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

We show three important tests for convergence of infinite series: the ratio, root, and alternating series tests.

License: Creative Commons BY-NC-SA
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MIT 14.01 Principles of Microeconomics, Fall 2023
Instructor: Prof. Jonathan Gruber
View the complete course: https://ocw.mit.edu/14-01F23
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60V7HxLYRaJMbFzP77bzEjb

Uploaded 02-04-25

In this lecture, Prof. Gruber introduces the topic of social insurance, a form of social welfare that provides insurance against economic risks. Additional topics include tradeoffs and social security. Keywords: insurance, tradeoffs, social security, risks, welfare, asymmetric information

License: Creative Commons BY-NC-SA
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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 study Taylor’s theorem, essentially a direct consequence of applying the Mean Value Theorem repeatedly. We also begin our study of the Riemann integral, defining partitions and Riemann sums.

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 14.01 Principles of Microeconomics, Fall 2023
Instructor: Prof. Jonathan Gruber
View the complete course: https://ocw.mit.edu/14-01F23
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60V7HxLYRaJMbFzP77bzEjb

Uploaded 02-04-25

Prof. Gruber introduces the class by explaining microeconomics as the study of individuals and firms who make themselves as well off as possible in a world full of scarcity. He then explains the core concepts of supply and demand. Keywords: microeconomics, scarcity, constrained optimization, supply and demand

License: Creative Commons BY-NC-SA
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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 introduce Cauchy sequences and prove the completeness of the real numbers: i.e. every Cauchy sequence is convergent. We also begin studying infinite series, which we will focus on for the next few lectures, starting with geometric series.

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 14.01 Principles of Microeconomics, Fall 2023
Instructor: Prof. Jonathan Gruber
View the complete course: https://ocw.mit.edu/14-01F23
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60V7HxLYRaJMbFzP77bzEjb

Uploaded 02-04-25

In this lecture, Prof. Gruber introduces the idea of oligopoly, where a small number of companies have significant control over the market and can influence prices, like the auto industry. Other topics covered include game theory and the Cournot model. Keywords: oligopoly, game theory, Cournot model, market structure, cooperation, cartel, competition

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 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 wrap up our discussion of cluster points and move towards continuity. We show that sine and cosine are continuous, prove facts about algebraic operations on continuous functions, and define the Dirichlet function.

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 14.01 Principles of Microeconomics, Fall 2023
Instructor: Prof. Jonathan Gruber
View the complete course: https://ocw.mit.edu/14-01F23
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60V7HxLYRaJMbFzP77bzEjb

Uploaded 02-04-25

In this lecture, Prof. Gruber talks about shocks to demand and supply, shapes of demand and supply, consumer and producer surplus, and how competition maximizes welfare. supply and demand, consumer surplus, producer surplus, competition

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 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 prove the humble, but powerful, triangle inequality, and show that the real numbers are uncountable, and thus the irrational numbers greatly outnumber the rational numbers. We introduce sequences and limits of real numbers.

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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MIT 14.01 Principles of Microeconomics, Fall 2023
Instructor: Prof. Jonathan Gruber
View the complete course: https://ocw.mit.edu/14-01F23
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60V7HxLYRaJMbFzP77bzEjb

Uploaded 02-04-25

In this lecture, Prof. Gruber introduces the concept of externalities, which are a positive or negative side effect or consequence of an activity that affects other people or firms who did not choose to be involved in the activity. Keywords: externality, consequence, externality theory, government, policy, practices   

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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