What are some good lecture series on YouTube for math and related topics?

[ModusPonens]

Hello,

This is a thread to collect youtube lecture series. I would appreciate if you would add your playlists. I tried not to overlap with Khan Academy, but if you have good lecture series that overlap, please share them.Mathematical Logic lecture series:

Mod-01 Lec-01 Sets and Strings - YouTube
----> 42 Lectures culminating in the Gödel incompleteness theorems.


Category Theory lecture series:

Catster Videos -----> This is the order in which the Catsters' videos should be watched

TheCatsters - YouTube ----> this is the Catsters youtube channel


Abstract Algebra lecture series:

Mystery Division Problem - YouTube
-----> Group Theory, Ring Theory, Field Theory and Galois TheoryGeneral Topology lecture series:

Topology #1 Metrics - YouTube ---> This is a playlist that has 29 lectures and a few others which are not in the same lecture series.Algebraic Topology lecture series:

AlgTop0: Introduction to Algebraic Topology - YouTube ----> Includes algebra reviewing material


Differential Geometry lecture series:

DiffGeom1: Classical curves - YouTube -----> Seems to be at beginner's levelAlgebraic Geometry lecture series:

Affine I - YouTube ----> Seems to be in order, although there is no explicit numbering of the lectures
It should be obvious by now, because of the comments on the videos, that I haven't watched them all. So if you have better (or equal or worse) playlists that are a coherent set of lecture series, please share them. I will add, in a second post, less central topics, such as homology, cohomology and homological algebra.

I would especially appreciate if you could provide with lecture series on Number Theory, Graph Theory and Combinatorics. Other central areas _ which I can't remember now _ are appreciated.

Enjoy

 

[ModusPonens]

Playlists on algebraic topology and algebraic geometry.

Algebraic Topology and Geometry

- Category Theory for Algebraic Topology: https://www.youtube.com/watch?v=fBe0nfp0nXs&list=PLCgncMh0TrCkaNUji9jJxqIJ5LoKkAmSw

- Algebraic Topology: https://www.youtube.com/watch?v=0tZCILVmPng&list=PLCgncMh0TrClLOU991FDEQK5LF_Aqm4FS - This is the introductory material: homotopy and covering spaces

- Homology: https://www.youtube.com/watch?v=bWCfAboTSs8&list=PL7BFF10190F42006E

- Cohomology: https://www.youtube.com/watch?v=UKyk5K7fTYw&list=PL01055907ED9ACA18

- Homological Algebra: https://www.youtube.com/watch?v=zlnfLg06QhA&list=PLCgncMh0TrCmqr36zCc6I96EhPwAt3ZVh

- Algebraic Geometry: https://www.youtube.com/watch?v=yWaH8B_wGzk&list=PLCgncMh0TrCkiiuBH1fcioW8uFO9S_KPE

- Vector Bundles and Char Classes: https://www.youtube.com/watch?v=sVFWrMCfje8&list=PLCgncMh0TrCmrkvT7zW0x32flMJLuYMT5

 

[ModusPonens]

These are MIT lectures on introductory mathematics, i.e., Discrete Mathematics, Linear Algebra, Calculus, Differential Equations and Probability and Statistics.Discrete Mathematics

https://www.youtube.com/watch?v=h_9WjWENWV8&list=PL3o9D4Dl2FJ9q0_gtFXPh_H4POI5dK0yG
Linear Algebra

- Theory: https://www.youtube.com/watch?v=ZK3O402wf1c&list=PLE7DDD91010BC51F8h

- Recitation Classes: https://www.youtube.com/watch?v=uNKDw46_Ev4&list=PL221E2BBF13BECF6C
Single Variable Calculus

- Theory: https://www.youtube.com/watch?v=7K1sB05pE0A&list=PL590CCC2BC5AF3BC1

- Recitation Classes: https://www.youtube.com/watch?v=2y4tCiWbVRI&list=PLF6742016BF0F7212
Multivariable Calculus

- Theory: https://www.youtube.com/watch?v=PxCxlsl_YwY&list=PL4C4C8A7D06566F38

- Recitation Classes: https://www.youtube.com/watch?v=AYixF5nY3Vc&list=PLF07555F3CC669D01
Differential Equations

- Theory: https://www.youtube.com/watch?v=XDhJ8lVGbl8&list=PLEC88901EBADDD980

- Recitation Classes: https://www.youtube.com/watch?v=76WdBlGpxVw&list=PL64BDFBDA2AF24F7E
Probability and Statistics

- Theory: https://www.youtube.com/watch?v=j9WZyLZCBzs&list=PLN56AJ9-AkJ2r-BFQbbNqoJ3TY9Dd-jus

- Recitation Classes: https://www.youtube.com/watch?v=j9WZyLZCBzs&list=PLUl4u3cNGP60A3XMwZ5sep719_nh95qOe
Enjoy!

PS: This changes my initial goal of not overlaping with Khan Academy, but I think this is worth it.

 

[ModusPonens]

These are several courses on computational mathematics and/or numerical methods in analysis. The disadvantage of these lectures is, of course, that each university around the world use its own programming languages. If you use the same programming language, it will probably be useful. Even if you don't, it might still be of use.Numerical Methods and Programing

https://www.youtube.com/playlist?list=PLCA944605A8EDE42A


Numerical Methods and Computation

https://www.youtube.com/playlist?list=PL6E313980EF23CA6EElementary Numerical Analysis

https://www.youtube.com/playlist?list=PL8B0C4C2274C2C04B


Numerical methods of Ordinary and Partial Differential Equations

https://www.youtube.com/playlist?list=PLbMVogVj5nJRILpJJO7KrZa8Ttj4_ZAgl

 

[ModusPonens]

These are courses in the area of analysis. But only courses more advanced than calculus.


[h=1]A Basic Course in Real Analysis [/h]
https://www.youtube.com/playlist?list=PLbMVogVj5nJQ1UXrOm7KqTg9UKk6eXRp_

[h=1]
Real Analysis [/h]
https://www.youtube.com/playlist?list=PLbMVogVj5nJSxFihV-ec4A3z_FOGPRCo-[h=1]Complex Analysis [/h]
https://www.youtube.com/playlist?list=PLbMVogVj5nJS_i8vfVWJG16mPcoEKMuWT[h=1]Measure and Integration [/h]
https://www.youtube.com/playlist?list=PL583C690FE66FF338


[h=1] Functional Analysis [/h]
https://www.youtube.com/playlist?list=PL5022A32B9BCFE3E4


[h=1]Calculus of Variations and Integral Equations[/h]
https://www.youtube.com/playlist?list=PL521C2DFD15FF568CThis is a more general course, in nature. As the name explains, it's directed at engineers.
[h=1]Advanced Engineering Mathematics [/h]
https://www.youtube.com/playlist?list=PLbMVogVj5nJSgrtwLEfYZIlrglCXYxgdo

 

[ModusPonens]

Hello

These are lectures in category theory. The best material is by the Catsters, as was posted above. But I'll repeat, because it's worth it:Category Theory Lectures by TheCatsters

Catster Videos - This link gives the order in which the videos should be watched. However, it's not entirely linear, as presented in this list. Sometimes you have to go a few videos ahead to understand what you're watching. However, these do not provide an introduction. Category Theory Foundations

https://www.youtube.com/watch?v=BF6kHD1DAeU&list=PLGCr8P_YncjVjwAxrifKgcQYtbZ3zuPlb - This is introductory material by Steve Awodey. He has a well known category theory introduction book at undergraduate level.Introduction to Category Theory

https://www.youtube.com/watch?v=pH0haHFiWLU&list=PL7a2OL9aVVFfTFGr-cbPv8AKqQ2j6vjVR - Introductory material by Valeria de Paiva.
After the introductory material and the Catsters videos, these should be accessibleIntroduction to Monoidal Categories

https://www.youtube.com/watch?v=cPmbwavObxk&list=PL7a2OL9aVVFeoOXky-S2nxHAO9n31fpLTTopos Theory Mini-Course

https://www.youtube.com/watch?v=v1vtBYDWiB4&list=PL7a2OL9aVVFdCmlHnj_xL-epEK4k-hDb3Categorical Logic

https://www.youtube.com/watch?v=SuALGpy2o6k&list=PL13E859FFF39E5832Category Theory Seminars

https://www.youtube.com/watch?v=6bnU7_6CNa0&list=PL7a2OL9aVVFdEw2WzgHo_lvvFN57DehEI



And now category theory for specific purposes.Category Theory for Algebraic Topology

https://www.youtube.com/watch?v=fBe0...JxqIJ5LoKkAmSwCategory Theory for JavaScript Programmers

https://www.youtube.com/watch?v=-FkgOHvNAU8&list=PLwuUlC2HlHGe7vmItFmrdBLn6p0AS8ALX
Enjoy :)

 

[Opalg]

LMS Popular Lectures Series

The London Mathematical Society's Popular Lecture Series is currently being uploaded to YouTube.

https://www.youtube.com/channel/UCvp7jsbXjx2k8sGEkdtWCAw