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Category Theory Crash Course

First stop Yoneda's Lemma
3.6
3.6/5
(10 reviews)
68 students
Created by

7.9

CourseMarks Score®

7.6

Freshness

7.1

Feedback

8.5

Content

Platform: Udemy
Video: 1h 39m
Language: English
Next start: On Demand

Table of contents

Description

Introduces the philosophy and basic results of category theory. The main one that has become quite well known is called Yoneda’s Lemma and is a really fun way to apply the philosophy of category theory. We also have simple but fundamental notions in theory such as duality and universality which relate many of the constructions we knew about but perhaps didn’t realise we related in this or that way. Will try to be a living course that grows with student participation.

You will learn

✓ Objects, morphisms, functors and natural transformations
✓ Universal properties
✓ Yoneda’s Lemma
✓ The principle of abstraction and generality

Requirements

• Familiarity with sets and functions would help
• Familiarity with linear algebra and vector spaces would help more
• In principle this could be taught first but slower

This course is for

• Advanced high school senior students who seek a proper foundation in maths
• Undergraduate students who want to study graduate maths
• Smart people who want to understand category theory for whatever purpose eg programming, research, etc
• Fans of Grothendieck
Mathematician
Join me for meaningful learning that will have lasting value.
Much of the content takes a student through the experience of solving a problem from scratch, learning a concept rigorously or applying a concept to a problem. This process is filmed and presented here with basically no editing. To be truly great at maths you cannot just memorise disconnected facts you need to learn how to think, how to link and how to learn. For younger students we have the luxury of applying the things we learn in math olympiad problems. I look forward to seeing you in class!
Background
PhD, first in graduating class USA (UOregon)
This is also where I learned to play Basketball.
M.Sc by research, fastest possible with publication, USyd, AUS
B.Sc (Honours), University Medal, all High Distinctions, USyd AUS
ATAR 99.95 NSW Australia
Postdoctoral research fellow Germany (Unimuenster)
Visiting scholar China (ECNU Shanghai)
Research publications and conference attendance.
Browse all courses by on Coursemarks.
Platform: Udemy
Video: 1h 39m
Language: English
Next start: On Demand

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