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They're millions of digits long, and it takes an army of mathematicians and machines to hunt them down -- what's not to love about monster primes? Adam Spencer, comedian and lifelong math geek, shares his passion for these odd numbers, and for the mysterious magic of math. TEDTalks is a daily video podcast of the best talks and performances from the TED Conference, where the world's leading thinkers and doers give the talk of their lives in 18 minutes (or less). Look for talks on Technology, Entertainment and Design -- plus science, business, global issues, the arts and much more. Find closed captions and translated subtitles in many languages at http://www.ted.com/translate Follow TED news on Twitter: http://www.twitter.com/tednews Like TED on Facebook: https://www.facebook.com/TED Subscribe to our channel: http://www.youtube.com/user/TEDtalksDirector
Views: 240319 TED

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This tutorial demonstrates how the euclidian algorithm can be used to find the greatest common denominator of two large numbers. Learn Math Tutorials Bookstore http://amzn.to/1HdY8vm Donate http://bit.ly/19AHMvX
Views: 236371 Learn Math Tutorials

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Sample video from Math Antics -- http://www.mathantics.com/ This video explains the concept of factoring and prime numbers. Check out the site for more videos in higher quality and for pdf exercise printouts.
Views: 23105 Rob Cozzens

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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Part 1: https://youtu.be/PkpFBK3wGJc Please consider being a supporter on Patreon! https://www.patreon.com/patrickjmt Twitter: @Patrick_JMT In this video I show mathematically for RSA encryption works by going through an example of sending an encrypted message! If you are interested in seeing how Euclid's algorithm would work, check out this video by Emily Jane: https://www.youtube.com/watch?v=fz1vxq5ts5I A big thanks to the 'Making & Science team at Google' for sponsoring this video! Please like and share using hashtag #sciencegoals Views: 34186 patrickJMT 01:05 How can a machine tell us if a number is prime? Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/comp-number-theory/v/what-is-computer-memory-prime-adventure-part-7?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Missed the previous lesson? https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/checkpoint-advanced-lessons?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: 22700 Khan Academy Labs 10:35 Fermat's Little Theorem was observed by Fermat and proven by Euler, who generalized the theorem significantly. This theorem aids in dividing extremely large numbers and can aid in testing numbers to see if they are prime. For more advanced students, this theorem can be easily proven using basic group theory. Prerequisites: To follow this video, you will want to first learn the basics of congruences. If you found this video helpful, please share it with your friends! You might like the other videos in our Number Theory Playlist: https://www.youtube.com/watch?v=VLFjOP7iFI0&list=PLi01XoE8jYojnxiwwAPRqEH19rx_mtcV_ Don't forget to Subscribe to our channels so you'll hear about our newest videos: http://www.youtube.com/subscription_center?add_user=SocraticaStudios Subject: Number Theory Teacher: Michael Harrison Artist: Katrina de Dios Views: 132523 Socratica 12:25 Dr James Grime discusses a type of number beyond the complex numbers, and why they are useful. Extra footage: https://youtu.be/ISbJ9S0fzwY More links & stuff in full description below ↓↓↓ Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphile Special thanks to these supporters: Jeff Straathof Christian Cooper Peggy Youell Ken Baron Today I Found Out Roman Urbanovski Mehdi Razavi John Buchan Bill Shillito Andrzej 'Yester' Fiedukowicz Susan Silver Lê OK Merli Spiked Math RexDex Thomas Buckingham Peter Kær Henry Reich George Greene Arnas Paul Bates Michael Surrago plusunim Tracy Parry Stan Ciprian Mark Klamerus Keith Vertrees Tyler O'Connor Kristian Joensen Valentin James P Buckley Michael Views: 627602 Numberphile 02:46 Views: 158 Anil Kumar 01:15:21 Coding Theory by Dr. Andrew Thangaraj, Department of Electronics & Communication Engineering, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in Views: 23292 nptelhrd 07:09 Views: 3213 Khan Academy Labs 55:52 Hacking is hard. It takes passion, dedication, and an unwavering attention to detail. Hacking requires a breadth of knowledge spread across many domains. We need to have experience with different platforms, operating systems, software packages, tools, programming languages, and technology trends. Being overly deficient in any one of these areas can add hours to our hack, or even worse, bring us total failure. And while all of these things are important for a well-rounded hacker, one of the key areas that is often overlooked is cryptography. In an era dominated by security breaches, an understanding of encryption and hashing algorithms provides a tremendous advantage. We can better hone our attack vectors, especially when looking for security holes. A few years ago I released the first Blu-Ray device key, AA856A1BA814AB99FFDEBA6AEFBE1C04, by exploiting a vulnerability in an implementation of the AACS protocol. As hacks go, it was a simple one. But it was the knowledge of crypto that made it all possible. This presentation is an overview of the most common crypto routines helpful to hackers. We'll review the strengths and weaknesses of each algorithm, which ones to embrace, and which ones to avoid. You'll get C++ code examples, high-level wrapper classes, and an open-source library that implements all the algorithms. We'll even talk about creative ways to merge algorithms to further increase entropy and key strength. If you've ever wanted to learn how crypto can give you an advantage as a hacker, then this talk is for you. With this information you'll be able to maximize your hacks and better protect your personal data. Speaker Bio: Eijah is the founder of demonsaw, a secure and anonymous content sharing platform, and a Senior Programmer at a world-renowned game development studio. He has over 15 years of software development and IT Security experience. His career has covered a broad range of Internet and mid-range technologies, core security, and system architecture. Eijah has been a faculty member at multiple colleges, has spoken about security and development at conferences, and holds a master’s degree in Computer Science. Eijah is an active member of the hacking community and is an avid proponent of Internet freedom. Views: 47189 DEFCONConference 41:59 Adam Marcus, Princeton University Two Existence Proofs of Ramanujan Graphs Expanders and Extractors Views: 455 Simons Institute 01:02:29 Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area We explain Chebotarev's theorem, which is The Fundamental Tool in proving whatever densities we have for sets of prime numbers, try to understand what makes it hard in the case of ifinite extensions, and see why such extensions arise in the case of primitive root problems. Recording during the thematic meeting: "Frobenius Distributions on curves" the February 17, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent 16:36 Classical computers struggle to crack modern encryption. But quantum computers using Shor’s Algorithm make short work of RSA cryptography. Find out how. Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode How to Break Cryptography https://www.youtube.com/watch?v=12Q3Mrh03Gk The Mathematics Behind Quantum Computers https://www.youtube.com/watch?v=IrbJYsep45E Additional Resources: Scott Aaronson's Blog (Great Intro to Shor's Alg.):: http://www.scottaaronson.com/blog/?p=208 Shor's Original Paper:: https://arxiv.org/abs/quant-ph/9508027v2 Lectures on Shor's Algorithm:: https://arxiv.org/pdf/quant-ph/0010034.pdf Decrypting secure messages often involves attempting to find the factors that make up extremely large numbers. This process is too time consuming for classical computers but Shor’s Algorithm shows us how Quantum Computers can greatly expedite the process. Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com) Thanks to Spiros Michalakis for helpful discussions and feedback. Comments answered by Kelsey: Neon Bull https://www.youtube.com/watch?v=12Q3Mrh03Gk&lc=z135uxf5cxenutmxj04cc3swkvm4tpcrxik Bhargav R https://www.youtube.com/watch?v=12Q3Mrh03Gk&lc=z13qjjioozbjdrqyz04cevdrtu3ti3y5sq40k BobC https://www.youtube.com/watch?v=12Q3Mrh03Gk&lc=z12pjpzastylzz2qx04cjtc5jrq2y3yhmlk0k Views: 157276 PBS Infinite Series 01:07:57 I will report on recent results about quantum algorithms for solving computational problems in number theory. I will show how they impact the security of certain post-quantum cryptosystems. Shor's quantum algorithm for factoring large integers and solving the discrete logarithm problem has been the motivation for an entire new area of research in cryptology: namely "post-quantum" cryptography. It consists of designing new cryptographic primitives which will resist attacks from quantum computers. In a recent work in collaboration with Fang Song, I presented a quantum polynomial time algorithm for solving the so-called "Principal Ideal Problem" (among other things) in arbitrary fields. We will see how this impacts the security of some ring-based proposals for quantum resistant cryptography. In collaboration with David Jao and Anirudh Sankar, I also described a quantum algorithm which finds an isogeny between two given supersingular curves over a finite field, a hard problem on which some post-quantum cryptosystem rely. Finally, if there is enough time, I'll mention some recent work on factorization. See more on this video at https://www.microsoft.com/en-us/research/video/quantum-algorithms-number-theory-relevance-cryptography/ Views: 1265 Microsoft Research 01:24:15 MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Srinivas Devadas In this lecture, Professor Devadas continues with cryptography, introducing encryption methods. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu Views: 14129 MIT OpenCourseWare 03:25 In modular arithmetic, the residue of the product of two numbers is congruent to the product of the residues of the individual numbers. This fact will be used to find the residue of the product of two very large numbers in this vide. Views: 598 Ms. Hearn 41:05 New insights into how the signs of exaltation and the houses that planets have joy in are related to each other. How prime numbers form a basis of the signs of exaltation. Views: 2264 David Cochrane 01:54 A prime number is a positive whole number with exactly two factors, which are one and itself. Identify a variety of prime numbers, such as seven and 11, with help from a math teacher in this free video on math help and prime numbers. Expert: Jimmy Chang Bio: Jimmy Chang has been a math teacher at St. Pete College for nearly a decade. He has a master's degree in math, and his specialties include calculus, algebra, liberal arts, math and trigonometry. Filmmaker: Christopher Rokosz Views: 3575 eHow 00:25 I animated the Gaussian Elimination step from my quadratic sieve program. Views: 1288 Sam Kennedy 06:35 Give your students practice finding prime factors as they construct the Tree of Numbers. Views: 1296 Gordon Hamilton 11:20 Roger Schank and Andrew Hacker dispel math instruction. Mathematics is highly overrated for most people and teaching it to everyone is why the standards have become so low. It pointlessly challenges those without interest in it and completely narrows and limits the content for people who want to know more than just BORING algebra. Norman Wildberger shows that they can't even teach trigonometry CORRECTLY. When I hear that grade schools are trying to include calculus, I burst out in laughter. It's OUTDATED! These kids can't even do a dot product, let alone do loopy belief propagation on probabilistic graphical models or use autoencoders in place of singular value decomposition or principal component analysis. These kids know so few areas and algorithms. Not only is mathematics one of the most automatable subjects on earth, it largely FOLLOWS discoveries. No, the modern computer was NOT based upon Turing (rehashed the silly diagonalizations of Godel and Cantor) and the airplane wasn't discovered by studying Newton (simple action-reaction displacing air) or Navier-Stokes. The mathematician couldn't even say why wings can fly UPSIDE DOWN (simple angle of attack ). Even the jet engine was not a straightforward application of math. People all talk about Maxwell's equations (can be reduce to one equation with geometric algebra), but the actual discoverer (Faraday) was not very good at math. The charlatans get all the credit. Grassmann was actually a theologian and he discovered the most useful branch of math, which is linear algebra. He also set the bases for geometric algebra, which shows you that imaginary numbers are just an ugly hack. Idiots like Gauss wondered about 17-gons but with a piece of string and Archimedes' spiral one can trisect the angle, square the circle, inscribe polygons and do inverse trig. They just refused to use string! Trivial! A simple bisection algorithm gives you guaranteed roots to ANY degree polynomial (in about 10 lines of code), where Galois showed analytical methods fail at the meager 5th degree. Simple N-body algorithms also solve more than the pathetic limit proved by Poincare of two bodies! They're trivial algorithms with computers. Poincare dispelled 20th century set theory and called it a useless Bourbaki disease, like modernist art. No TRULY creative math is done using ZFC and modern analysis has been ripped to shreds by those like Doron Zeilberger and Solomon Feferman. The proofs don't even work logically! Analysis is really just a cover for finite algebra. If you study modern gauge theory, you will understand that physicists pretend to have problems like chiral fermions in the lattice but it has all been solved. String theory is a comical joke. Mathematicians pretend we need to study prime factoring for cryptography but lattice-based methods make this silly. Even GPS can forget about SR and GR, making them systematic calibration errors (much larger calibrations are to do with other phenomena). Optimization, bootstrapping, numerical methods, perturbation, approximation, finite element method, computational fluid flow, machine learning, computer algebra systems, etc... takes care of all the real world mathematics with little skill involved. Modern mathematics is more like post-modern art subsidized by the government, so Ivy League jerkoffs can live at the public's expense. Don't listen to the Sputnik propaganda. 16:31 (Sous-titres en français bientôt disponibles) Amid today's debate on electronic surveillance and the ongoing Arab Spring protests, this young 22 year old Montreal hacktivist founded Cryptocat, a free, accessible, and open source encrypted chat application. His mission: make private communication on the web available to all. Dans le contexte du printemps arabe et des enjeux de surveillance électronique, ce jeune cybertactiviste montréalais a fondé à l'âge 22 ans Cryptocat: un logiciel de conversation protégé par cryptographie simple à utiliser, gratuit et à code source ouvert. Sa mission: rendre accessible à tous la communication privée sur le web. https://twitter.com/kaepora https://crypto.cat/ For more information, please visit http://tedmontreal.com/ Introduction motion animation by: http://www.departement.ca/ 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: 11104 TEDx Talks 03:47 An edit of a longer interview. Shit for brains (worthless history degree) Amber Rudd, Tory home secretary knows nothing about maths or IT, demands backdoors to encryption to stop applications like Whatsapp having end-to-end encryption..... also the think online banking relies on etc. etc. Tragic how suck Nazi supporting nutjobs with zero decent degree can come up with this kind of stupid shit. Long live maths and large prime numbers to thwart the expanding power of Nazis like in current UK government, who HATE freedom of speech and freedom of expression. Recorded from BBC1 HD, Andrew Marr Show, 26 March 2017. Views: 2115 liarpoliticians2 54:00 The complex multiplication method (CM method) builds an algebraic curve over a given finite field GF(q) and having an easily computable cardinality. Used at first for elliptic curves, this method is one of the building blocks of the ECPP algorithm that proves the primality of large integers, and it appeared interesting for other applications, the most recent of which being the construction of pairing friendly curves. The aim of the talk is to recall the method, give some applications, and survey recent advances on several parts of the method, due to various authors, concentrating on elliptic curves. This includes class invariant computations, and the potential use of the Montgomery/Edwards parametrization of elliptic curves. Views: 68 Microsoft Research 01:26 Read more: http://www.newscientist.com/blogs/nstv/2011/07/quantum-graphs-make-haunting-music.html Views: 4634 New Scientist 25:53 Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area This talk will focus on the last step of the number field sive algorithm used to compute discrete logarithms in finite fields. We consider here non-prime finite fields of very small extension degree: 1≤n≤6. These cases are interesting in pairing-based cryptography: the pairing output is an element in such a finite field. The discrete logarithm in that finite field must be hard enough to prevent from attacks in a given time (e.g. 10 years). Within the CATREL project we aim to compute DL records in finite fields of moderate size (e.g. in GF(pn) of global size from 600 to 800 bits) to estimate more tightly the hardness of DL in fields of cryptographic size (2048 bits at the moment). The best algorithm known to compute discrete logarithms in large finite fields (with small n) is the number field sieve (NFS) [...] Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' the May 20, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent 38:37 My Experience with the puzzle and how it started for me. I'm going over the runes and words before I did the calculations Views: 6755 Defango 03:38 Quick explanation of how I got "the Lucas angle is about 100 degrees" in this video: http://youtu.be/14-NdQwKz9w Related: Doodling Stars http://youtu.be/CfJzrmS9UfY Views: 73719 vihartvihart 01:01:51 Correlations of von Mangoldt and higher order divisor functions - Kaisa Matomäki (University of Turku) I will discuss joint work with M. Radziwill and T. Tao on asymptotics for the sums$\sum_{n \leq x} \Lambda(n) \Lambda(n+h)$and$\sum_{n \leq x} d_k(n) d_l(n+h)$where$\Lambda$is the von Mangoldt function and$d_k$is the kth divisor function. For the first sum we show that the expected asymptotics hold for almost all$|h| \leq X^{8/33}$and for the second sum we show that the expected asymptotics hold for almost all$|h| \leq (\log X)^{O_{k, l} ( 1) }$. MAY 03, 2017 WEDNESDAY Views: 1180 Graduate Mathematics 01:03:44 We review existing cryptographic schemes based on the hardness of computing isogenies between supersingular isogenies, and present some attacks against them. In particular, we present new techniques to accelerate the resolution of isogeny problems when the action of the isogeny on a large torsion subgroup is known, and we discuss the impact of these techniques on the supersingular key exchange protocol of Jao-de Feo. See more on this video at https://www.microsoft.com/en-us/research/video/post-quantum-cryptography-supersingular-isogeny-problems/ Views: 800 Microsoft Research 24:28 How e to the pi i can be made more intuitive with some perspectives from group theory, and why exactly e^(pi i) = -1. Apply to work at Emerald Cloud Lab: - Application software engineer: http://3b1b.co/ecl-app-se - Infrastructure engineer: http://3b1b.co/ecl-infra-se - Lab focused engineer: http://3b1b.co/ecl-lab-se - Scientific computing engineer: http://3b1b.co/ecl-sci-comp Special thanks to the following Patrons: http://3b1b.co/epii-thanks There's a slight mistake at 13:33, where the angle should be arctan(1/2) = 26.565 degrees, not 30 degrees. Arg! If anyone asks, I was just...er...rounding to the nearest 10's. For those looking to read more into group theory, I'm a fan of Keith Conrads expository papers: http://www.math.uconn.edu/~kconrad/blurbs/ ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown Views: 677536 3Blue1Brown 02:56 Finding all the prime numbers between 1 and 100 using the technique devised by the ancient Greek mathematician Eratosthenes Views: 139615 Ron Barrow 08:05 There are different sizes of infinity. It turns out that some are larger than others. Mathematician Kelsey Houston-Edwards breaks down what these different sizes are and where they belong in The Hierarchy of Infinities. Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com) Sources: Proof that the real numbers are a bigger infinity than the natural numbers: http://germain.its.maine.edu/~farlow/sec25.pdf http://www.people.vcu.edu/~rhammack/BookOfProof/Cardinality.pdf Thanks James Barnes and Iian Smythe! Views: 159787 PBS Infinite Series 00:46 People without rh factor are known as negative, while people with the and a 'factor tree' can help find any factors of number, then those prime factorization is very important to who try make (or break) 7 apr 2015 out why production critical for real economic growth, where wages rise consumer goods costs fall due increased literally, greatest common biggest expression that will go into no matter how many terms polynomial has, it always check use divisibility rules given numbers through each rule disability, but you know understand them just in case we 3x2x5 30. Because establishing fluency in identifying factors is important to. If a number only has itself and 1 as factors, then the is students can find factors of given number, searching systematically if necessary. Various types to find the pf, divide 100 kw by 125 kva yield a pf of 80. Use divisibility rules to find factors mountain heights academy competitiveness key factor s the organization's internal google books result. 30 is a multiple of each of 3, 2, and 5. Learn to factor? Math forum ask drunderstanding algebra why do we factor equations factors and multiples kids need Seismic importance isat seismic bracing. Understanding power factor and why it's important. Why do i need to know about prime numbers and factorization? You can use the factorization of a rh factor is blood protein that plays critical role in some pregnancies. Factors and fractions when students ask. Math why do i need to learn factor expressions if i'm going be a fashion the most important one, think, is habit of looking for ways turn that factoring rocks we re arrange our error system into fragile teepee, so can break it. Why do we teach factoring of numbers into prime factors? Quora. Rh factor importance of the rh factor, in pregnancy prime factorization math is fun. We'll find what obliterates our errors and puts system in factors multiples are especially important working with expanding prime of a number skills you will learn this section 14 may 2012 but it occurred to me that the entire premise here was flawed just how is factoring teach learn? My second year teacher component importance factor (ip) any project either be assigned as i would like speak rep about options cut because gives nice way gcd lcm two numbers even kids given composite number, by using powers these 20 2015 why does journal impact remain such an motivator for many things might not know 24 mar 2017 there various at play, turns out most thing millennials instagram great place holiday inspiration too 9 nov perform factorization, understand appreciate so power measure effectively electricity. So 2, 3, and 5 are factors of 30. Why are the factors of production important to economic growth how factor a polynomial expression dummies. Why is impact factor so important? 'instagrammability' most important for millennials on choosing the math dude how to numbers quick and dirty tips. Learn to factor? Math forum ask dr. The hormone factor in mental health bridging the mind body gap google books result. Edisto electric factors and fractions when students ask education place. Views: 34 sweet sparky 01:36 Prove in various ways that ZERO is an even number, odd number or neither! 26:02 How do you set a quantum bit? Is RSA dead? Click to subscribe! ► http://bit.ly/Scopes_Sub ◄ https://www.eestalktech.com/quantum-bits Twitter: @Keysight_Daniel https://twitter.com/Keysight_Daniel Learn more about using oscilloscopes: http://oscilloscopelearningcenter.com Check out the EEs Talk Tech electrical engineering podcast: https://www.eestalktech.com More about Keysight oscilloscopes: http://bit.ly/SCOPES Check out our blog: http://bit.ly/ScopesBlog Agenda: 00:40 Lee talks about how to crack RSA and Shor's algorithm The history of quantum computing. The 1st to propose it was Richard Feynman in the 1960s. Interest soon died out. 1990s - Dr. Shor published a paper saying if one could build a quantum computer with certain parameters, then one could factor a very large number Today's security uses the RSA public key system and the Diffie Hellman Key Exchange algorithm HTTPS uses the Diffie Hellmen Key Exchange algorithm. RSA stands for Rivest, Shamir, and Adelman 4:00 RSA works only for people known to each other, Diffie Hellman works for anyone 5:00 Factoring numbers that consist of large prime numbers is the basis for RSA. The processing needed to factor them is too large to be practical 6:45 Shor's algorithm is fast enough to crack RSA. If one could build a quantum computer with enough quantum bits then use a machine language cycle time that is us or ms, then one could factor thousand bit numbers 7:50 When will they be built? Some say 10 years, others 50 8:45 What does a quantum computer look like? An architectural description is easier to describe. A quantum computer similar to a classical computer, a quantum computer is a co-processor that will co-exist with current forms of digital electronics 9:15 Shor's algorithm has a lot of common commands - if statements and for loops. But, quantum gates are used in a quantum processor 10:00 Because a quantum gate operates in time instead of space, the term "gate" isn't accurate 10:30 What quantum computers exist today? Some exist with just a few quantum bits. People claim they've created quantum computers with 21 quantum bits. But, there can be a lot of errors and noise. For example, can a proper setup and hold time be maintained? 11:50 The Schrodinger's Cat analogy - In reality, if you've put a piece of physics into a superimposed quantum state, a disturbance of it (photon impact) will cause it to collapse into the wrong state or collapse too early 13:15 Quantum bits have to be thoroughly isolated. We use vacuums or extreme cold temperatures (well below 1 degree Kelvin!) 13:45 Research companies making claims about the number quantum bits are not using solid state quantum computers. The isolation of a quantum computer isn't be perfect, so there's a short lifetime for the computation before the probability of errors get's too high. 14:35 Why do we use a superposition of states? Why does the timing matter? If it collapses at the wrong time it returns a wrong answer. Shor's algorithm makes it easy to check for the right answer. And, you get a remainder of 0 or your don't. If mod(x) = 0, you know the answer is correct. The computation only has to be reliable enough because you can check your answer 16:15 If the odds of getting the right answer is high enough, it's ok to get the wrong answer on occasion. 16:50 How do you write a quantum bit? It depends on the physical system. You can write a quantum bit by putting energy in the system, i.e. using a very small number photon pulse with a specific timing and phase 18:15 Keysight helps quantum computer researchers generate and measure pulses with high levels of precision The pulses are carefully timed and correlated with sub-nanosecond precision 19:40 What is a quantum bit? There are two common kinds. 1 - Ions in a vacuum trapped by lasers. The ions are static because they are held in place by standing waves. The vacuum can be at room temperature and the ions are low temp because they can't move 2. Josephson junctions in tank circuits (resonant circuit, LC circuit, tuned circuit) makes oscillations at microwave frequencies. Under the right conditions, they can behave like an abstract two state quantum system. You simply have to designate zero and one to different states of the system. Probabilities are the wrong description, it;s actually complex quantum amplitudes. 24:30 Stupid question section: "If you had Schrodinger's cat in a box, would you look or not?" Watch to find out Lee's answer! #quantumcomputing #quantumbits #quantumcomputer #electricalengineeringpodcast #engineeringpodcast #podcast #RSA #computing #computer #electronics #electricalengineering #computerengineering Views: 1080 Keysight Labs 01:01:55 The NATO Cooperative Cyber Defence Centre of Excellence (CCDCOE) organised its 10th International Conference on Cyber Conflict (CyCon 2018) in Tallinn, on the theme of maximising effects in the cyber domain. In the coming years, quantum computers (QCs) will bring the biggest single advance in the information age. All the prototyped and proposed QCs can solve extremely large and specific problems – the kinds of problems that are intractable on even the largest computers today. Although only a few companies presently sell QC-related products, all areas of information processing – especially those relying on intractability – should prepare for the global availability of QCs. Much of cryptography is built on classical intractability (factoring numbers, finding elliptic curves, etc.), with implications for secrecy, privacy, key exchange and signatures. These will be vulnerable and easily broken by QC. As a result, much groundwork has been done on both post-QC cryptography and key-exchange, as well as QC-based cryptanalysis. By contrast, relatively little work has been done in other QC-based aspects of cybersecurity, such as malware generation and detection, advanced multi vector threat detection, mapping the cyber battlefield and optimising cyber battle plans. Many of these cybersecurity problems are very large-scale, involve search and optimisation and can likely be executed in new ways with QC giving an entirely new cyber conflict asymmetry. This panel will discuss the full breadth of QC’s impact on all aspects of cybersecurity, from cryptography to cyberwarfare. Panelists: 1. Prof. Barry C. Sanders, University of Calgary 2. Prof. Norbert Lütkenhaus, Institute for Quantum Computing, Department of Physics, University of Waterloo, Canada 3. Prof. Troy Lee, Associate Professor, Nanyang Technological University Moderator: Prof. Bruce W. Watson, Chief Scientist, IP Blox **Note that some presentations were submitted and created in a personal capacity and are not necessarily affiliated with, nor representative of, the views of the speakers’ respective organisations** The NATO Cooperative Cyber Defence Centre of Excellence (CCDCOE) is a NATO-accredited cyber defence hub focusing on research, training and exercises. The international military organisation based in Estonia is a community of currently 21 nations providing a 360-degree look at cyber defence, with expertise in the areas of technology, strategy, operations and law. Views: 92 natoccdcoe 01:31:29 The world of investing/finance is divided into two camps. In one, you have the number-crunchers, who believe that the only things that matter are the numbers and that imagination/creativity are dangerous distractions. In the other, you have the storytellers, who build on the stories they tell about companies and how these stories will bring untold wealth. Each side believes it has a monopoly on the truth and looks with contempt at the other. Prof. Damodaran contends that stories matter, but only if they are connected with numbers. And numbers are empty, unless they are connected with narratives. In this talk, he looks at the process by which one might build narratives, check them against reality and convert them into valuations. Uber and Ferrari examples are used to illustrate the process. Slides for the talk: https://goo.gl/zKVaQL Check out the book on Google Play: https://goo.gl/tnGlDe This talk was moderated by Saurabh Madaan. Views: 70775 Talks at Google 02:16:22 Apple WWDC 2018. Four OS updates. One big day. Take a look at updates for iPhone and iPad, Mac, Apple Watch, and Apple TV. 9:54 — Announcing iOS 12 Learn how you can FaceTime with up to 32 people. Share AR experiences with friends. And be more aware of how you and your kids use apps. 1:05:17 — Announcing watchOS 5 Discover how you can challenge someone to an Activity competition. Track brand-new workouts. And learn more about Walkie-Talkie, a fun and easy way to connect with friends and family. 1:24:27 Announcing the new tvOS Learn more about immersive Dolby Atmos 3D sound. Watch TV shows and movies in 4K HDR. And tune in to live news and sports. 1:35:02 — Announcing macOS Mojave Now you can stay focused on your work with Dark Mode. Edit and share files without opening them. And explore a completely redesigned Mac App Store. Views: 1500615 Apple 39:18 Kristin Lauter, Microsoft Research Wednesday Nov 9, 2011 11:00 - 11:40 Numerical evidence for the Bruinier-Yang conjecture and comparison with denominators of Igusa class polynomials Women in Numbers Conference Video taken from: http://www.birs.ca/events/2011/5-day-workshops/11w5075/videos 01:49 How to factories any number with the help of Fermat method. Fermat's method to solve numericals. NUMBER THEORY. Fermat's little theorem. 02:22 Subscribe Now: http://www.youtube.com/subscription_center?add_user=ehoweducation Watch More: http://www.youtube.com/ehoweducation When using a math factoring ladder, you're essentially going to be dividing with a few other important steps. Use a math factoring ladder with help from an expert in computers, with two degrees in both Computer Science and Applied Mathematics, in this free video clip. Expert: Stefan Robert Filmmaker: Victor Varnado Series Description: Mathematics will be very important all throughout your life, not just when you're seated inside a classroom in school. Get tips on the theories of applied mathematics with help from an expert in computers, with two degrees in both Computer Science and Applied Mathematics, in this free video series. Views: 224 eHowEducation 02:28 Factoring (called "Factorising" in the UK) is the process of finding the factors: Factoring: Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions. Factorization is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained. The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. The opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms. Integer factorization for large integers appears to be a difficult problem. There is no known method to carry it out quickly. Its complexity is the basis of the assumed security of some public key cryptography algorithms. Modern techniques for factoring polynomials are fast and efficient, but use sophisticated mathematical ideas (see Factorization of polynomials). These techniques are used in the construction of computer routines for carrying out polynomial factorization in Computer algebra systems. The more classical hand techniques rely on either the polynomial to be factored having low degree or the recognition of the polynomial as belonging to a certain class of known examples and are not very suitable for computer implementation Students who are introduced to factoring as a primary method of solving quadratic equations might be surprised to know it is one of the newest methods of solving them -~-~~-~~~-~~-~- Please watch: "Theory of Quadratic Equations 10th Maths Ex No 2 .7 Complete Solution" https://www.youtube.com/watch?v=0UP-z-hsaxY -~-~~-~~~-~~-~- 01:32:08 Google Tech Talks December, 19 2007 Topics include: Introduction to Modern Cryptography, Using Cryptography in Practice and at Google, Proofs of Security and Security Definitions and A Special Topic in Cryptography This talk is one in a series hosted by Google University: Wednesdays, 11/28/07 - 12/19/07 from 1-2pm Speaker: Steve Weis Steve Weis received his PhD from the Cryptography and Information Security group at MIT, where he was advised by Ron Rivest. He is a member of Google's Applied Security (AppSec) team and is the technical lead for Google's internal cryptographic library, KeyMaster. Views: 69689 GoogleTechTalks 24:45 An algorithm for numerically solving certain 2d equations. Brought to you by...you! https://patreon.com/3blue1brown Special thanks to these supporters: http://3b1b.co/winding-thanks Even though we described how winding numbers can be used to solve 2d equations at a high level, it's worth pointing out that there are a few details missing for if you wanted to actually implement this. For example, in order to determine how often to sample points, you'd want to have some bounds on the rate at which the direction of the output changes. We will perhaps discuss this more in a follow-on video! Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown Views: 342049 3Blue1Brown 10:44 Join Here$10 equals 1000 tokens! https://vrlps.co/a?pt=24egHeF-mYgN9sCzFHAbpvZzKrw&referralCode=rJEiz4ZNG&refSource=copy Digitex offers zero trading fees along with 100X leverage on Bitcoin, Litecoin, and Etherium. Traders speculate on the price of Bitcoin against the US dollar, but their trading profits and losses are paid out in DGTX tokens. 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Zero Trading Fees One Click Trading Interface Digitex Native Cryptocurrency Large Tick Sizes Decentralized Governance By Blockchain Bitcoin, Ethereum & Litecoin Futures Advanced Technology Complete Privacy Decentralized Account Balances Highly Liquid Futures Markets Token Issuance Revenue Model Automated Market Makers Off-Chain Negotiation & On-Chain Settlement High Leverage Futures Trading Blockchain Driven No Auto Deleveraging Join Bitconnect here. https://bitconnect.co/?ref=Hyperthinks1 Join Davor Coin here. https://davor.io/Account/Registration?r=282D77 Tip Jar BTC: 1P9Ke5we1zDL1FFbFbHuAbdrU2xSFPGhux Free Bitcoin Course!! https://futuremoney.io/?id=Hyperthink1 **DISCLAIMER**: I am not a financial advisor nor am I giving financial advice. I am sharing my biased opinion based off speculation. You should not take my opinion as financial advice. You should always do your research before making any investment. You should also understand the risks of investing. 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Views: 207 Hyperthinks

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Lecture title: "The Growth of Cryptography" Ronald L. Rivest, a professor of electrical engineering and computer science who helped develop one of the world's most widely used Internet security systems, was MIT’s James R. Killian, Jr. Faculty Achievement Award winner for 2010–2011. Rivest, the Andrew and Erna Viterbi professor in MIT's Department of Electrical Engineering and Computer Science, is known for his pioneering work in the field of cryptography, computer, and network security. February 8, 2011 Huntington Hall (10-250)

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