engineering
Special Relativity · Intro to Organic Chemistry
Princeton
Global Politics: Human Rights and Justice
Human Nature and Technology
Politics and Film · Epidemiology
The Mathematics of Competitive Behavior
Science, Technology and Public Policy
Race and Politics · Politics in the Middle East
The Global Environment
Civic Leadership Institute (PBD/BRK)
Service, Leadership & Community Transformation
Defunct Courses
Beginning Ancient Greek · German 1
German 2
Latin 2
French 1 · French 2
Great Revolutions
American History
Modern European History · Eastern European History
Music Theory
History of Western Art
Renaissance Art
Introduction to American Studies: Race and Class
Medieval Art
Twentieth Century Art · Gandhi's India
American Studies: The Sixties · Women and US Social Reform
American Studies: The Harlem Renaissance
Intermediate Ancient Greek
Islam · The Asian Pacific Rim
Russian History
TCE: Literature and the Arts · TCE: Popular Culture
The Crafting of Drama
The Crafting of Poetry · TCE: Shakespeare
TCE: Science Fiction
TCE: Beyond the Ring and the Wardrobe
Advanced Mathematical Modeling
Advanced Mathematical Reasoning
Statistics · Calculus: A Conceptual Approach
Topics in Precalculus
Set Theory · Digital Logic
Theoretical Foundations of Computer Science
Introduction to Laboratory Sciences · Archaeology
Ecology
Microbiology · Selected Topics in Advanced Biology
Selected Topics in Advanced Chemistry
Selected Topics in Advanced Physics · Physical Anthropology
Advanced Physics: Mechanics
Scientific Investigations: St. Mary's River · Genomics
Volcanoes
Etymologies · Oceanography: The Hawaiian Pacific
Life Cycle of an Island: Hawaii
The History of Disease · The Critical Essay: Film
Wicked Art: Pictures, Pixels, and Pens
Latin I
Goodwives and Witches: Women in Colonial America
Freaks and Geeks in Popular Media
The Digital Revolution
Advanced Robotics
Playing God: The Ethics of Human Subjects Research
Theory of Computation

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?

Reception by Students

Reactions to the course from its pilot run in 19.1 were largely but not entirely positive, with most complaints centering around the brutal difficulty of the class (and to a lesser extent Pichelmeyer's excessive timekeeping when it came to returning from meals or breaks). Covering large amounts of highly abstract and theoretical content from the upper undergraduate and graduate levels in only three weeks, it was agreed upon by students as well as the instructor and TA that it was the hardest class offered at CTY by far. This intense difficulty and complexity spawned many AI jokes, most of which involved a student entering Park Bench or a similar game and reciting the very common first line of a topological proof or definition "let X be a topological space", causing the student already in the center to flee in fear from the difficult math.

An oft-recited quote from Pichelmeyer on the first day of the class was:

The curriculum I've made here is ridiculous, it's silly, we won't get through all of it, the other instructors made fun of me for even trying to teach it in 3 weeks, and I'll be happy if you walk out of here with even 20% of the content.

Despite this difficulty, most students reported that they did in most part enjoy the class, due in no small way to Pichelmeyer's teaching. There was also a sense among everyone involved of being in it together in testing out this brand-new class.