►Support the Channel Patreon: https://patreon.com/majorprep PayPal: https://www.paypal.me/majorprep Computer science majors have to learn a different kind of math compared to MOST other majors (with the exception of math majors, plus computer and software engineers). This kind of math is important especially for those looking to go into research in fields like computer science, A.I., or even pure mathematics. Join Facebook Group: https://www.facebook.com/groups/majorprep/ Follow MajorPrep on Twitter: https://twitter.com/MajorPrep1 ►Check out the MajorPrep Amazon Store: https://www.amazon.com/shop/majorprep *************************************************** ► For more information on math, science, and engineering majors, check us out at https://majorprep.com Best Ways to Contact Me: Facebook, twitter, or email ([email protected])
Views: 293707 MajorPrep
(NOTE: This new upload has improved audio; the initial upload had 267 views) JOHN VOIGHT John Voight is an assistant professor of mathematics and computer science. His research interests include computational and algorithmic aspects of number theory and arithmetic algebraic geometry, with applications in cryptography and coding theory. About TEDx In the spirit of ideas worth spreading, TEDx is a program of local, self-organized events that bring people together to share a TED-like experience. At a TEDx event, TEDTalks video and live speakers combine to spark deep discussion and connection in a small group. These local, self-organized events are branded TEDx, where x = independently organized TED event. The TED Conference provides general guidance for the TEDx program, but individual TEDx events are self-organized.* (*Subject to certain rules and regulations)
Views: 2197 TEDx Talks
Learn more advanced front-end and full-stack development at: https://www.fullstackacademy.com Elliptic Curve Cryptography (ECC) is a type of public key cryptography that relies on the math of both elliptic curves as well as number theory. This technique can be used to create smaller, faster, and more efficient cryptographic keys. In this Elliptic Curve Cryptography tutorial, we build off of the Diffie-Hellman encryption scheme and show how we can change the Diffie-Hellman procedure with elliptic curve equations. Watch this video to learn: - The basics of Elliptic Curve Cryptography - Why Elliptic Curve Cryptography is an important trend - A comparison between Elliptic Curve Cryptography and the Diffie-Hellman Key Exchange
Views: 22199 Fullstack Academy
Elliptic Curve Cryptography (ECC) is hot. Far better scalable than traditional encryption, more and more data and networks are being protected using ECC. Not many people know the gory details of ECC though, which given its increasing prevalence is a very bad thing. In this presentation I will turn all members of the audience into ECC experts who will be able to implement the relevant algorithms and also audit existing implementations to find weaknesses or backdoors. Actually, I won't. To fully understand ECC to a point where you could use it in practice, you would need to spend years inside university lecture rooms to study number theory, geometry and software engineering. And then you can probably still be fooled by a backdoored implementation. What I will do, however, is explain the basics of ECC. I'll skip over the gory maths (it will help if you can add up, but that's about the extent of it) and explain how this funny thing referred to as "point addition on curves" can be used to exchange a secret code between two entities over a public connection. I will also explain how the infamous backdoor in Dual_EC_DRGB (a random number generator that uses the same kind of maths) worked. At the end of the presentation, you'll still not be able to find such backdoors yourselves and you probably realise you never will. But you will be able to understand articles about ECC a little better. And, hopefully, you will be convinced it is important that we educate more people to become ECC-experts.
Views: 24338 Security BSides London
Computer Science/Discrete Mathematics Seminar Topic: Algebraic geometric codes and their applications Speaker: Gil Cohen Affiliation: Princeton University For more videos, visit http://video.ias.edu
Views: 1617 Institute for Advanced Study
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Symmetric keys are essential to encrypting messages. How can two people share the same key without someone else getting a hold of it? Upfront asymmetric encryption is one way, but another is Diffie-Hellman key exchange. This is part 3 in our Cryptography 101 series. Check out the playlist here for parts 1 & 2: https://www.youtube.com/watch?v=NOs34_-eREk&list=PLa6IE8XPP_gmVt-Q4ldHi56mYsBuOg2Qw Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode Topology vs. “a” Topology https://www.youtube.com/watch?v=tdOaMOcxY7U&t=13s Symmetric single-key encryption schemes have become the workhorses of secure communication for a good reason. They’re fast and practically bulletproof… once two parties like Alice and Bob have a single shared key in hand. And that’s the challenge -- they can’t use symmetric key encryption to share the original symmetric key, so how do they get started? Written and Hosted by Gabe Perez-Giz Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington Made by Kornhaber Brown (www.kornhaberbrown.com) Thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level! And thanks to Nicholas Rose, Jason Hise, Thomas Scheer, Marting Sergio H. Faester, CSS, and Mauricio Pacheco who are supporting us at the Lemma level!
Views: 51493 PBS Infinite Series
Learn more advanced front-end and full-stack development at: https://www.fullstackacademy.com Elliptic Curve Cryptography (ECC) is a type of public key cryptography that relies on the math of both elliptic curves as well as number theory. This technique can be used to create smaller, faster, and more efficient cryptographic keys. In this Elliptic Curve Cryptography tutorial, we introduce the mathematical structure behind this new algorithm. Watch this video to learn: - What Elliptic Curve Cryptography is - The advantages of Elliptic Curve Cryptography vs. old algorithms - An example of Elliptic Curve Cryptography
Views: 11425 Fullstack Academy
AGNES is a series of weekend workshops in algebraic geometry. One of our goals is to introduce graduate students to a broad spectrum of current research in algebraic geometry. AGNES is held twice a year at participating universities in the Northeast. Lecture presented by Kiran Kedlaya.
Views: 1115 Brown University
Basic Number theory by Ikram Mahmood : http://www.progkriya.org/gyan/basic-number-theory.html You might find these following videos helpful :-) Introduction to Java playlist: https://goo.gl/3Bw2FU C/C++ Programming :: https://goo.gl/99s2tV Android Development: https://goo.gl/oRcdDq Data Structure in C/C++ Playlist: https://goo.gl/CSK1Iq CSS : https://goo.gl/LYzYBC Java Swing Playlist: https://goo.gl/O4iaAV Java Multithreading: https://goo.gl/5mXDYN C++ STL: https://goo.gl/s1Jdwp
Views: 1062 LoveExtendsCode
Leonhard Euler was the greatest mathematician of modern times. His work on pentagonal numbers shows that they connect naturally to sums of divisors of numbers, and also to the partition functions. These are both really surprising facts. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature=view_all A screenshot PDF which includes MathFoundations46 to 79 can be found at my WildEgg website here: http://www.wildegg.com/store/p101/product-Math-Foundations-screenshot-pdf
Views: 8585 njwildberger
Trainer: Mehdi Rahman, Ex-Contestant, DU.
Views: 2616 Bangladesh Advanced Computing Society - BACS
Computing Community Consortium (CCC) Symposium on Computing Research, May 2016 Short Talks and Panel Discussion- Jonathan Katz, University of Maryland (Better Privacy and Security via Secure Multiparty Computation) Shai Halevi, IBM (Computing with Encrypted Data and Programs) Seny Kamara, Brown University (Encrypted Search From Theory to Practice)
Views: 536 computingresearch
MIT 6.858 Computer Systems Security, Fall 2014 View the complete course: http://ocw.mit.edu/6-858F14 Instructor: Nickolai Zeldovich In this lecture, Professor Zeldovich gives a brief overview of the class, summarizing class organization and the concept of threat models. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 382312 MIT OpenCourseWare
A video profile of the 2014 Fields medalist Manjul Bhargava, whose search for artistic truth and beauty has led to some of the most profound recent discoveries in number theory. QUANTA MAGAZINE Website: https://www.quantamagazine.org/ Facebook: https://www.facebook.com/QuantaNews Twitter: https://twitter.com/QuantaMagazine You can also sign up for our weekly newsletter: http://eepurl.com/6FnWj. Manjul Bhargava is a professor of mathematics at Princeton University. Read more about the work that won him a 2014 Fields Medal: https://www.quantamagazine.org/20140812-the-musical-magical-number-theorist/. Video produced by the Simons Foundation, with the cooperation of the International Mathematical Union. Quanta Magazine is an editorially independent publication launched by the Simons Foundation.
Views: 8888 Quanta Magazine
Number Theory For ISI/CMI/RMO !
Views: 933 ANS ACADEMY
View full lesson: http://ed.ted.com/lessons/how-to-organize-add-and-multiply-matrices-bill-shillito When you're working on a problem with lots of numbers, as in economics, cryptography or 3D graphics, it helps to organize those numbers into a grid, or matrix. Bill Shillito shows us how to work with matrices, with tips for adding, subtracting and multiplying (but not dividing!). Lesson by Bill Shillito, animation by The Leading Sheep Studios.
Views: 270891 TED-Ed
Using EA and EEA to solve inverse mod.
Views: 395168 Emily Jane
For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com (Don't worry, I start in German but at minute 2:00 I am switiching to English for the remainder of the lecture :)
Views: 50739 Introduction to Cryptography by Christof Paar
The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to a specified integer. It was created by the ancient Greek mathematician Eratosthenes. The animation is collected from Wikipedia: http://en.wikipedia.org/wiki/File:Sieve_of_Eratosthenes_animation.gif
Views: 6270 Anupam M
Subscribe Now: http://www.youtube.com/subscription_center?add_user=ehoweducation Watch More: http://www.youtube.com/ehoweducation Solving for primitive roots will require you to call your prime number "P" for easy reference. Solve for primitive roots with help from an experienced math professional in this free video clip. Expert: Ryan Ault Filmmaker: bjorn wilde Series Description: Math problems will vary in intensity depending on exactly what type of math you're talking about. Get tips on math problems with help from an experienced math professional in this free video series.
Views: 32063 eHowEducation
Part 1 of 4. These videos convey the thought process in discovering several methods to study Prime Numbers. Great visualizations will guide you through the beauty of the primes, while compelling insights will lay a foundation for the "Twin Prime Conjecture". Recommended to watch in HD mode. Go to www.sievesofchaos.com for more information and visualizations.
Views: 157967 Carlos Paris
AGNES is a series of weekend workshops in algebraic geometry. One of our goals is to introduce graduate students to a broad spectrum of current research in algebraic geometry. AGNES is held twice a year at participating universities in the Northeast. Pre-talk presented by Kiran Kedlaya.
Views: 1008 Brown University
Continuing Education links: Free Energy: Vortex Based Mathematics - SHARE & MAKE VIRAL! - http://bit.ly/2pi5IAE Energy In Motion: Mathematical Fingerprint of the Universe - http://bit.ly/2pfCPEw Rense.com on the Rodin Coil - http://bit.ly/2piCZvJ Website: http://www.destroyingtheillusion.com (Subscribe to the newsletter to stay in touch!) Social Media: Twitter: @destroyillusion Facebook: @destroyingtheillusion Instagram: @jaysather Vids also on: Steemit/Dtube: https://goo.gl/quLMKi BitChute: https://goo.gl/mSB8VB ++ DTI Apparel & Accessories (conscious swag) - https://goo.gl/X99wTD ++ Get my Secret Space Program Webcasts here - https://goo.gl/48Aeyg ++ Earn 10% off high quality superfoods from Raw Revelations with this link - http://bit.ly/2tM2VEP ++ Sign up for the “Awakened Netflix” streaming channel, Gaia! - http://bit.ly/2hURz9b Support on: Patreon: https://goo.gl/qipbjt PayPal: https://goo.gl/wGZbmG Donate via Crypto: BitCoin: 1Ce5QjiEqUnaHzAeU8jDR1mX8BdJLgdMZe Ethereum: 0x0B096d467BB4D8B65489a3Fa224FC02Be25227CE LiteCoin: LRKx8dJjV5ZTxtayh1sc6uckTJG7e9XoQD BitcCoin Cash: 15iuUBXL8ZTiYjA8oAkBv37mfnv4jpStzz Thank YOU for watching and supporting!
Views: 41829 Destroying the Illusion
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Despite what many believe, the essence of encryption isn’t really about factoring or prime numbers. So what is it about? Thanks to Vanessa Hill for playing the part of our evil hacker! Be sure to check out Braincraft https://www.youtube.com/channel/UCt_t6FwNsqr3WWoL6dFqG9w Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode Associahedra: The Shapes of Multiplication | Infinite Series https://www.youtube.com/watch?v=N7wNWQ4aTLQ In previous episodes, Kelsey explained how you could crack RSA encryption with an algorithm capable of quickly factoring ginormous numbers into primes. That might give you the impression that fast factoring algorithms would compromise all digital encryption. But not so -- for instance, YouTube's encryption of this video would be unaffected. And that's because the essence of encryption isn’t really about factoring or prime numbers per se. So what is it about? Written and Hosted by Gabe Perez-Giz Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington Made by Kornhaber Brown (www.kornhaberbrown.com) Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level! And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!
Views: 75734 PBS Infinite Series
Topology, sometimes called rubber sheet geometry, is an important and young branch of Maths: http://www.gresham.ac.uk/lectures-and-events/surfaces-and-topology If we count the number of vertices, v, on a cube, v = 8, number of edges e = 12, and number of faces f = 6, then v¬ -- e + f = 2. The same is true for a tetrahedron where v¬ = 4, e = 6 and f = 4. In fact, the mathematician Leonhard Euler obtained the amazing result that v¬ -- e + f = 2 for a wide class of polyhedrons. This theorem of Euler is a result in topology, a subject which tries to find those properties of geometrical objects that are invariant under continuous deformation -- a tetrahedron can be changed in this way into a cube. The transcript and downloadable versions of the lecture are available from the Gresham College website: http://www.gresham.ac.uk/lectures-and-events/surfaces-and-topology Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently over 1,500 lectures free to access or download from the website. Website: http://www.gresham.ac.uk Twitter: http://twitter.com/GreshamCollege Facebook: https://www.facebook.com/greshamcollege
Views: 29096 Gresham College
In this video we look into few of the remainder theorems like Fermat's little theorem, Euler's Theorem which help us in calculating remainders. Math Tricks Workout by JustQuant.com: https://play.google.com/store/apps/details?id=com.sankhyantra.mathstricks&hl=en
Views: 73164 JustQuant.com
Avi Wigderson is a professor of Mathematics at the Institute for Advanced Study in Princeton. After studying Computer Science at Technion in Haifa, he obtained his PhD in 1983 from Princeton University. He held then various visiting positions including IBM Research at San Jose, MSRI Berkeley, and IAS Princeton. From 1986 to 2003 he was associate professor at the Hebrew University in Jerusalem. Wigderson has been for two decades a leading figure in the field of Mathematics of Computer Science, with fundamental contributions, in particular in Complexity Theory, Randomness, and Cryptography. He has been invited speaker at ICM in Tokyo (1990), and Zurich (1994), and plenary speaker in Madrid (2006). Among many awards he received both the Nevanlinna Prize (1994), and the Gödel Prize (2009). This lecture about cryptography was hold on 8 May 2012 at ETH Zurich, when Avi Wigderson was invited as guest speaker of the Wolfgang Pauli Lectures. The Wolfgang Pauli Lectures are an annual lecture series that is devoted alternately to physics, mathematics and biology. They are named after the great theoretical physicist and Nobel laureate Wolfgang Pauli, who was professor at ETH Zurich from 1928 until his death in 1958.
Views: 5850 ETH Zürich
NEW COURSE: https://chartguys.com/courses/entries-exits/ Introduction to Trend Lines Technical Analysis Basics Technical Analysis for Beginners Introduction to Stock Charts Please Signup for a FREE trial on our website to learn Technical Analysis: We offer multiple hours of live webcam coverage a day, in addition to continuous chat room coverage. Join the community today. Chartguys.com Technical Analysis Facebook Page: https://www.facebook.com/thechartguys... Chartguys.com Technical Analysis FREE facebook community: https://www.facebook.com/groups/thech... Stocktwits: http://stocktwits.com/ChartGuysDan
Views: 223592 TheChartGuys
We give you an introduction to probability through the example of flipping a quarter and rolling a die. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/probability/independent-dependent-probability/basic_probability/e/dice_probability?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics Watch the next lesson: https://www.khanacademy.org/math/probability/independent-dependent-probability/basic_probability/v/probability-space-exercise-example?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it! About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Probability and Statistics channel: https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 3603673 Khan Academy
#MathOlympiad #NumberTheory #MathVideos #Learn_with_Pavel
Views: 2250 Learn With Pavel
What is Cryptography? A story which takes us from Caesar to Claude Shannon. Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/caesar-cipher?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Missed the previous lesson? https://www.khanacademy.org/computing/computer-science/algorithms/intro-to-algorithms/v/what-are-algorithms?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Computer Science on Khan Academy: Learn select topics from computer science - algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress information). About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Computer Science channel: https://www.youtube.com/channel/UC8uHgAVBOy5h1fDsjQghWCw?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 793096 Khan Academy
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi What is the best voting system? Voting seems relatively straightforward, yet four of the most widely used voting systems can produce four completely different winners. Get 10% off a custom domain and email address by going to https://www.hover.com/InfiniteSeries *Correction: The ballots at 1:20 were labeled incorrectly. At 1:20 the top ballot should read 1 Green, 2 Blue and 3 Purple and the bottom ballot should read 2 Green, 3 Blue and 1 Purple. Thank you to Hoarder who first noted this. *Correction: What's stated is the converse of the Condorcet Criterion. Oops - Stating conditionals can be tricky! For more details, see: https://www.reddit.com/r/math/comments/6hh9sb/voting_systems_and_the_condorcet_paradox_infinite/diyft53/ Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode Pantographs and the https://www.youtube.com/watch?v=KYaCtHPCARc Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com) With access to a complete set of ranked ballots - which means we know every person’s opinions - it seems like a clear winner should emerge. But it doesn’t. The outcome of the election depends critically on what process you use to convert all those individual’s preferences into a group preference. Further Resources: Voting and Election Decision Methods http://www.ams.org/samplings/feature-column/fcarc-voting-decision The Mathematics of Voting https://www.math.ku.edu/~jmartin/courses/math105-F11/Lectures/chapter1-part1.pdf The Mathematics of Voting, Power and Sharing http://web.math.princeton.edu/math_alive/6/Notes1.pdf CGP Grey Voting Playlist https://www.youtube.com/playlist?list=PLej2SlXPEd37YwwEY7mm0WyZ8cfB1TxXa Comments answered by Kelsey: FossilFighters101 https://www.youtube.com/watch?v=XOzhF3QoTCA&lc=z12fi1jgnle5wre0k22puzfojxnbzjirk04 Abi Gail https://www.youtube.com/watch?v=XOzhF3QoTCA&lc=z13kin5rcqatih1i004cjdfwsofhi1hopgo Lucas Hoffses https://www.youtube.com/watch?v=XOzhF3QoTCA&lc=z13nilewrtbmfp24t04cgdlziqafvzbahkk0k
Views: 88793 PBS Infinite Series
I'm sorry the clip from the show has been blocked. For more on game theory in Breaking Bad, see my post: http://mindyourdecisions.com/blog/2013/10/01/game-theory-in-breaking-bad/#.U1rSevldV8E If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog: http://mindyourdecisions.com/blog/ Twitter: http://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965 Google+: https://plus.google.com/108336608566588374147/posts Pinterest: https://www.pinterest.com/preshtalwalkar/ Tumblr: http://preshtalwalkar.tumblr.com/ Instagram: https://instagram.com/preshtalwalkar/ Patreon: http://www.patreon.com/mindyourdecisions Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) https://www.amazon.com/gp/product/1500497444 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1523231467/ "Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. https://www.amazon.com/gp/product/1517421624/ "Math Puzzles Volume 2" is a sequel book with more great problems. https://www.amazon.com/gp/product/1517531624/ "Math Puzzles Volume 3" is the third in the series. https://www.amazon.com/gp/product/1517596351/ "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) https://www.amazon.com/gp/product/1517319307/ "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 3 reviews) https://www.amazon.com/gp/product/150779651X/ "Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1500866148/
Views: 2611 MindYourDecisions
To hear more of Hans Bethe’s stories, go to the playlist: https://www.youtube.com/watch?v=LvgLyzTEmJk&list=PLVV0r6CmEsFyUDSroBQVEcbnNud7I9xom German-born theoretical physicist Hans Bethe (1906-2005) was one of the first scientists to join the Manhattan Project, later strongly advocating nuclear disarmament. In 1967, he was awarded the Nobel Prize in Physics for his theory of stellar nucleosynthesis. [Listener: Sam Schweber] TRANSCRIPT: The important thing in the early days of quantum mechanics was atomic spectra. From atomic spectra Bohr had derived the initial quantum theory and the people around Sommerfeld, and Sommerfeld himself, had deepened it greatly and got many details. So I thought the most important thing now was to apply the new quantum mechanics to atomic spectra including the ionization potential of atoms, and there were very important papers by Wigner and von Neumann about the application of group theory to... to the theory of atoms, and so I decided the most important thing for me was to study group theory, which I did. [SS] From... in which... in which book at the time? There was a book by Speiser about group theory which I worked through at least half way, and at that time I really knew quite a lot about group theory. And then it's no use studying a book unless you apply it, unless you do some work of your own using it. Now I had learned about crystals from the Davisson-Germer theory and so I thought, let me apply this group theory to crystals. In fact that had been done many decades earlier, crystal groups, symmetry groups had been found by the crystallographers and Ewald knew all about that, but then it occurred to me that if an atom were put into a crystal then it no longer had spherical symmetry, but it had the symmetry of the crystal which is lower. So you would have a splitting of the energy levels in the crystalline field, just as you have in the Stark effect, a splitting in the electric... constant electric field. But of course it's different in a crystal and I proceeded to get all the possible groups and the representations of groups which applied inside the symmetry of a crystal and I calculated the splitting of atomic energy levels in... in that medium. And for instance, in... in the most symmetrical position in a crystal, in a cubic crystal, you have the three directions of space, x, y and z. But when you then have a D-state electron, the five wave functions of that are no longer all at one energy level, but they split; one wave function becomes like: x2 - y2 and the other becomes like xy and... [SS] Cubic Harmonics. These are the cubic wave functions, and I figured out for all types of crystal symmetries how the splitting would go.
NOte that if we have two numbers that can be expressed as the sum of two squares, for example 5=1^2+2^2 and 13=2^2+3^2, the product of these two numbers, which is 5.13=65 again can be expresses as the sum of two squares, since 65=^4^2+7^2. Is this coincidence? In this video we will prove identity to show that the phenomena is always true in general
Views: 177 Bermatematika.com