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MIT 18.226 Probabilistic Methods in Combinatorics, Fall 2024
Instructor: Yufei Zhao

Uploaded 06-11-24

View the complete course: https://ocw.mit.edu/courses/18-226-probabilistic-methods-in-combinatorics-fall-2022/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61cYB5ymvFiEbIb-wWHfaqO

A simple application of the probabilistic method in combinatorics: a proof that every graph contains a large bipartite subgraph with at least half of the edges.

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MIT IDS.333 Risk and Decision Analysis, Fall 2021
Instructor: Richard de Neufville
View the complete course: https://ocw.mit.edu/courses/ids-333-risk-and-decision-analysis-fall-2021/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62jwhTqp8_1kwrkDkxZhpQC

Uploaded 28-09-22

This video shows how Flexibility can reduce downside performance (e.g. by committing less at start) and take advantage of favorable situations (by being able to add capacity of functions or both).

This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu.

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MIT 18.226 Probabilistic Methods in Combinatorics, Fall 2024
Instructor: Yufei Zhao

Uploaded 06-11-24

View the complete course: https://ocw.mit.edu/courses/18-226-probabilistic-methods-in-combinatorics-fall-2022/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61cYB5ymvFiEbIb-wWHfaqO

Two quick combinatorial applications of linearity of expectations: (1) the number of fixed points of a random permutation (2) Hamilton paths in tournaments.

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MIT IDS.333 Risk and Decision Analysis, Fall 2021
Instructor: Richard de Neufville
View the complete course: https://ocw.mit.edu/courses/ids-333-risk-and-decision-analysis-fall-2021/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62jwhTqp8_1kwrkDkxZhpQC

Uploaded 28-09-22

The take-aways from the Garage are: (1) you need to deal with uncertainties to get correct answers in uncertain world, and (2) in this context Flexibility in Design offers the possibility of Win-Win solutions.

This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu.

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MIT 18.226 Probabilistic Methods in Combinatorics, Fall 2024
Instructor: Yufei Zhao

Uploaded 06-11-24

View the complete course: https://ocw.mit.edu/courses/18-226-probabilistic-methods-in-combinatorics-fall-2022/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61cYB5ymvFiEbIb-wWHfaqO

Application of the probabilistic method in combinatorics to extremal set theory. How many subsets of an n-element set can you have without having one subset containing another?

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MIT IDS.333 Risk and Decision Analysis, Fall 2021
Instructor: Richard de Neufville
View the complete course: https://ocw.mit.edu/courses/ids-333-risk-and-decision-analysis-fall-2021/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62jwhTqp8_1kwrkDkxZhpQC

Uploaded 28-09-22

This introduces the 'Garage case' as a simple example that illustrates (1) how to calculate system performance in an uncertain world, and (2) that Flexibility provides Win-Win designs.

This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu.

License: Creative Commons BY-NC-SA
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More courses at https://ocw.mit.edu
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MIT 18.226 Probabilistic Methods in Combinatorics, Fall 2024
Instructor: Yufei Zhao

Uploaded 06-11-24

View the complete course: https://ocw.mit.edu/courses/18-226-probabilistic-methods-in-combinatorics-fall-2022/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61cYB5ymvFiEbIb-wWHfaqO

Application of the probabilistic method in combinatorics to graph theory. Proof of a classic and ingenious result of Erdős that there exists graph with arbitrarily high girth and chromatic number.

License: Creative Commons BY-NC-SA
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MIT IDS.333 Risk and Decision Analysis, Fall 2021
Instructor: Richard de Neufville
View the complete course: https://ocw.mit.edu/courses/ids-333-risk-and-decision-analysis-fall-2021/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62jwhTqp8_1kwrkDkxZhpQC

Uploaded 28-09-22

This video summarizes the simulation and valuation of flexibility on in the Antamina mine project.

This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu.

License: Creative Commons BY-NC-SA
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More courses at https://ocw.mit.edu
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MIT 18.226 Probabilistic Methods in Combinatorics, Fall 2024
Instructor: Yufei Zhao

Uploaded 06-11-24

View the complete course: https://ocw.mit.edu/courses/18-226-probabilistic-methods-in-combinatorics-fall-2022/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61cYB5ymvFiEbIb-wWHfaqO

Application of the probabilistic method in combinatorics to extremal set theory. What is the largest intersecting family of k-element subsets of an n-element set? Erdős-Ko-Rado theorem.

License: Creative Commons BY-NC-SA
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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.



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MIT IDS.333 Risk and Decision Analysis, Fall 2021
Instructor: Richard de Neufville
View the complete course: https://ocw.mit.edu/courses/ids-333-risk-and-decision-analysis-fall-2021/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62jwhTqp8_1kwrkDkxZhpQC

Uploaded 28-09-22

Discount rate lowers present cost of later investments. This makes smaller, modular facilities cheaper than large initial investments. Learning from improved design and repetition, similarly counteracts the value of economies of scale.

This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu.

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.



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