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  1. MHB Apprentice
    ModusPonens's Avatar
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    #1
    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:


    ----> 42 Lectures culminating in the Gödel incompleteness theorems.


    Category Theory lecture series:


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

    ----> this is the Catsters youtube channel


    Abstract Algebra lecture series:



    -----> Group Theory, Ring Theory, Field Theory and Galois Theory


    General Topology lecture series:

    ---> This is a playlist that has 29 lectures and a few others which are not in the same lecture series.


    Algebraic Topology lecture series:

    ----> Includes algebra reviewing material


    Differential Geometry lecture series:


    -----> Seems to be at beginner's level


    Algebraic Geometry lecture series:

    ----> 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
    Last edited by ModusPonens; February 14th, 2014 at 08:15.

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  3. MHB Apprentice
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    #2 Thread Author
    Playlists on algebraic topology and algebraic geometry.

    Algebraic Topology and Geometry

    - Category Theory for Algebraic Topology:

    - Algebraic Topology: - This is the introductory material: homotopy and covering spaces

    - Homology:

    - Cohomology:

    - Homological Algebra:

    - Algebraic Geometry:

    - Vector Bundles and Char Classes:

  4. MHB Apprentice
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    #3 Thread Author
    These are MIT lectures on introductory mathematics, i.e., Discrete Mathematics, Linear Algebra, Calculus, Differential Equations and Probability and Statistics.


    Discrete Mathematics





    Linear Algebra

    - Theory:

    - Recitation Classes:



    Single Variable Calculus

    - Theory:

    - Recitation Classes:



    Multivariable Calculus

    - Theory:

    - Recitation Classes:



    Differential Equations

    - Theory:

    - Recitation Classes:



    Probability and Statistics


    - Theory:

    - Recitation Classes:



    Enjoy!




    PS: This changes my initial goal of not overlaping with Khan Academy, but I think this is worth it.
    Last edited by ModusPonens; March 14th, 2014 at 16:35.

  5. MHB Apprentice
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    #4 Thread Author
    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




    Numerical Methods and Computation




    Elementary Numerical Analysis




    Numerical methods of Ordinary and Partial Differential Equations

    Last edited by ModusPonens; March 18th, 2014 at 17:56.

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    #5 Thread Author
    These are courses in the area of analysis. But only courses more advanced than calculus.


    A Basic Course in Real Analysis




    Real Analysis





    Complex Analysis




    Measure and Integration




    Functional Analysis




    Calculus of Variations and Integral Equations




    This is a more general course, in nature. As the name explains, it's directed at engineers.
    Advanced Engineering Mathematics


  7. MHB Apprentice
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    #6 Thread Author
    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

    - 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

    - This is introductory material by Steve Awodey. He has a well known category theory introduction book at undergraduate level.


    Introduction to Category Theory

    - Introductory material by Valeria de Paiva.



    After the introductory material and the Catsters videos, these should be accessible


    Introduction to Monoidal Categories




    Topos Theory Mini-Course




    Categorical Logic




    Category Theory Seminars





    And now category theory for specific purposes.


    Category Theory for Algebraic Topology




    Category Theory for JavaScript Programmers





    Enjoy

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    #7
    The London Mathematical Society's Popular Lecture Series is currently being uploaded to YouTube.


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