MIT OpenCourseWare: Free Courses from the institute

MIT 18.100B Real Analysis, Spring 2025
Instructor: Tobias Holck Colding
View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG

Uploaded 02-09-25

We will get deeper into some of the properties of the real numbers that we will need and use in the class. This will include completeness in the form of least upper bound property of a bounded subset of the reals. We will also see that the set of rational numbers is not complete and we will therefore need a larger set of numbers. This larger set is the reals.

License: Creative Commons BY-NC-SA
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MIT 9.01 Neuroscience and Behavior, Fall 2003
Instructor: Prof. Gerald E. Schneider
View the complete course: http://ocw.mit.edu/courses/brain-and-cognitive-sciences/9-01-neuroscience-and-behavior-fall-2003
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63U7FmbKD9KClb-94dyPJim

Uploaded 16-05-22

Spinal Cord; Autonomic NS

License: Creative Commons BY-NC-SA
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Speakers: Prof. Gerald E. Schneider



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MIT 18.100B Real Analysis, Spring 2025
Instructor: Tobias Holck Colding
View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG

Uploaded 02-09-25

We begin by giving a useful characterization of what it means for a set to be closed. This is the notion that a set contains all its limit points. After that, we turn to the notion of a cover and, in particular, open covers and use it to define compact subsets of a metric space.

License: Creative Commons BY-NC-SA
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MIT RES.6-013 Neuroscience and Behavior, Fall 2021
Instructor: Brandon Leshchinskiy
View the complete course: http://ocw.mit.edu/courses/res-6-013-ai-101-fall-2021/

Uploaded 20-05-22

This is a video of Brandon Leshchinskiy's presentation "AI 101," which provides an introductory overview of the application of artificial intelligence in solving real-world problems: which tasks machine learning handles well, how it works, and what its shortcomings are.

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Speakers: Brandon Leshchinskiy



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MIT 18.100B Real Analysis, Spring 2025
Instructor: Tobias Holck Colding
View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG

Uploaded 02-09-25

The Bolzano-Weierstrass theorem say that any bounded sequence has a convergent subsequence. This crucial fact can be used to show other important theorems. An almost immediate consequence of it is the Cauchy convergence theorem. We also introduce the notion of a series and get acquainted with perhaps the single most important series: the geometric series. For series, the most important question is whether or not it is convergent. To determine that, there are a number of tests beginning with the two versions of the comparison test.

License: Creative Commons BY-NC-SA
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MIT ESD.932 Engineering Ethics, Spring 2006
Instructor: Dr. Taft Broome
View the complete course: https://ocw.mit.edu/courses/esd-932-engineering-ethics-spring-2006/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61YF5HCMnGUwJ8D-PNNs3OR

Uploaded 06-06-22

This course introduces the theory and the practice of engineering ethics using a multi-disciplinary and cross-cultural approach. Theory includes ethics and philosophy of engineering. Historical cases are taken primarily from the scholarly literatures on engineering ethics, and hypothetical cases are written by students. Each student will write a story by selecting an ancestor or mythic hero as a substitute for a character in a historical case. Students will compare these cases and recommend action.

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



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MIT 18.100B Real Analysis, Spring 2025
Instructor: Tobias Holck Colding
View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG

Uploaded 02-09-25

We use Weierstrass M-test to prove continuity of power series inside the radius of convergence. We also show that C([a; b]) with the supremum norm is Cauchy complete. This will later play an important role when we establish existence and uniqueness of solutions to ordinary differential equations. Toward the end of the lecture we show that integrals and differentiation behave well under uniform convergence.

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.



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MIT ESD.932 Engineering Ethics, Spring 2006
Instructor: Dr. Taft Broome
View the complete course: https://ocw.mit.edu/courses/esd-932-engineering-ethics-spring-2006/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61YF5HCMnGUwJ8D-PNNs3OR

Uploaded 06-06-22

This course introduces the theory and the practice of engineering ethics using a multi-disciplinary and cross-cultural approach. Theory includes ethics and philosophy of engineering. Historical cases are taken primarily from the scholarly literatures on engineering ethics, and hypothetical cases are written by students. Each student will write a story by selecting an ancestor or mythic hero as a substitute for a character in a historical case. Students will compare these cases and recommend action.

License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
Support OCW at http://ow.ly/a1If50zVRlQ

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: Dr. Taft Broome



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MIT 6.1200J Mathematics for Computer Science, Spring 2024
Instructor: Erik Demaine

Uploaded 23-07-25

View the complete course: https://ocw.mit.edu/courses/6-1200j-mathematics-for-computer-science-spring-2024/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61VNvICqk2HXJTonnKgAc9d

Today we’re going to introduce a new abstraction called a state machine, that lets us model how algorithms work. We’ll show how to use induction to prove properties of state machines.

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.



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MIT ESD.932 Engineering Ethics, Spring 2006
Instructor: Dr. Taft Broome
View the complete course: https://ocw.mit.edu/courses/esd-932-engineering-ethics-spring-2006/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61YF5HCMnGUwJ8D-PNNs3OR

Uploaded 06-06-22

This course introduces the theory and the practice of engineering ethics using a multi-disciplinary and cross-cultural approach. Theory includes ethics and philosophy of engineering. Historical cases are taken primarily from the scholarly literatures on engineering ethics, and hypothetical cases are written by students. Each student will write a story by selecting an ancestor or mythic hero as a substitute for a character in a historical case. Students will compare these cases and recommend action.

License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
Support OCW at http://ow.ly/a1If50zVRlQ

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: Dr. Taft Broome



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