MIT OpenCourseWare: Free Courses from the institute

MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez
View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw

Uploaded 21-06-22

Instead of sequences of real numbers, what can we say about sequences of functions? We start a study of Power series, defining pointwise and uniform convergence of sequences of functions.

License: Creative Commons BY-NC-SA
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A Vision of Linear Algebra
Instructor: Gilbert Strang
View the complete course: https://ocw.mit.edu/2020-vision
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61iQEFiWLE21EJCxwmWvvek

Uploaded 12-03-25

The four subspaces are the column spaces and the nullspaces of A and A^T: Two perpendicular subspaces in m-dimensional space and two more in n-dimensional space. A is invertible when m=n and both nullspaces contain only the zero vector. When A is NOT invertible, we look for the vector x in the row space that makes || Ax - b || AS SMALL AS POSSIBLE in the column space. This video finds that winning vector! Instead of x = A^-1 b (that inverse doesn't exist) we introduce the  "pseudoinverse" of A.

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MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez
View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw

Uploaded 21-06-22

We begin proving key properties of derivatives, such as the infamous product rule, quotient rule, and chain rule. We also prove the Mean Value Theorem (MVT), the low-key hero of calculus, and consider some applications.

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A Vision of Linear Algebra
Instructor: Gilbert Strang
View the complete course: https://ocw.mit.edu/2020-vision
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61iQEFiWLE21EJCxwmWvvek

Uploaded 12-03-25

If a matrix A has rank r, then its row echelon form (after elimination) contains the identity matrix in its first r independent columns. How do we interpret the matrix F that appears in the remaining n−r columns of that echelon form? F multiplies those first r independent columns of A to give its n−r dependent columns. Then F reveals bases for the row space and the nullspace of the original matrix A. And F is the key to the column-row factorization A = CR

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Episode 9: Visualizing Calculus with Prof. Gigliola Staffilani

Uploaded 30-06-22

Professor Gigliola Staffilani, who teaches in MIT’s Department of Mathematics, was closely involved in designing and teaching the introductory-level 18.01 Calculus I course series now found on the MIT Open Learning Library. She’s also been involved in teaching calculus to students on campus. To help students become proficient in a notoriously intimidating subject, she has tried to design learning experiences that bridge the gap between the pure abstractions that mathematicians love, exemplified by the use of conventional notation such as x, y, and f(x), and the concrete real-world situations in which calculus is typically applied in other fields such as chemistry or physics. In this episode, Prof. Staffilani discusses her efforts to make calculus less abstract and more intuitive for learners–efforts that draw on a diverse mix of teaching tools and props: digital applets, sketching tools, bagels, croissants, donuts, and even a balloon in a box. She also discusses her commitment to increasing equity and fighting implicit bias in her field.

Relevant Resources:

MIT OpenCourseWare
https://ocw.mit.edu/?utm_source=youtube&utm_medium=youtube&utm_campaign=chalkradio&utm_term=s3e9

The OCW Educator Portal
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Share your teaching insights
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Professor Staffilani’s faculty page
https://math.mit.edu/~gigliola/

Single variable calculus courses on MIT’s Open Learning Library
https://openlearning.mit.edu/courses-programs/open-learning-library?search_api_fulltext=Calculus%2018.01&f[0]=open_moocs_departments%3A29?utm_source=simplecast&utm_medium=simplecast&utm_campaign=chalkradio&utm_term=s3e9?utm_source=youtube&utm_medium=youtube&utm_campaign=chalkradio&utm_term=s3e9

18.01 Calculus I: Single Variable Calculus on OCW
https://ocw.mit.edu/courses/18-01-calculus-i-single-variable-calculus-fall-2020/?utm_source=simplecast&utm_medium=simplecast&utm_campaign=chalkradio&utm_term=s3e9?utm_source=youtube&utm_medium=youtube&utm_campaign=chalkradio&utm_term=s3e9

Music in this episode by Blue Dot Sessions
https://www.sessions.blue

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Show notes by Peter Chipman



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MIT 6.5630 Advanced Topics in Cryptography, Fall 2023
Instructor: Yael T. Kalai

Uploaded 29-01-25

View the complete course: https://ocw.mit.edu/courses/6-5630-advanced-topics-in-cryptography-fall-2023/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61EZllk7zwgvPbI4kbnKhWz

This lecture covers the topics, including the probabilistically checkable proofs (PCP), definition and construction from GKR and the interactive succinct argument for NP.

License: Creative Commons BY-NC-SA
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Speakers: Yael T. Kalai



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MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez
View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw

Uploaded 11-07-22

We begin to discuss limits of functions, introducing cluster points and left and right sided limits. This will help us better understand continuity in the next lecture.

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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MIT 6.5630 Advanced Topics in Cryptography, Fall 2023
Instructor: Rachel Y. Zhang

Uploaded 29-01-25

View the complete course: https://ocw.mit.edu/courses/6-5630-advanced-topics-in-cryptography-fall-2023/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61EZllk7zwgvPbI4kbnKhWz

This lecture covers the topic of IP=PSPACE and its application.

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Speakers: Rachel Y. Zhang



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MIT HST.508 Genomics and Computational Biology, Fall 2002
Instructor: George Church
View the complete course: https://ocw.mit.edu/courses/hst-508-genomics-and-computational-biology-fall-2002/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61gaHWysmlYNeGsuUI8y5GV

Uploaded 22-08-22

We're going to discuss the innards of computers that are going to be helping us with computational biology. We have a schematic diagram here, illustrating in part-- we'll have similar schematic diagrams for biological systems or biochemical systems.

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MIT 6.5630 Advanced Topics in Cryptography, Fall 2023
Instructor: Yael T. Kalai

Uploaded 29-01-25

View the complete course: https://ocw.mit.edu/courses/6-5630-advanced-topics-in-cryptography-fall-2023/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61EZllk7zwgvPbI4kbnKhWz

This lecture covers the topics, including the definition of CI hash functions, existence in the ROM and simple counter example in the plain model.

License: Creative Commons BY-NC-SA
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More courses at https://ocw.mit.edu
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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.

Speakers: Yael T. Kalai



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