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MIT OpenCourseWare: Free Courses from the institute

MIT OpenCourseWare

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 OCW website, each course includes a syllabus, instructional material like notes and reading lists, and learning activities like assignments and solutions. Some courses also have videos, online textbooks, and faculty insights on teaching.Knowledge is your reward. There"s no signup or enrollment, and no

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51:11

Lecture 4 Part 2: Nonlinear Root Finding,...

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/06

MIT 18.S096 Matrix Calculus For Machine Learning And Beyond, IAP 2023Instructors: Alan Edelman, Steven G. JohnsonUploaded 23-10-23View 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_VCN4izBKK6OEDescription: Nonlinear root finding by Newton’s method and optimization by gradient descent. “Adjoint” methods (reverse-mode/backpropagation) lets us find

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86:22

19. Games, Generalized Geography

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/06

MIT 18.404J Theory of Computation, Fall 2020Instructor: Michael SipserView the complete course: https://ocw.mit.edu/18-404JF20YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWYUploaded 06-10-21Quickly reviewed last lecture. Discussed a connection between games and quantifiers. Described the formula game and showed that generalized geography is PSPACE-complete. Introduced log space: L and NL. Defined the configuration graph to prove NL is a subset of

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52:53

Lecture 7 Part 2: Second Derivatives, Bilinear Forms,...

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/06

MIT 18.S096 Matrix Calculus For Machine Learning And Beyond, IAP 2023Instructors: Alan Edelman, Steven G. JohnsonUploaded 23-10-23View 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_VCN4izBKK6OEDescription: First derivatives are linear operators, so second derivatives are bilinear forms, sometimes called “Hessians” (especially for scalar-valued

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86:50

20. L and NL, NL = coNL

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/06

MIT 18.404J Theory of Computation, Fall 2020Instructor: Michael SipserView the complete course: https://ocw.mit.edu/18-404JF20YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWYUploaded 06-10-21Reviewed log space: NL is a subset of SPACE(log^2n) and NL is a subset of P. Introduced log-space transducers and log-space reducibility. Defined NL-completeness. Proved that PATH is NL-complete. Also proved the Immerman-Szelepcsényi theorem: NL = coNL.License: Creative

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70:33

Lecture 4 Part 1: Gradients and Inner Products in...

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/06

MIT 18.S096 Matrix Calculus For Machine Learning And Beyond, IAP 2023Instructors: Alan Edelman, Steven G. JohnsonView 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_VCN4izBKK6OEDescription: We can generalize the concept of a “gradient” beyond column vectors, e.g. to “matrix gradients” if we first generalize the concept of inner product.License:

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90:00

24. Probabilistic Computation (cont.)

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/06

MIT 18.404J Theory of Computation, Fall 2020Instructor: Michael SipserView the complete course: https://ocw.mit.edu/18-404JF20YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWYQuickly reviewed last lecture. Simulated read-once branching programs by polynomials. Gave a probabilistic polynomial equality testing method. Concluded proving that EQ for ROBP is in BPP.License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at

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37:02

Lecture 2 Part 2: Vectorization of Matrix Functions

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/05

MIT 18.S096 Matrix Calculus For Machine Learning And Beyond, IAP 2023Instructors: Alan Edelman, Steven G. JohnsonView 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_VCN4izBKK6OEDescription: We can view matrix functions (matrix inputs/outputs) as “ordinary” multivariable calculus by “vectorizing” a matrix into a column vector.License: Creative

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86:07

14. P and NP, SAT, Poly-Time Reducibility

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/05

MIT 18.404J Theory of Computation, Fall 2020Instructor: Michael SipserView the complete course: https://ocw.mit.edu/18-404JF20YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWYNOTE: There is no video for Lecture 13 as that was the day for the Midterm Exam.Quickly reviewed last lecture. Defined NTIME(t(n)) complexity classes and the class NP. Showed that COMPOSITES is in NP. Discussed the P versus NP question. Proved that acceptance problem for CFG is in P

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55:12

Lecture 1 Part 2: Derivatives as Linear Operators

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/05

MIT 18.S096 Matrix Calculus For Machine Learning And Beyond, IAP 2023Instructors: Alan Edelman, Steven G. JohnsonView 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_VCN4izBKK6OEDescription: The key to generalizing derivatives is to realize that they are linear operators, relating small changes in a functions input to small changes in the

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76:46

3. Regular Pumping Lemma, Conversion of FA to Regular...

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/05

MIT 18.404J Theory of Computation, Fall 2020Instructor: Michael SipserView the complete course: https://ocw.mit.edu/18-404JF20YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWYQuickly reviewed last lecture. Showed conversion of DFAs to regular expressions. Gave a method for proving languages not regular by using the pumping lemma and closure properties. Introduced context free grammars (CFGs).License: Creative Commons BY-NC-SAMore information at

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72:14

Lecture 8 Part 2: Automatic Differentiation on...

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/05

MIT 18.S096 Matrix Calculus For Machine Learning And Beyond, IAP 2023Instructors: Alan Edelman, Steven G. JohnsonView 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_VCN4izBKK6OEDescription: Complicated computational processes can be expressed as “graphs” of computational steps that flow from inputs to outputs. Forward/reverse-mode automatic

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83:21

9. Reducibility

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/05

MIT 18.404J Theory of Computation, Fall 2020Instructor: Michael SipserView the complete course: https://ocw.mit.edu/18-404JF20YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWYQuickly reviewed last lecture. Discussed the reducibility method to prove undecidability and T-unrecognizability. Defined mapping reducibility as a type of reducibility. Showed that emptiness problem for TMs is undecidable and T-unrecognizable.License: Creative Commons BY-NC-SAMore

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73:02

Lecture 7 Part 1: Derivatives of Random Functions

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/05

MIT 18.S096 Matrix Calculus For Machine Learning And Beyond, IAP 2023Instructors: Alan Edelman, Steven G. JohnsonView 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_VCN4izBKK6OEDescription: Even if a function f is stochastic (has random numbers in it), we can still define a derivative “on average” (whose expectation value is the derivative of the

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80:43

5. CF Pumping Lemma, Turing Machines

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/05

MIT 18.404J Theory of Computation, Fall 2020Instructor: Michael SipserView the complete course: https://ocw.mit.edu/18-404JF20YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWYQuickly reviewed last lecture. Proved the CFL pumping lemma as a tool for showing that languages are not context free. Defined Turing machines (TMs). Defined TM deciders (halt on all inputs).License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at

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79:11

Lecture 4: Smart Contracts as a Solution to a...

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/05

MIT 14.129 Blockchain and the Design of Financial Systems, Spring 2025Instructor: Robert M. TownsendView the complete course: https://ocw.mit.edu/courses/14-129-blockchain-and-the-design-of-financial-systems-spring-2025YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60gb6cVqrZQXQ217r0PwZJgThis lecture covers the commodity space, the policy objective, implementation with privately issued securities, uncoordinated Issues, and market crises.License: Creative Commons BY-NC-SAMore

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76:27

12. Carbohydrates/Introduction to Membranes

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/04

MIT 7.05 General Biochemistry, Spring 2020Instructor: Matthew Vander HeidenView the complete course: https://ocw.mit.edu/7-05S20YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62wNcIMfinU64CAfreShjptIn this pre-COVID-19 pandemic lecture of 2020, Professor Vander Heiden discusses two classes of biomolecules: carbohydrates and lipids including their nomenclature, structures, and properties. License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses

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78:12

Lecture 10: Designs of Financial Infrastructure...

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/04

MIT 14.129 Blockchain and the Design of Financial Systems, Spring 2025Instructor: Robert M. TownsendView the complete course: https://ocw.mit.edu/courses/14-129-blockchain-and-the-design-of-financial-systems-spring-2025YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60gb6cVqrZQXQ217r0PwZJgThis lecture covers auctions, hybrid credit, and insurance. License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at https://ocw.mit.eduSupport OCW at

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65:05

Lecture 6 Part 1: Adjoint Differentiation of ODE...

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/04

MIT 18.S096 Matrix Calculus For Machine Learning And Beyond, IAP 2023Instructors: Alan Edelman, Steven G. JohnsonView 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_VCN4izBKK6OEDescription: Many systems are modeled by ordinary differential equations (ODEs), and often you want the derivative of the ODE solution with respect to parameters of the

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78:47

20. Asynchronous Distributed Algorithms:...

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/04

MIT 6.046J Design and Analysis of Algorithms, Spring 2015View the complete course: http://ocw.mit.edu/6-046JS15Complete course playlist: https://www.youtube.com/watch?v=2P-yW7LQr08&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGpInstructor: Nancy Ann LynchIn this lecture, Professor Lynch introduces asynchronous distributed algorithms.License: Creative Commons BY-NC-SAMore information at http://ocw.mit.edu/termsMore courses at http://ocw.mit.eduLearn more about your ad choices. Visit

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83:38

Lecture 7: Stochastic Financial Networks

MIT OpenCourseWare: Free Courses from the institute ·

2026/10/04

MIT 14.129 Blockchain and the Design of Financial Systems, Spring 2025Instructor: Robert M. TownsendView the complete course: https://ocw.mit.edu/courses/14-129-blockchain-and-the-design-of-financial-systems-spring-2025YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60gb6cVqrZQXQ217r0PwZJgThis lecture addresses liquidity and the value of key players versus contagion dynamics.License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at

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