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Elliptic Curve Back Door - Computerphile
 
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The back door that may not be a back door... The suspicion about Dual_EC_DRBG - The Dual Elliptic Curve Deterministic Random Bit Generator - with Dr Mike Pound. EXTRA BITS: https://youtu.be/XEmoD06_mZ0 Nothing up my sleeve Numbers: https://youtu.be/oJWwaQm-Exs Elliptic Curves: https://youtu.be/NF1pwjL9-DE https://www.facebook.com/computerphile https://twitter.com/computer_phile This video was filmed and edited by Sean Riley. Computer Science at the University of Nottingham: https://bit.ly/nottscomputer Computerphile is a sister project to Brady Haran's Numberphile. More at http://www.bradyharan.com
Views: 191245 Computerphile
Abstraction (Scheme programming)
 
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This video looks at how passing functions as arguments to other functions can be used to produce abstractions. This allows us the ability to write a single function which does the job several functions had been doing before as well as other things that we hadn't written previously.
Views: 6488 Mark Lewis
Binary lambda calculus
 
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If you find our videos helpful you can support us by buying something from amazon. https://www.amazon.com/?tag=wiki-audio-20 Binary lambda calculus Binary lambda calculus (BLC) is a technique for using the lambda calculus to study Kolmogorov complexity, by working with a standard binary encoding of lambda terms, and a designated universal machine.Binary lambda calculus is a new idea introduced by John Tromp in 2004. -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=ZAb1QK1gMUs
Views: 199 WikiAudio
Data made out of functions
 
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Ken Scambler https://linux.conf.au/schedule/30359/view_talk Church Encoding is a fascinating technique whereby numbers, data structures, and just about anything can be built out of nothing but functions. Ken will introduce Church Encoding and show how it can make numbers and data types materialise out of thin air. Even better, he’ll show how Church Encoding is not only a neat party trick, but actually useful in real code, using examples in Haskell and Java.
F-algebra
 
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If you find our videos helpful you can support us by buying something from amazon. https://www.amazon.com/?tag=wiki-audio-20 F-algebra In mathematics, specifically in category theory, F-algebras generalize algebraic structure.Rewriting the algebraic laws in terms of morphisms eliminates all references to quantified elements from the axioms, and these algebraic laws may then be glued together in terms of a single functor F, the signature. =======Image-Copyright-Info======== License: Creative Commons Attribution-Share Alike 4.0 (CC BY-SA 4.0) LicenseLink: http://creativecommons.org/licenses/by-sa/4.0 Author-Info: IkamusumeFan Image Source: https://en.wikipedia.org/wiki/File:F_algebra.svg =======Image-Copyright-Info======== -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=LRRT6Pg6LeU
Views: 259 WikiAudio
Complex Tori are the same as Elliptic Algebraic Projective Curves
 
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An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves by Dr. T.E. Venkata Balaji, Department of Mathematics, IIT Madras. For more details on NPTEL visit http://www.nptel.iitm.ac.in/syllabus/111106044/ Goals of Lecture 45B: * In Part A of this lecture, we defined complex projective 2-space and showed how it can be turned into a two-dimensional complex manifold. In Part B, we show that any complex torus is holomorphically isomorphic to the natural Riemann surface structure on the associated elliptic algebraic cubic plane projective curve embedded in complex projective 2-space Keywords for Lecture 45B: Upper half-plane, complex torus associated to a lattice (or) grid in the plane, fundamental parallelogram associated to a lattice, doubly-periodic meromorphic function (or) elliptic function associated to a lattice, Weierstrass phe-function associated to a lattice, ordinary differential equation satisfied by the Weierstrass phe-function, zeros of the derivative of the Weierstrass phe-function, pole of order two (or) double pole with residue zero, triple pole (or) pole of order three, cubic equation, elliptic algebraic cubic curve, zeros of a polynomial equation, bicontinuous map (or) homeomorphism, open map, order of an elliptic function, elliptic integral, Argument principle, even function, odd function, analytic branch of the square root, simply connected, punctured torus, elliptic algebraic affine cubic plane curve, projective plane cubic curve, complex affine two-space, complex projective two-space, one-point compactification by adding a point at infinity, Implicit function theorem, graph of a holomorphic function, nonsingular (or) smooth polynomial in two variables, zero locus of a polynomial, solving an implicit equation locally for an explicit function, nonsingular (or) smooth point of the zero locus of a polynomial in two variables, Hausdorff, second countable, connected component, nonsingular cubic polynomial, discriminant of a polynomial, cubic discriminant, homogeneous coordinates on projective 2-space, punctured complex 3-space, quotient topology, open map, complex two-dimensional manifold (or) complex surface, complex one-dimensional manifold (or) Riemann surface, complex coordinate chart in two complex variables, holomorphic (or) complex analytic function of two complex variables, glueing of Riemann surfaces, glueing of complex planes, zero set of a homogeneous polynomial in projective space, degree of homogeneity, Euler's formula for homogeneous functions, homogenisation, dehomogenisation, a complex curve is a real surface, a complex surface is a real 4-manifold
Views: 2064 nptelhrd
[Mathematical Linguistics] Groups
 
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In this video I introduce groups, go through some examples, and do a proof of unique identities. LIKE AND SHARE THE VIDEO IF IT HELPED! Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Like us on Facebook: http://on.fb.me/1vWwDRc Submit your questions on Reddit: http://bit.ly/1GwZZrP Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
Views: 1052 TheTrevTutor
Lec 5 | MIT 6.042J Mathematics for Computer Science, Fall 2010
 
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Lecture 5: Number Theory II Instructor: Marten van Dijk View the complete course: http://ocw.mit.edu/6-042JF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 78081 MIT OpenCourseWare
DEVCON1: Formal Semantics for Protocols - Peter McBurney
 
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DEVCON1 5.30pm Day 1 Peter McBurney presents on Formal Semantics for Protocols at Ethereum's DEVCON1.
Views: 467 Ethereum
DrRacket 07 -- Defining and Applying Functions
 
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Defining functions, applying functions, functions that produce numbers and images.
Views: 14140 John Clements
Multiple Processor Systems - Computerphile
 
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Just what does it mean to have a multi-processor system? Dr Steve Bagley on symmetric and assymmetric multi-processor systems. https://www.facebook.com/computerphile https://twitter.com/computer_phile This video was filmed and edited by Sean Riley. Computer Science at the University of Nottingham: https://bit.ly/nottscomputer Computerphile is a sister project to Brady Haran's Numberphile. More at http://www.bradyharan.com
Views: 72799 Computerphile
Alan Turing: Crash Course Computer Science #15
 
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Today we’re going to take a step back from programming and discuss the person who formulated many of the theoretical concepts that underlie modern computation - the father of computer science himself: Alan Turing. Now normally we try to avoid “Great Man" history in Crash Course because truthfully all milestones in humanity are much more complex than just an individual or through a single lens - but for Turing we are going to make an exception. From his theoretical Turing Machine and work on the Bombe to break Nazi Enigma codes during World War II, to his contributions in the field of Artificial Intelligence (before it was even called that), Alan Turing helped inspire the first generation of computer scientists - despite a life tragically cut short. Special thanks to Contributing Writer Robert Xiao whom we should have (and forgot) to include in the credits. His help with this episode was invaluable. Ps. Have you had the chance to play the Grace Hopper game we made in episode 12. Check it out here! http://thoughtcafe.ca/hopper/ Produced in collaboration with PBS Digital Studios: http://youtube.com/pbsdigitalstudios Want to know more about Carrie Anne? https://about.me/carrieannephilbin The Latest from PBS Digital Studios: https://www.youtube.com/playlist?list=PL1mtdjDVOoOqJzeaJAV15Tq0tZ1vKj7ZV Want to find Crash Course elsewhere on the internet? Facebook - https://www.facebook.com/YouTubeCrash... Twitter - http://www.twitter.com/TheCrashCourse Tumblr - http://thecrashcourse.tumblr.com Support Crash Course on Patreon: http://patreon.com/crashcourse CC Kids: http://www.youtube.com/crashcoursekids
Views: 290953 CrashCourse
racket aggregates video 2.9/6 --- maps
 
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Video from http://www.cdf.toronto.edu/~heap/racket_lectures.html on using map to transform list elements to create a new list.
Views: 1738 Danny Heap
Fundamental of the analysis of algo efficiency
 
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What is ALGORITHM? What does ALGORITHM mean? ALGORITHM meaning - ALGORITHM definition - ALGORITHM explanation. Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/... license. In mathematics and computer science, an algorithm is a self-contained step-by-step set of operations to be performed. Algorithms perform calculation, data processing, and/or automated reasoning tasks. The words 'algorithm' and 'algorism' come from the name al-Khwarizmi. Al-Khwarizmi was a Persian mathematician, astronomer, geographer, and scholar. An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input. The concept of algorithm has existed for centuries; however, a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation 1" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem. An informal definition could be "a set of rules that precisely defines a sequence of operations." which would include all computer programs, including programs that do not perform numeric calculations. Generally, a program is only an algorithm if it stops eventually. Algorithms are essential to the way computers process data. Many computer programs contain algorithms that detail the specific instructions a computer should perform (in a specific order) to carry out a specified task, such as calculating employees' paychecks or printing students' report cards. Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system. Typically, when an algorithm is associated with processing information, data are read from an input source, written to an output device, and/or stored for further processing. Stored data are regarded as part of the internal state of the entity performing the algorithm. In practice, the state is stored in one or more data structures. For some such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise. That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable). Because an algorithm is a precise list of precise steps, the order of computation is always critical to the functioning of the algorithm. Instructions are usually assumed to be listed explicitly, and are described as starting "from the top" and going "down to the bottom", an idea that is described more formally by flow of control.
Views: 39 Algorithm
Partial Derivatives of Regular Expressions
 
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Brian Hurt New York Haskell Meetup (http://www.meetup.com/NY-Haskell/even...) March 23, 2016 Slides: https://github.com/bhurt/presentation... Brian Hurt explains a different approach, with a number of advantages, to implementing regular expressions. Despite the title, no math is actually required- so if you don't remember calculus (or never took it), that's OK. A pragmatic understanding of regular expressions is assumed however.
Jason Adaska - How to Program like a Five Year Old in Haskell - λC 2017
 
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Description: In this talk, we show how the features of logic programming and strongly typed, functional programming can be used to write programs that dynamically "assemble" complex functionality using an ensemble of small atomic pieces and logic declarations. The abstraction of arrows is used as a basis of the construction. This method is metaphorically similar to children's programming “manipulatives,” in which a program's behavior is created by fitting together puzzle pieces that must connect in a certain way (e.g, cubelets, project blocks, etc.). In accordance with this metaphor, arrows are the pieces and types provide constraints on how they can fit together. Logic programming allows this assembly process to be done automatically via backtracking. A primary benefit of this approach is that it enables a large of amount of complexity to be encoded implicitly without requiring a developer to reason through, implement, and debug tortured case logic. Examples will be taken from a legal automation platform developed in Haskell. Slides: https://github.com/lambdaconf/lambdaconf-2017-assets/blob/master/Jason%20Adaska%20-%20How%20to%20Program%20like%20a%205%20Year%20Old%20-%20No%20Video.pptx Repository: https://github.com/jadaska/assemble-lc17
Views: 1680 LambdaConf
Fiat Cryptography: Automatic Correct-by-Construction Generation of Low-Level Cryptographic Code
 
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Some of the most widely used cryptographic protocols, including TLS, depend on fast execution of modular big-number arithmetic. Cryptographic primitives are coded by an elite set of implementation experts, and most programmers are shocked to learn that performance-competitive implementations are rewritten from scratch for each new prime-number modulus and each significantly different hardware architecture. In the Fiat Cryptography project, we show for the first time that an automatic compiler can produce this modulus-specialized code, via formalized versions of the number-theoretic optimizations that had previously only been applied by hand. Through experiments for a wide range of moduli, compiled for 64-bit x86 and 32-bit ARM processors, we demonstrate typical speedups vs. an off-the-shelf big-integer library in the neighborhood of 5X, sometimes going up to 10X. As a bonus, our compiler is implemented in the Coq proof assistant and generates proofs of functional correctness. These combined benefits of rigorous correctness/security guarantees and labor-saving were enough to convince the Google Chrome team to adopt our compiler for parts of their TLS implementation in the BoringSSL library. The project is joint work with Andres Erbsen, Jade Philipoom, Jason Gross, and Robert Sloan.  See more at https://www.microsoft.com/en-us/research/video/fiat-cryptography-automatic-correct-by-construction-generation-of-low-level-cryptographic-code/
Views: 1162 Microsoft Research
Solved: The function evaluation requires all threads to run
 
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Visual Studio during Debugging: The function evaluation requires all threads to run
Views: 7184 CodeDocu_com
Garbage Collection - Realm of Racket
 
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DrRacket describes to Pedestrian Language the advantages to automatic garbage collection. Check out our other video shorts and then visit our site www.realmofracket.com for more information!
Views: 3297 Realm of Racket
Extending F* in F*: Proof automation and Metaprogramming for Typeclasses
 
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Abstract for Talk Title 1: Extending F* in F*: Proof automation and Metaprogramming for Typeclasses, Concurrency, Optimizations and More In this talk we will provide an overview of the road we've been following for the past year with Meta-F*, the tactics and metaprogramming engine for F*. While F* itself is a highly-automated theorem prover and program verifier, there are unavoidable limitations to its automation. Meta-F* aims to put the programmer in near full control of F*'s behaviour, allowing to nudge, tweak, twist and compose its internal components in a safe fashion. We introduce the "meta" into F* via a custom effect, making Meta-F* a part of F*, and not something above it. We provide several "hooks" into Meta-F*, allowing to preprocess or solve proof obligations, generate terms and top-level definitions, implement custom strategies for solving implicit arguments (birthing F*'s typeclasses), and transforming programs before extracting (to OCaml, F#, or C). We ensure the safety of these transformations by designing Meta-F* to closely follow F*'s static semantics. Further, metaprograms can be compiled and linked into the compiler, obtaining fast-and-safe extension capabilities for F*, and blurring the line between the compiler's source code and Meta-F* metaprograms. We will describe some interesting use cases for Meta-F*, including arithmetic expression canonicalization, automated provably-memory-safe parser and printer generation, and some ongoing work in reasoning about concurrent programs in F*. Abstract for Talk Title 2: Layered DSLs for Verified Stateful Programming Cryptographic code is security- and performance-critical and hence it calls for high-assurance, efficient implementations. However, optimized low-level code is not a good target for formal verification. To mitigate this, a two-layered verification approach is often employed: the efficient low-level code is shown to adhere to a high-level implementation, which is more amenable to formal verification. Low* is a subset of C, shallowly embedded in F*, that was build to assist this process. It gives access to the full memory model of C while supporting F*-style formal verification, allowing efficient crypto programs to be verified against their purely functional specs. This work aims to further reduce the gap between high-level code written with verification in mind and low-level code optimized for efficiency. In particular, following ideas from bidirectional programing, we allow the user to express their algorithms as pure programs that operate on some high-level, purely functional state that provides a view of C’s memory. High-level programs written in this style enjoy a straight-forward interpretation as low-level programs. To further optimize these low-level programs we provide a set of rewrite rules whose soundness has been verified in F* and can be applied using F*’s tactic engine, in order to obtain an efficient and correct by construction Low* program. See more at https://www.microsoft.com/en-us/research/video/extending-f-in-f-proof-automation-and-metaprogramming-for-typeclasses-concurrency-optimizations-and-more-and-layered-dsls-for-verified-stateful-programming/
Views: 1016 Microsoft Research
LambdaConf 2015 - Introducing Emily  Simplifying Functional Programming   Andi McClure
 
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Emily is an experimental language project focusing on simplifying the basis of programming languages: it models all language operations through composition of function-like entities, equivalent to combinators with state. This means functions, objects, classes, and variable scopes have the same interface and are generally interchangeable. The goal is to make FP language capabilities accessible to entry-level and FP-wary programmers by means of simple concepts and a configurable, scripting-language-like syntax. Help us caption & translate this video! http://amara.org/v/HcNJ/
Views: 3968 Confreaks
MegaProcessor - Computerphile
 
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Walk around inside a working processor and see all the components operating. Jason Fitzpatrick shows us the Centre for Computer History's MegaProcessor . MegaProcessor was built by James Newman and is the largest working model processor in the world. Thanks once again to the Centre for Computing History in Cambridge Sun Microsystems Server: https://youtu.be/c5qH-LW3tq8 Altair 8800: https://youtu.be/cwEmnfy2BhI http://www.facebook.com/computerphile https://twitter.com/computer_phile This video was filmed and edited by Sean Riley. Computer Science at the University of Nottingham: http://bit.ly/nottscomputer Computerphile is a sister project to Brady Haran's Numberphile. More at http://www.bradyharan.com
Views: 239379 Computerphile
AI "Stop Button" Problem - Computerphile
 
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How do you implement an on/off switch on a General Artificial Intelligence? Rob Miles explains the perils. Part 1: https://www.youtube.com/watch?v=4l7Is6vOAOA Rob's Original Discussions on General AI: https://www.youtube.com/playlist?list=PLzH6n4zXuckquVnQ0KlMDxyT5YE-sA8Ps Stop Button Solution?: https://youtu.be/9nktr1MgS-A More from Rob Miles: http://bit.ly/Rob_Miles_YouTube Thanks to Nottingham Hackspace for providing the filming location: http://bit.ly/notthack http://www.facebook.com/computerphile https://twitter.com/computer_phile This video was filmed and edited by Sean Riley. Computer Science at the University of Nottingham: http://bit.ly/nottscomputer Computerphile is a sister project to Brady Haran's Numberphile. More at http://www.bradyharan.com
Views: 717906 Computerphile
GOTO 2017 • Programming Across Paradigms • Anjana Vakil
 
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This presentation was recorded at GOTO Chicago 2017. #gotocon #gotochgo http://gotochgo.com Anjana Vakil - Engineer at ÜberResearch ABSTRACT What's in a programming paradigm? How did the major paradigms come to be, and why? Once we've sworn our love to one paradigm, does a program written under any other still smell as sweet? Can functional programmers learn anything from [...] Download slides and read the full abstract here: https://gotochgo.com/2017/sessions/78 https://twitter.com/gotochgo https://www.facebook.com/GOTOConference http://gotocon.com #FunctionalProgramming #ProgrammingParadigms #ObjectOrientedProgramming #ImperativeProgramming
Views: 57726 GOTO Conferences
Andrew Appel: Turing, Gödel, and Church at Princeton in the 1930s
 
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In this keynote dinner address at Princeton University's Turing Centennial Celebration, Andrew Appel talks about models of computation and systems of logic in the context of Turing, Gödel, and Church at Princeton during the 1930s. He is introduced by Rpbert Sedgewick, William O. Baker Professor of Computer Science at Princeton. Appel is chair of the department of computer science and Eugene Higgins Professor of Computer Science at Princeton. He is the editor of a new imprint of Alan Turing's thesis, published by Princeton University Press: http://press.princeton.edu/titles/9780.html www.princeton.edu/turing #turingprinceton
Views: 7702 princetonacademics
GOTO 2016 • Conflict Resolution for Eventual Consistency • Martin Kleppmann
 
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This presentation was recorded at GOTO Berlin 2016 http://gotober.com Martin Kleppmann - Researcher at University of Cambridge ABSTRACT What do collaborative editors like Google Docs, the calendar app on your phone, and multi-datacenter database clusters have in common? Answer: They all need to cope with network interruptions, and still work offline. They all allow state to be updated [...] Download slides and read the full abstract here: https://gotocon.com/berlin-2016/presentations/show_talk.jsp?oid=7910 https://twitter.com/gotober https://www.facebook.com/GOTOConference http://gotocon.com
Views: 13509 GOTO Conferences
Map of Computer Science
 
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The field of computer science summarised. Learn more at this video's sponsor https://brilliant.org/dos Computer science is the subject that studies what computers can do and investigates the best ways you can solve the problems of the world with them. It is a huge field overlapping pure mathematics, engineering and many other scientific disciplines. In this video I summarise as much of the subject as I can and show how the areas are related to each other. You can buy this poster here: North America: https://store.dftba.com/products/map-of-computer-science-poster Everywhere else: https://www.redbubble.com/people/dominicwalliman/works/27929629-map-of-computer-science?p=poster&finish=semi_gloss&size=small Get all my other posters here: https://www.redbubble.com/people/dominicwalliman A couple of notes on this video: 1. Some people have commented that I should have included computer security alongside hacking, and I completely agree, that was an oversight on my part. Apologies to all the computer security professionals, and thanks for all the hard work! 2. I also failed to mention interpreters alongside compilers in the complier section. Again, I’m kicking myself because of course this is an important concept for people to hear about. Also the layers of languages being compiled to other languages is overly convoluted, in practice it is more simple than this. I guess I should have picked one simple example. 3. NP-complete problems are possible to solve, they just become very difficult to solve very quickly as they get bigger. When I said NP-complete and then "impossible to solve", I meant that the large NP-complete problems that industry is interested in solving were thought to be practically impossible to solve. And free downloadable versions of this and the other posters here. If you want to print them out for educational purposes please do! https://www.flickr.com/photos/[email protected]/ Thanks so much to my supporters on Patreon. If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience I also write a series of children’s science books call Professor Astro Cat, these links are to the publisher, but they are available in all good bookshops around the world in 18 languages and counting: Frontiers of Space (age 7+): http://nobrow.net/shop/professor-astro-cats-frontiers-of-space/ Atomic Adventure (age 7+): http://nobrow.net/shop/professor-astro-cats-atomic-adventure/ Intergalactic Activity Book (age 7+): http://nobrow.net/shop/professor-astro-cats-intergalactic-activity-book/ Solar System Book (age 3+, available in UK now, and rest of world in spring 2018): http://nobrow.net/shop/professor-astro-cats-solar-system/? Solar System App: http://www.minilabstudios.com/apps/professor-astro-cats-solar-system/ And the new Professor Astro Cat App: https://itunes.apple.com/us/app/galactic-genius-with-astro-cat/id1212841840?mt=8 Find me on twitter, Instagram, and my website: http://dominicwalliman.com https://twitter.com/DominicWalliman https://www.instagram.com/dominicwalliman https://www.facebook.com/dominicwalliman
Views: 1634242 Domain of Science
24. Entanglement — QComputing, EPR, and Bell
 
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MIT 8.04 Quantum Physics I, Spring 2013 View the complete course: http://ocw.mit.edu/8-04S13 Instructor: Allan Adams In this lecture, Prof. Adams discusses the basic principles of quantum computing. No-cloning theorem and Deutsch-Jozsa algorithm are introduced. The last part of the lecture is devoted to the EPR experiment and Bell's inequality. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 61561 MIT OpenCourseWare
LambdaConf 2015 - Programming and Math   Harold Carr
 
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Design patterns are a useful way to organize software. Unfortunately, "gang-of-four"-like patterns are not composable, due to side-effects. In a pure (i.e., no side-effects) language, functions can be composed. That makes it possible to leverage patterns from mathematics. This talk shows an algebra of function composition, identity functions, isomorphisms, (co)products (gluing functions that do not compose) and functors. It shows how this algebra relates to real-world programming. The goal of this talk is to provide an initial intuition of how to apply patterns from math to programming and to motivate you to continue studying on your own (perhaps by looking at the "uber" patterns of Category Theory). Note: knowing these patterns is NOT necessary for getting work done in a functional language, but this talk should give a glimpse of why they may be useful. The talk illustrates ideas using Haskell. It is aimed at FP beginners. Help us caption & translate this video! http://amara.org/v/HdCy/
Views: 2964 Confreaks
Intro to CS 005 - Procedures
 
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Procedures in scheme using the lambda keyword.
Views: 410 otherwaydotorg
Mod-01 Lec-03 Naming and Storing
 
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Storage Systems by Dr. K. Gopinath,Department of Computer Science and Engineering,IISc Bangalore.For more details on NPTEL visit http://nptel.ac.in
Views: 1906 nptelhrd
LambdaConf 2015 - Parametricity  The Essence of Information Hiding   Kris Nuttycombe
 
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This introductory talk is designed to help students new to functional programming understand how type parameters enable us to more easily reason about the behavior of functions and create APIs that enforce their invariants with type-level constraints. We will cover the principles of universal and existential quantification, review examples of reasoning about behavior from function types, and discuss implications for compositionality in API design. While most examples will be in Haskell, we will discuss how the principles generalize even to code written in unityped languages. Help us caption & translate this video! http://amara.org/v/HdDA/
Views: 1121 Confreaks
HaSKI: FPGA-based SKI calculus evaluator
 
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An FPGA-based SKI calculus evaluator written in Haskell/Cλash. Blog: http://yager.io/HaSKI/HaSKI.html Github: https://github.com/wyager/HaSKI SKI calculus: https://en.wikipedia.org/wiki/SKI_combinator_calculus Cλash: http://www.clash-lang.org
Views: 897 Will Yager
Recursive Visual Cryptography Scheme
 
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http://demonstrations.wolfram.com/RecursiveVisualCryptographyScheme The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. This Demonstration implements a recursive visual cryptography scheme, specifically using two images (main image and recursive image) and two shares. Move the shares around to reveal the main image and the recursive image. If finding the recursive image ... Contributed by: Marvin Jones and Ryan Nikin-Beers
Views: 171 wolframmathematica
Largest Eigen Value and Eigen Vector of 3x3 Matrix on Casio fx-991ES Scientific Calculator
 
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http://www.youtube.com/sujoyn70 http://www.indiastudychannel.com/r/sujoy70.aspx Hi friends, I'm Sujoy. Today I'll tell you how to find the Eigen Value and corresponding Eigen Vector of a 3x3 matrix using the Casio fx-991ES Scientific Calculator. I make educational video tutorials on- Statistics,Financial and Business Mathematics,Numerical Methods,Operation Research(OR),Computer Science & Engineering(CSE),Number Systems,Probability,Scientific Calculator Tutorials,Math Magic Tricks,Science Experiments etc. I also make- India Travel and Tourism videos,Street Foods videos,Restaurant Reviews,Do-It-Yourself(DIY) videos,How-to guides,Life Hacks & Life Tips videos. And a series of videos showing how to use your scientific calculators Casio fx-991ES & fx-82MS to do maths easily. Click my YouTube channel's link below to watch them. Subscribe to my youtube channel below- http://www.youtube.com/sujoyn70 Please like & share this video :-) Also visit my blog- http://www.sujoyn70.blogspot.com And my IndiaStudyChannel profile- http://www.indiastudychannel.com/r/sujoy70.aspx Incoming Tags- z score statistics,find mean median mode statistics in ms excel,variance,standard deviation,linear regression,data processing,confidence intervals,average value,probability theory,binomial distribution,matrix,random numbers,error propagation,t statistics analysis,hypothesis testing,theorem,chi square,time series,data collection,sampling,p value,scatterplots,statistics lectures,statistics tutorials,business mathematics statistics,share stock market statistics in calculator,business analytics,GTA,continuous frequency distribution,statistics mathematics in real life,modal class,n is even,n is odd,median mean of series of numbers,math help,Sujoy Krishna Das,n+1/2 element,measurement of variation,measurement of central tendency,range of numbers,interquartile range,casio fx991,casio fx82,casio fx570,casio fx115es,casio 9860,casio 9750,casio 83gt,TI BAII+ financial,casio piano,casio calculator tricks and hacks,how to cheat in exam and not get caught,grouped interval data,equation of triangle rectangle curve parabola hyperbola,graph theory,operation research(OR),numerical methods,decision making,pie chart,bar graph,computer data analysis,histogram,statistics formula,matlab tutorial,find arithmetic mean geometric mean,find population standard deviation,find sample standard deviation,how to use a graphic calculator,pre algebra,pre calculus,absolute deviation,TI Nspire,TI 84 TI83 calculator tutorial,texas instruments calculator,grouped data,set theory,IIT JEE,AIEEE,GCSE,CAT,MAT,SAT,GMAT,MBBS,JELET,JEXPO,VOCLET,Indiastudychannel,IAS,IPS,IFS,GATE,B-Tech,M-Tech,AMIE,MBA,BBA,BCA,MCA,XAT,TOEFL,CBSE,ICSE,HS,WBUT,SSC,IUPAC,Narendra Modi,Sachin Tendulkar Farewell Speech,Dhoom 3,Arvind Kejriwal,maths revision,how to score good marks in exams,how to pass math exams easily,JEE 12th physics chemistry maths PCM,JEE maths shortcut techniques,quadratic equations,competition exams tips and ticks,competition maths,govt job,JEE KOTA,college math,mean value theorem,L hospital rule,tech guru awaaz,derivation,cryptography,iphone 5 fingerprint hack,crash course,CCNA,converting fractions,solve word problem,cipher,game theory,GDP,how to earn money online on youtube,demand curve,computer science,prime factorization,LCM & GCF,gauss elimination,vector,complex numbers,number systems,vector algebra,logarithm,trigonometry,organic chemistry,electrical math problem,eigen value eigen vectors,runge kutta,gauss jordan,simpson 1/3 3/8 trapezoidal rule,solved problem example,newton raphson,interpolation,integration,differentiation,regula falsi,programming,algorithm,gauss seidal,gauss jacobi,taylor series,iteration,binary arithmetic,logic gates,matrix inverse,determinant of matrix,matrix calculator program,sex in ranchi,sex in kolkata,vogel approximation VAM optimization problem,North west NWCR,Matrix minima,Modi method,assignment problem,transportation problem,simplex,k map,boolean algebra,android,casio FC 200v 100v financial,management mathematics tutorials,net present value NPV,time value of money TVM,internal rate of return IRR Bond price,present value PV and future value FV of annuity casio,simple interest SI & compound interest CI casio,break even point,amortization calculation,HP 10b financial calculator,banking and money,income tax e filing,economics,finance,profit & loss,yield of investment bond,Sharp EL 735S,cash flow casio,re finance,insurance and financial planning,investment appraisal,shortcut keys,depreciation,discounting,university lectures
Views: 88933 Sujoy Krishna Das
Dr. Manuel Chakravarty, IOHK Language Architect, on Cardano programming - Episode 14
 
01:09:50
Follow Dr. Manuel Chakravarty https://twitter.com/tacticalgrace Trezor Model T hardware wallet now supports ADA https://shop.trezor.io/product/trezor-model-t?offer_id=15&aff_id=1728 Download Yoroi https://yoroiwallet.com Follow us on https://twitter.com/CardanoEffect https://www.facebook.com/cardano.effect https://www.reddit.com/r/thecardanoeffect Contact us with questions [email protected] Youtube Channels https://www.youtube.com/c/sebastienguillemot https://www.youtube.com/c/DigitalFortress https://www.youtube.com/c/philpa6 For greater community involvement you can visit the conversations at: Forum: https://forum.cardano.org Telegram: https://t.me/CardanoGeneral Music from ProleteR: Bandcamp : https://proleter.bandcamp.com/album/curses-from-past-times-ep Facebook : https://www.facebook.com/ProleteR.beats Soundcloud : https://soundcloud.com/proleter-beatmaker The Cardano Effect is licensed under Creative Commons CC BY 4.0: https://creativecommons.org/licenses/by/4.0/ ADA Tip Jar: DdzFFzCqrhsviEQfHp1HMbXBk7LMoPXGPijAgDk2D3rpWD3i9sHhsviUB1TiZFyMbTM2z8kkPLHKeB6G5fTzNkY93GGUTBxiAyDXbXn1 #thecardanoeffect #cardano #ada
Views: 2643 The Cardano Effect
Blackbox Polynomial Identity Testing for Depth 3 Circuits
 
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Testing to see if a Boolean circuit computes the identically zero function is a fundamental problem in computational complexity. Known as the SAT (for satisfiability) problem, it is the first NP-complete problem, and a polynomial time algorithm for this problem would show P=NP. The algebraic analog of this problem, which attempts to determine if an arithmetic circuit (whose inputs are integers, and gates add or multiply their inputs) computes the identically zero function turns to be an equally interesting problem. Every gate of such a circuit computes a polynomial in the input variables and so the goal here is to test if the output polynomial is the identically zero function, leading to this problem being known as the Polynomial Identity Testing problem (PIT). Unlike SAT, PIT does have fast randomized solutions: Just pick random values for the input variables and the output is very unlikely to be zero if the polynomial is not identically zero. However a deterministic solution to this problem is not known and, as recent work by Impagliazzo and Kabanets, and Agrawal and Vinay have shown, such solutions have major implications for both complexity theory and algorithm design. A complete derandomization of PIT would imply superpolynomial circuit lower bounds, one of the major quests of complexity theory. In addition, special cases of PIT play an important role in algorithmic problems like primality testing and perfect matching. In this talk I will describe a recent work giving a deterministic polynomial time algorithm for blackbox identity testing for depth three circuits with bounded top fanin. Obtaining a similar result for general circuits of depth 4 would essentially derandomize identity testing for general circuits (Agrawal-Vinay 08)! Our result resolves a question posed by Klivans and Spielman in 2001. The main technical result that I will describe is a structure theorem for depth 3 circuits that compute the zero polynomial. I will show that under mild assumptions, any such circuit is essentially made up of only constantly many variables. This proves a conjecture of Dvir and Shpilka from 2005. Our blackbox identity test follows from this structure theorem by combining it with a construction of Karnin and Shpilka.
Views: 161 Microsoft Research
Trapezoidal Rule Explained On Casio fx-991ES and Casio fx-82MS Calculators!
 
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http://www.indiastudychannel.com/r/sujoy70.aspx Watch all my Numerical Methods videos below- http://www.youtube.com/playlist?list=PLHGJFOxCJ5Iwm8kTk52LAQ-_T0IMwZZHD Today I'll tell you how to solve Numerical Integration problems by Trapezoidal Rule on Casio fx-991ES and fx-82MS calculators easily. Topics explained in this video- 1. Finding interval gap using upper limit,lower limit and number of intervals 2. How to construct the iteration table for Trapezoidal Rule? - Explained 3. Doing Trapezoidal Rule iterations on Casio fx-991ES and Casio fx-82MS very easily! 4. Understanding General Formula of Trapezoidal Rule That's it! I've uploaded videos on Statistics,Numerical Methods, Business & Financial Mathematics,Operation Research,Computer Science & Engineering(CSE),Android Application Reviews,India Travel & Tourism,Street Foods,Life Tips and many other topics. And a series of videos showing how to use your scientific calculators Casio fx-991ES & fx-82MS to do maths easily. Click my YouTube channel's link below to watch them. Subscribe to my youtube channel below- http://www.youtube.com/sujoyn70 Please like & share this video :-) My blog- http://www.sujoyn70.blogspot.com Incoming Tags- z score statistics,find mean median mode statistics in ms excel,variance,standard deviation,linear regression,data processing,confidence intervals,average value,probability theory,binomial distribution,matrix,random numbers,error propagation,t statistics analysis,hypothesis testing,theorem,chi square,time series,data collection,sampling,p value,scatterplots,statistics lectures,statistics tutorials,business mathematics statistics,share stock market statistics in calculator,business analytics,GTA,continuous frequency distribution,statistics mathematics in real life,modal class,n is even,n is odd,median mean of series of numbers,math help,Sujoy Krishna Das,n+1/2 element,measurement of variation,measurement of central tendency,range of numbers,interquartile range,casio fx991,casio fx82,casio fx570,casio fx115es,casio 9860,casio 9750,casio 83gt,TI BAII+ financial,casio piano,casio calculator tricks and hacks,how to cheat in exam and not get caught,grouped interval data,equation of triangle rectangle curve parabola hyperbola,graph theory,operation research(OR),numerical methods,decision making,pie chart,bar graph,computer data analysis,histogram,statistics formula,matlab tutorial,find arithmetic mean geometric mean,find population standard deviation,find sample standard deviation,how to use a graphic calculator,pre algebra,pre calculus,absolute deviation,TI Nspire,TI 84 TI83 calculator tutorial,texas instruments calculator,grouped data,set theory,IIT JEE,AIEEE,GCSE,CAT,MAT,SAT,GMAT,MBBS,JELET,JEXPO,VOCLET,Indiastudychannel,IAS,IPS,IFS,GATE,B-Tech,M-Tech,AMIE,MBA,BBA,BCA,MCA,XAT,TOEFL,CBSE,ICSE,HS,WBUT,SSC,IUPAC,Narendra Modi,Sachin Tendulkar Farewell Speech,Dhoom 3,Arvind Kejriwal,maths revision,how to score good marks in exams,how to pass math exams easily,JEE 12th physics chemistry maths PCM,JEE maths shortcut techniques,quadratic equations,competition exams tips and ticks,competition maths,govt job,JEE KOTA,college math,mean value theorem,L hospital rule,tech guru awaaz,derivation,cryptography,iphone 5 fingerprint hack,crash course,CCNA,converting fractions,solve word problem,cipher,game theory,GDP,how to earn money online on youtube,demand curve,computer science,prime factorization,LCM & GCF,gauss elimination,vector,complex numbers,number systems,vector algebra,logarithm,trigonometry,organic chemistry,electrical math problem,eigen value eigen vectors,runge kutta,gauss jordan,simpson 1/3 3/8 trapezoidal rule,solved problem example,newton raphson,interpolation,integration,differentiation,regula falsi,programming,algorithm,gauss seidal,gauss jacobi,taylor series,iteration,binary arithmetic,logic gates,matrix inverse,determinant of matrix,matrix calculator program,sex in ranchi,sex in kolkata,vogel approximation VAM optimization problem,North west NWCR,Matrix minima,Modi method,assignment problem,transportation problem,simplex,k map,boolean algebra,android,casio FC 200v 100v financial,management mathematics tutorials,net present value NPV,time value of money TVM,internal rate of return IRR Bond price,present value PV and future value FV of annuity casio,simple interest SI & compound interest CI casio,break even point,amortization calculation,HP 10b financial calculator,banking and money,income tax e filing,economics,finance,profit & loss,yield of investment bond,Sharp EL 735S,cash flow casio,re finance,insurance and financial planning,investment appraisal,shortcut keys,depreciation,discounting,commerce,comedy
Views: 53835 Sujoy Krishna Das
NIPS 2011 Learning Semantics Workshop: Towards More Human-like Machine Learning of Word Meanings
 
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Learning Semantics Workshop at NIPS 2011 Invited Talk: Towards More Human-like Machine Learning of Word Meanings by Josh Tenenbaum Josh Tenenbaum is a Professor in the Department of Brain and Cognitive Sciences at Massachusetts Institute of Technology. Him and his colleagues in the Computational Cognitive Science group study one of the most basic and distinctively human aspects of cognition: the ability to learn so much about the world, rapidly and flexibly. Abstract: How can we build machines that learn the meanings of words more like the way that human children do? I will talk about several challenges and how we are beginning to address them using sophisticated probabilistic models. Children can learn words from minimal data, often just one or a few positive examples (one-shot learning). Children learn to learn: they acquire powerful inductive biases for new word meanings in the course of learning their first words. Children can learn words for abstract concepts or types of concepts that have no little or no direct perceptual correlate. Children's language can be highly context-sensitive, with parameters of word meaning that must be computed anew for each context rather than simply stored. Children learn function words: words whose meanings are expressed purely in how they compose with the meanings of other words. Children learn whole systems of words together, in mutually constraining ways, such as color terms, number words, or spatial prepositions. Children learn word meanings that not only describe the world but can be used for reasoning, including causal and counterfactual reasoning. Bayesian learning defined over appropriately structured representations — hierarchical probabilistic models, generative process models, and compositional probabilistic languages — provides a basis for beginning to address these challenges.
Views: 2538 GoogleTechTalks
Martin Davis: Universality is Ubiquitous
 
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Martin Davis, Professor Emeritus of New York University, discusses how the work of Turing, Post, Church, Gödel, and Kleene during the 1930s fundamentally altered our notion of the nature of computation. He discusses this in terms of the theoretical underpinnings of the development of all-purpose computers and of modern computer science and speculates about the role of computation in the human mind and in biological evolution. Learn more at www.princeton.edu/turing #turingprinceton
Views: 1080 princetonacademics
Profile of Luca Trevisan, the Simons Institute's Incoming Senior Scientist
 
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The Simons Institute is pleased to announce the appointment of Luca Trevisan as our first permanent Senior Scientist. Luca rejoined UC Berkeley this fall, with joint appointments at the Simons Institute and Department of Electrical Engineering and Computer Sciences, and the Department of Mathematics. He comes to us most recently from Stanford University, where he was a Professor of Computer Science. He has also held posts at Columbia University, MIT and DIMACS, and earned his Ph.D. from the Sapienza University of Rome, under Pierluigi Crescenzi. This video introduction features Luca in conversation with Interim Senior Scientist, Christos Papdimitriou. View a full transcript of the interview: http://simons.berkeley.edu/news/profile-luca-trevisan
Views: 2006 Simons Institute
DrRacket 01.5 -- Keyboard Editing 1
 
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Starting with arrow keys, moving upward through s-expression based movement & cutting & pasting, ending with c-x;c-o
Views: 6078 John Clements
Timeline of United States inventions (1890–1945) | Wikipedia audio article
 
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This is an audio version of the Wikipedia Article: Timeline of United States inventions (1890–1945) Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago. Learning by listening is a great way to: - increases imagination and understanding - improves your listening skills - improves your own spoken accent - learn while on the move - reduce eye strain Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone. You can find other Wikipedia audio articles too at: https://www.youtube.com/channel/UCuKfABj2eGyjH3ntPxp4YeQ You can upload your own Wikipedia articles through: https://github.com/nodef/wikipedia-tts "The only true wisdom is in knowing you know nothing." - Socrates SUMMARY ======= A timeline of United States inventions (1890–1945) encompasses the ingenuity and innovative advancements of the United States within a historical context, dating from the Progressive Era to the end of World War II, which have been achieved by inventors who are either native-born or naturalized citizens of the United States. Copyright protection secures a person's right to his or her first-to-invent claim of the original invention in question, highlighted in Article I, Section 8, Clause 8 of the United States Constitution which gives the following enumerated power to the United States Congress: In 1641, the first patent in North America was issued to Samuel Winslow by the General Court of Massachusetts for a new method of making salt. On April 10, 1790, President George Washington signed the Patent Act of 1790 (1 Stat. 109) into law which proclaimed that patents were to be authorized for "any useful art, manufacture, engine, machine, or device, or any improvement therein not before known or used." On July 31, 1790, Samuel Hopkins of Philadelphia, Pennsylvania, became the first person in the United States to file and to be granted a patent under the new U.S. patent statute. The Patent Act of 1836 (Ch. 357, 5 Stat. 117) further clarified United States patent law to the extent of establishing a patent office where patent applications are filed, processed, and granted, contingent upon the language and scope of the claimant's invention, for a patent term of 14 years with an extension of up to an additional 7 years.From 1836 to 2011, the United States Patent and Trademark Office (USPTO) has granted a total of 7,861,317 patents relating to several well-known inventions appearing throughout the timeline below. Some examples of patented inventions between the years 1890 and 1945 include John Froelich's tractor (1892), Ransom Eli Olds' assembly line (1901), Willis Carrier's air-conditioning (1902), the Wright Brothers' airplane (1903), and Robert H. Goddard's liquid-fuel rocket (1926).
Views: 276 wikipedia tts
Turing machine
 
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A Turing machine is a hypothetical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a computer. The "Turing" machine was invented in 1936 by Alan Turing who called it an "a-machine" (automatic machine). The Turing machine is not intended as practical computing technology, but rather as a hypothetical device representing a computing machine. Turing machines help computer scientists understand the limits of mechanical computation. This video is targeted to blind users. Attribution: Article text available under CC-BY-SA Creative Commons image source in video
Views: 618 Audiopedia
cs224n lecture02
 
01:14:29
Views: 1736 pikarenx
Computational complexity | Wikipedia audio article
 
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This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Computational_complexity 00:01:33 1 Resources 00:01:42 1.1 Time 00:02:27 1.2 Space 00:02:42 1.3 Others 00:04:17 2 Complexity as a function of input size 00:05:30 3 Asymptotic complexity 00:07:54 4 Models of computation 00:08:22 4.1 Deterministic models 00:09:16 4.2 Non-deterministic computation 00:10:24 4.3 Parallel and distributed computation 00:11:57 4.4 Quantum computing 00:13:05 5 Problem complexity (lower bounds) 00:14:02 6 Use in algorithm design 00:18:22 7 See also 00:20:24 8 References Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago. Learning by listening is a great way to: - increases imagination and understanding - improves your listening skills - improves your own spoken accent - learn while on the move - reduce eye strain Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone. Listen on Google Assistant through Extra Audio: https://assistant.google.com/services/invoke/uid/0000001a130b3f91 Other Wikipedia audio articles at: https://www.youtube.com/results?search_query=wikipedia+tts Upload your own Wikipedia articles through: https://github.com/nodef/wikipedia-tts Speaking Rate: 0.9568617800371617 Voice name: en-US-Wavenet-F "I cannot teach anybody anything, I can only make them think." - Socrates SUMMARY ======= In computer science, the computational complexity, or simply complexity of an algorithm is the amount of resources required for running it. The computational complexity of a problem is the minimum of the complexities of all possible algorithms for this problem (including the unknown algorithms). As the amount of needed resources varies with the input, the complexity is generally expressed as a function n → f(n), where n is the size of the input, and f(n) is either the worst-case complexity, that is the maximum of the amount of resources that are needed for all inputs of size n, or the average-case complexity, that is average of the amount of resources over all input of size n. When the nature of the resources is not explicitly given, this is usually the time needed for running the algorithm, and one talks of time complexity. However, this depends on the computer that is used, and the time is generally expressed as the number of needed elementary operations, which are supposed to take a constant time on a given computer, and to change by a constant factor when one changes of computer. Otherwise, the resource that is considered is often the size of the memory that is needed, and one talks of space complexity. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory. Clearly, both areas are strongly related, as the complexity of an algorithm is always an upper bound of the complexity of the problem solved by this algorithm.
Views: 0 wikipedia tts
Matrix (mathematics) | Wikipedia audio article
 
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This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Matrix_(mathematics) 00:04:07 1 Definition 00:05:09 1.1 Size 00:06:01 2 Notation 00:09:53 3 Basic operations 00:10:30 3.1 Addition, scalar multiplication and transposition 00:10:48 3.2 Matrix multiplication 00:11:12 3.3 Row operations 00:11:24 3.4 Submatrix 00:12:20 4 Linear equations 00:12:42 5 Linear transformations 00:13:13 6 Square matrix 00:13:27 6.1 Main types 00:13:30 6.1.1 Diagonal and triangular matrix 00:16:29 6.1.2 Identity matrix 00:18:19 6.1.3 Symmetric or skew-symmetric matrix 00:18:51 6.1.4 Invertible matrix and its inverse 00:20:38 6.1.5 Definite matrix 00:23:04 6.1.6 Orthogonal matrix 00:25:23 6.2 Main operations 00:25:34 6.2.1 Trace 00:26:13 6.2.2 Determinant 00:26:46 6.2.3 Eigenvalues and eigenvectors 00:26:55 7 Computational aspects 00:27:23 8 Decomposition 00:28:55 9 Abstract algebraic aspects and generalizations 00:29:23 9.1 Matrices with more general entries 00:29:37 9.2 Relationship to linear maps 00:30:33 9.3 Matrix groups 00:30:49 9.4 Infinite matrices 00:31:12 9.5 Empty matrices 00:32:22 10 Applications 00:32:26 10.1 Graph theory 00:33:41 10.2 Analysis and geometry 00:34:38 10.3 Probability theory and statistics 00:34:46 10.4 Symmetries and transformations in physics 00:36:25 10.5 Linear combinations of quantum states 00:36:28 10.6 Normal modes 00:37:26 10.7 Geometrical optics 00:38:30 10.8 Electronics 00:39:29 11 History 00:39:59 11.1 Other historical usages of the word "matrix" in mathematics 00:42:04 12 See also 00:42:44 13 Notes 00:44:49 14 References 00:45:06 14.1 Physics references 00:45:37 14.2 Historical references 00:45:49 15 External links 00:46:40 Matrices with more general entries 00:48:31 1) associative algebra over R. The determinant of square matrices over a commutative ring R can still be defined using the Leibniz formula; such a matrix is invertible if and only if its determinant is invertible in R, generalising the situation over a field F, where every nonzero element is invertible. Matrices over superrings are called supermatrices.Matrices do not always have all their entries in the same ring – or even in any ring at all. One special but common case is block matrices, which may be considered as matrices whose entries themselves are matrices. The entries need not be square matrices, and thus need not be members of any ring; but their sizes must fulfil certain compatibility conditions. 00:49:15 Relationship to linear maps 00:49:25 Linear maps Rn → Rm are equivalent to m-by-n matrices, as described above. More generally, any linear map f: V → W between finite-dimensional vector spaces can be described by a matrix A 00:51:37 m composition of these maps is possible, and this gives rise to the matrix ring of n×n matrices representing the endomorphism ring of Rn. 00:51:49 Matrix groups 00:53:18 Infinite matrices 00:57:16 Empty matrices 00:58:17 Applications 01:00:13 Graph theory 01:01:06 Analysis and geometry 01:03:52 Probability theory and statistics 01:05:08 1, …, Nwhich can be formulated in terms of matrices, related to the singular value decomposition of matrices.Random matrices are matrices whose entries are random numbers, subject to suitable probability distributions, such as matrix normal distribution. Beyond probability theory, they are applied in domains ranging from number theory to physics. 01:05:31 Symmetries and transformations in physics 01:05:42 Linear transformations and the associated symmetries play a key role in modern physics. For example, elementary particles in quantum field theory are classified as representations of the Lorentz group of special relativity and, more specifically, by their behavior under the spin group. Concrete representations involving the Pauli matrices and more general gamma matrices are an integral part of the physical description of fermions, which behave as spinors. For the three lightest quarks, there is a group-theoretical representation involving the special unitary group SU(3); for their calculations, physicists use a convenient matrix representation known as the Gell-Mann matrices, which are also used for the SU(3) gauge group that forms the basis of the modern description of strong nuclear interactions, quantum chromodynamics. The Cabibbo–Kobayashi–Maskawa matrix, in turn, expresses the fact that the basic quark states that are important for weak interactions are not the same as, but linearly related to the basic quark states that define particles with specific and distinct masses. 01:06:47 Linear combinations of quantum states 01:06:58 The first model of quantum mechanics (Heisenberg, 1925) represented the theory's operators by infinite-dimensional matrices acting on quantum states. This is also referred to as matrix mechanics. One particular example is the density matrix that characterizes the "mixed" state of a quantum system as a linear combination of elementary, "pure" eigenstates.Another matrix serves as a k ...
Views: 9 wikipedia tts
Matrix (math) | Wikipedia audio article
 
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This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Matrix_(mathematics) 00:04:39 1 Definition 00:05:49 1.1 Size 00:06:48 2 Notation 00:11:06 3 Basic operations 00:11:48 3.1 Addition, scalar multiplication and transposition 00:12:07 3.2 Matrix multiplication 00:12:34 3.3 Row operations 00:12:47 3.4 Submatrix 00:13:50 4 Linear equations 00:14:15 5 Linear transformations 00:14:49 6 Square matrix 00:15:04 6.1 Main types 00:15:07 6.1.1 Diagonal and triangular matrix 00:18:33 6.1.2 Identity matrix 00:20:36 6.1.3 Symmetric or skew-symmetric matrix 00:21:11 6.1.4 Invertible matrix and its inverse 00:23:14 6.1.5 Definite matrix 00:26:00 6.1.6 Orthogonal matrix 00:28:37 6.2 Main operations 00:28:49 6.2.1 Trace 00:29:32 6.2.2 Determinant 00:30:09 6.2.3 Eigenvalues and eigenvectors 00:30:19 7 Computational aspects 00:30:50 8 Decomposition 00:32:33 9 Abstract algebraic aspects and generalizations 00:33:03 9.1 Matrices with more general entries 00:33:19 9.2 Relationship to linear maps 00:34:21 9.3 Matrix groups 00:34:40 9.4 Infinite matrices 00:35:04 9.5 Empty matrices 00:36:24 10 Applications 00:36:28 10.1 Graph theory 00:37:53 10.2 Analysis and geometry 00:38:56 10.3 Probability theory and statistics 00:39:05 10.4 Symmetries and transformations in physics 00:40:53 10.5 Linear combinations of quantum states 00:40:57 10.6 Normal modes 00:42:02 10.7 Geometrical optics 00:43:15 10.8 Electronics 00:44:21 11 History 00:44:55 11.1 Other historical usages of the word "matrix" in mathematics 00:47:16 12 See also 00:48:01 13 Notes 00:50:24 14 References 00:50:42 14.1 Physics references 00:51:17 14.2 Historical references 00:51:31 15 External links 00:52:29 Matrices with more general entries 00:54:34 1) associative algebra over R. The determinant of square matrices over a commutative ring R can still be defined using the Leibniz formula; such a matrix is invertible if and only if its determinant is invertible in R, generalising the situation over a field F, where every nonzero element is invertible. Matrices over superrings are called supermatrices.Matrices do not always have all their entries in the same ring – or even in any ring at all. One special but common case is block matrices, which may be considered as matrices whose entries themselves are matrices. The entries need not be square matrices, and thus need not be members of any ring; but their sizes must fulfil certain compatibility conditions. 00:55:24 Relationship to linear maps 00:55:35 Linear maps Rn → Rm are equivalent to m-by-n matrices, as described above. More generally, any linear map f: V → W between finite-dimensional vector spaces can be described by a matrix A 00:58:02 m composition of these maps is possible, and this gives rise to the matrix ring of n×n matrices representing the endomorphism ring of Rn. 00:58:15 Matrix groups 00:59:55 Infinite matrices 01:04:24 Empty matrices 01:05:34 Applications 01:07:44 Graph theory 01:08:44 Analysis and geometry 01:11:51 Probability theory and statistics 01:13:16 1, …, Nwhich can be formulated in terms of matrices, related to the singular value decomposition of matrices.Random matrices are matrices whose entries are random numbers, subject to suitable probability distributions, such as matrix normal distribution. Beyond probability theory, they are applied in domains ranging from number theory to physics. 01:13:42 Symmetries and transformations in physics 01:13:54 Linear transformations and the associated symmetries play a key role in modern physics. For example, elementary particles in quantum field theory are classified as representations of the Lorentz group of special relativity and, more specifically, by their behavior under the spin group. Concrete representations involving the Pauli matrices and more general gamma matrices are an integral part of the physical description of fermions, which behave as spinors. For the three lightest quarks, there is a group-theoretical representation involving the special unitary group SU(3); for their calculations, physicists use a convenient matrix representation known as the Gell-Mann matrices, which are also used for the SU(3) gauge group that forms the basis of the modern description of strong nuclear interactions, quantum chromodynamics. The Cabibbo–Kobayashi–Maskawa matrix, in turn, expresses the fact that the basic quark states that are important for weak interactions are not the same as, but linearly related to the basic quark states that define particles with specific and distinct masses. 01:15:08 Linear combinations of quantum states 01:15:19 The first model of quantum mechanics (Heisenberg, 1925) represented the theory's operators by infinite-dimensional matrices acting on quantum states. This is also referred to as matrix mechanics. One particular example is the density matrix that characterizes the "mixed" state of a quantum system as a linear combination of elementary, "pure" eigenstates.Another matrix serves as a k ...
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