MIT OpenCourseWare: Free Courses from the institute

MIT OpenCourseWare: Free Courses from the institute

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  • 26. coNP is a subset of IP

    MIT 18.404J Theory of Computation, Fall 2020
    Instructor: Michael Sipser
    View the complete course: https://ocw.mit.edu/18-404JF20
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY

    Uploaded 06-10-21

    Quickly reviewed last lecture. Discussed the arithmetization of Boolean formulas. Finished the theorem: #SAT is in IP and concluded that coNP is a subset of IP.

    License: Creative Commons BY-NC-SA
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    1 hr 31 min
  • Lecture 17: Bayesian Nash Equilibrium: Applications

    MIT 14.12 Economic Applications of Game Theory, Fall 2025
    Instructor: Ian Ball
    View the complete course: https://ocw.mit.edu/courses/14-12-economic-applications-of-game-theory-fall-2025/
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63quuKvMHCt3cmTmt0O2qpv

    In this lecture, Ian Ball continues explaining the Bayesian Nash Equilibrium, and includes applications such as the Cournot competition and auctions.

    License: Creative Commons BY-NC-SA
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    1 hr 17 min
  • L2.1 Symmetries: Introduction

    MIT 8.701 Introduction to Nuclear and Particle Physics, Fall 2020
    Instructor: Markus Klute
    View the complete course: https://ocw.mit.edu/8-701F20
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Do91PdN978llIsvjKW0au

    A brief introduction to the importance of symmetries and Noether's theorem.

    License: Creative Commons BY-NC-SA
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    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.

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    10 min
  • Lecture 20: Ad Auctions

    MIT 14.12 Economic Applications of Game Theory, Fall 2025
    Instructor: Ian Ball
    View the complete course: https://ocw.mit.edu/courses/14-12-economic-applications-of-game-theory-fall-2025/
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63quuKvMHCt3cmTmt0O2qpv

    Ian Ball begins this lecture by reviewing revenue equivalence and then transitions to talking about keyword search auctions, like Google ads.

    License: Creative Commons BY-NC-SA
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    1 hr 23 min
  • Lecture 3 Part 1: Kronecker Products and Jacobians

    MIT 18.S096 Matrix Calculus For Machine Learning And Beyond, IAP 2023
    Instructors: Alan Edelman, Steven G. Johnson

    Uploaded 23-10-23

    View the complete course: https://ocw.mit.edu/courses/18-s096-matrix-calculus-for-machine-learning-and-beyond-january-iap-2023/
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62EaLLH92E_VCN4izBKK6OE

    Description: Matrix-function derivatives are linear operators on matrices, but they can often be turned into “ordinary” Jacobian matrices using Kronecker products.

    License: Creative Commons BY-NC-SA
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    1 hr
  • L7.2 Higgs Physics: Fermion Masses

    MIT 8.701 Introduction to Nuclear and Particle Physics, Fall 2020
    Instructor: Markus Klute
    View the complete course: https://ocw.mit.edu/8-701F20
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Do91PdN978llIsvjKW0au

    A brief discussion of fermion masses.

    License: Creative Commons BY-NC-SA
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    6 min
  • Lecture 5: Nash Equilibrium

    MIT 14.12 Economic Applications of Game Theory, Fall 2025
    Instructor: Ian Ball
    View the complete course: https://ocw.mit.edu/courses/14-12-economic-applications-of-game-theory-fall-2025/
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63quuKvMHCt3cmTmt0O2qpv

    In this lecture, Ian Ball explains Nash equilibrium, a game theory idea that describes a situation where each person is choosing the best response to everyone else, so no one gains by changing alone. Using examples like two friends choosing between a Celtics game and a Red Sox game and a hide-and-seek game, the lesson also shows why people sometimes need to randomize their choices to avoid being predictable.

    License: Creative Commons BY-NC-SA
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    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.

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    1 hr 27 min
  • L4.6 QED: Examples

    MIT 8.701 Introduction to Nuclear and Particle Physics, Fall 2020
    Instructor: Markus Klute
    View the complete course: https://ocw.mit.edu/8-701F20
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Do91PdN978llIsvjKW0au

    With all tools in place, we can now start calculating transition amplitudes for QED processes. In this video, we look at electron muon scattering as one example.

    License: Creative Commons BY-NC-SA
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    7 min
  • 7. Decision Problems for Automata and Grammars

    MIT 18.404J Theory of Computation, Fall 2020
    Instructor: Michael Sipser
    View the complete course: https://ocw.mit.edu/18-404JF20
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY

    Uploaded 06-10-21

    Quickly reviewed last lecture. Showed the decidability of various problems about automata and grammars. Also showed that acceptance problem for TMs is T-recognizable.

    License: Creative Commons BY-NC-SA
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    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.



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    1 hr 24 min
  • Lecture 15: Implicit Cartels

    MIT 14.12 Economic Applications of Game Theory, Fall 2025
    Instructor: Ian Ball
    View the complete course: https://ocw.mit.edu/courses/14-12-economic-applications-of-game-theory-fall-2025/
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63quuKvMHCt3cmTmt0O2qpv

    In this lecture, Ian Ball discusses cartels, which is a group of independent market participants who collaborate with each other and avoid competing with each other in order to improve their profits and dominate the market. OPEC is a classic example.

    License: Creative Commons BY-NC-SA
    More information at https://ocw.mit.edu/terms
    More courses at https://ocw.mit.edu
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    1 hr 29 min

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A free and open online publication of educational material from thousands of MIT courses, covering the entire MIT curriculum, ranging from introductory to the most advanced graduate courses. On the…