8.2 Introduction to 4-Vector Notation

MIT 8.20 Introduction to Special Relativity, January IAP 2021Instructor: Markus KluteView the complete course: https://ocw.mit.edu/8-20IAP21YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61Zc3rR6wVM0kpsiyIq0fk8Uploaded 08-11-21Introduction of 4-vectors.License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at https://ocw.mit.eduSupport OCW at http://ow.ly/a1If50zVRlQWe 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. Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

MIT 9.14 Brain Structure and Its Origins, Spring 2014Instructor: Gerard E. SchneiderUploaded 04-10-23View the complete course (or resource): https://ocw.mit.edu/9-14S14YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62ABe0O-0qtaHHxyKQi1ZwRThis lecture begins the discussion of specializations in the evolving CNS, including sketching the brain and basic pathways of ancestral mammals.License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at https://ocw.mit.eduSupport OCW at http://ow.ly/a1If50zVRlQWe 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. Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

MIT 8.20 Introduction to Special Relativity, January IAP 2021Instructor: Markus KluteView the complete course: https://ocw.mit.edu/8-20IAP21YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61Zc3rR6wVM0kpsiyIq0fk8Uploaded 08-11-21Discussion of properties of waves.License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at https://ocw.mit.eduSupport OCW at http://ow.ly/a1If50zVRlQWe 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. Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

You thought Chalk Radio was a podcast about inspired teaching at MIT? Yes and no! “We don't do a lot of teaching,” says Dr. Ari Epstein, our guest for this week’s episode. Dr. Epstein is associate director of the Terrascope program, a learning community for first-year undergraduates. Each year the program focuses on one particular issue relating to sustainability, and participants in the program learn by direct experience, launching themselves into projects focused on solving complex environmental problems. The role of the program’s instructional staff, Dr. Epstein says, is to create an environment where learning can happen, rather than to impart knowledge or teach skills directly. Toward the end of the semester, the students create a website describing their proposed solutions in as much technical detail as they can. And then a week later, they present their proposals in front of an invited panel of outside experts. In the process of preparing for this presentation, students often come to realize that understanding the history and cultural implications of an issue are just as important as understanding the science behind it and the technology available for dealing with it.Uploaded 22-05-24Relevant Resources:MIT OpenCourseWare (https://ocw.mit.edu)The OCW Educator Portal (https://ocw.mit.edu/educator)Dr. Epstein’s faculty page (https://terrascope.mit.edu/ari-w-epstein/)The Terrascope program (https://terrascope.mit.edu/overview/)RES.12-002 Terrascope on MIT OpenCourseWare (https://ocw.mit.edu/courses/res-12-002-terrascope-spring-2023/)DigDeep (https://www.digdeep.org/)Music in this episode by Blue Dot Sessions (https://www.sessions.blue/) Connect with Us If you have a suggestion for a new episode or have used OCW to change your life or those of others, tell us your story. We’d love to hear from you! Call us @ 617-715-2517 On our site (https://ocw.mit.edu/contact/) On Facebook (https://www.facebook.com/MITOCW/) On X (https://twitter.com/MITOCW?ref_src=twsrc%5Egoogle%7Ctwcamp%5Eserp%7Ctwgr%5Eauthor) On Instagram (https://www.instagram.com/mitocw/) Stay Current Subscribe to the free monthly "MIT OpenCourseWare Update" e-newsletter. (https://ocw.mit.edu/newsletter/) Support OCWIf you like Chalk Radio and OpenCourseware, donate to help keep these programs going! (https://giving.mit.edu/give/to/ocw/?utm_source=ocw&utm_medium=podcast&utm_campaign=donate) CreditsSarah Hansen, host and producer (https://www.linkedin.com/in/sarah-e-hansen/)Brett Paci, producer (https://twitter.com/Brett_Paci)Dave Lishansky, producer (https://twitter.com/DaveResonates)Show notes by Peter Chipman Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

MIT 9.14 Brain Structure and Its Origins, Spring 2014Instructor: Gerard E. SchneiderUploaded 04-10-23View the complete course (or resource): https://ocw.mit.edu/9-14S14YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62ABe0O-0qtaHHxyKQi1ZwRThis lecture completes the discussion about the evolution of multicellular organisms and the initial steps to the CNS of advanced chordates.License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at https://ocw.mit.eduSupport OCW at http://ow.ly/a1If50zVRlQWe 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. Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

MIT RES.21G-505 Kanji Learning Any Time, Any Place for Japanese V, Spring 2022Instructor: Takako AikawaUploaded 15-03-23View the complete resource: https://ocw.mit.edu/courses/res-21g-505-kanji-learning-any-time-any-place-for-japanese-v-spring-2022YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Mr5APSizHgFa0hRiWgPlnThis is a dual-language video, with content in both Japanese and English. Selecting either English or Japanese captions will provide the same dual-language captions. This video covers the Japanese kanji characters in Lesson 1 of the textbook, "Tobira: Gateway to Advanced Japanese Learning Through Content and Multimedia," at https://tobiraweb.9640.jp/.License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at https://ocw.mit.eduSupport OCW at http://ow.ly/a1If50zVRlQWe 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: Takako Aikawa Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

MIT 8.20 Introduction to Special Relativity, January IAP 2021Instructor: Markus KluteView the complete course: https://ocw.mit.edu/8-20IAP21YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61Zc3rR6wVM0kpsiyIq0fk8Uploaded 08-11-21We talk about the algebra of Lorentz transformations.License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at https://ocw.mit.eduSupport OCW at http://ow.ly/a1If50zVRlQWe 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. Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

MIT 9.14 Brain Structure and Its Origins, Spring 2014Instructor: Gerard E. SchneiderUploaded 04-10-23View the complete course (or resource): https://ocw.mit.edu/9-14S14YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62ABe0O-0qtaHHxyKQi1ZwRThis lecture concludes the discussion of specializations in the evolving CNS, including sketching the brain and basic pathways of ancestral mammals.License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at https://ocw.mit.eduSupport OCW at http://ow.ly/a1If50zVRlQWe 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. Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

MIT 8.20 Introduction to Special Relativity, January IAP 2021Instructor: Markus KluteView the complete course: https://ocw.mit.edu/8-20IAP21YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61Zc3rR6wVM0kpsiyIq0fk8Uploaded 08-11-21We talk about the large electron-positron collider LEP and the velocity of electrons and positrons.License: Creative Commons BY-NC-SAMore information at https://ocw.mit.edu/termsMore courses at https://ocw.mit.eduSupport OCW at http://ow.ly/a1If50zVRlQWe 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. Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

In this episode we meet professor and Nobel laureate Esther Duflo and her colleague Dr. Sara Ellison for a discussion about economics: what it is, how it differs from sociology, how it incorporates classic intellectual tools like probability and statistics with newer technologies like machine learning, and how it can itself be a tool for improving the world by solving problems of inequity one problem at a time. As Duflo and Ellison explain, economics has shifted in recent decades from a primarily solo endeavor to an intensely collaborative one, in which any given paper is likely to have multiple co-authors but also to be based on the work of an even larger group of people—not only professional economists but also psychologists, teachers, NGO workers, and so on. (Fittingly, Duflo’s and Ellison’s teaching is collaborative as well; they work together as co-instructors on the course 14.310x Data Analysis for Social Scientists, available on both MITx Online and MIT OpenCourseWare.) Other topics covered in the episode include why online shopping isn’t as cheap as it seems like it should be and why you should disable some of your spreadsheet’s default settings. Uploaded 15-05-24Relevant Resources:MIT OpenCourseWare (https://ocw.mit.edu)The OCW Educator Portal (https://ocw.mit.edu/educator)Professor Duflo’s faculty page (https://economics.mit.edu/people/faculty/esther-duflo)Dr. Ellison’s faculty page (https://economics.mit.edu/people/faculty/sara-fisher-ellison)14.310x Data Analysis for Social Scientists on MIT OpenCourseWare (https://ocw.mit.edu/courses/14-310x-data-analysis-for-social-scientists-spring-2023/)14.310x Data Analysis for Social Scientists on MITx Online (https://mitxonline.mit.edu/courses/course-v1:MITxT+14.310x/)MITx MicroMasters Program in Statistics and Data Science (https://micromasters.mit.edu/ds/) Music in this episode by Blue Dot Sessions (https://www.sessions.blue/) Connect with Us If you have a suggestion for a new episode or have used OCW to change your life or those of others, tell us your story. We’d love to hear from you! Call us @ 617-715-2517 On our site (https://ocw.mit.edu/contact/) On Facebook (https://www.facebook.com/MITOCW/) On X (https://twitter.com/MITOCW?ref_src=twsrc%5Egoogle%7Ctwcamp%5Eserp%7Ctwgr%5Eauthor) On Instagram (https://www.instagram.com/mitocw/) Stay Current Subscribe to the free monthly "MIT OpenCourseWare Update" e-newsletter. (https://ocw.mit.edu/newsletter/) Support OCWIf you like Chalk Radio and OpenCourseware, donate to help keep these programs going! (https://giving.mit.edu/give/to/ocw/?utm_source=ocw&utm_medium=podcast&utm_campaign=donate) CreditsSarah Hansen, host and producer (https://www.linkedin.com/in/sarah-e-hansen/)Brett Paci, producer (https://twitter.com/Brett_Paci)Dave Lishansky, producer (https://twitter.com/DaveResonates)Show notes by Peter Chipman Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices