Proof of the Rabin-Miller Theorem, Showing the Validity of the Rabin-Miller Test for Composite Numbers
In this video we have discussed about how the Primality Testing failed proving Fermat's Theorem so to overcome that we learned about this new method known as Miller Rabin Test.
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Views: 29391
Quick Trixx

Using the Miller-Rabin (probabilistic) primality test.
NOTE: if bo (and only bo) had been either +1 OR -1, n would be prime (it was 263, in this example). BUT for b1, b2, and so on, +1 implies composite, -1 implies prime.
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 41934
Theoretically

This talk will consist of a series of light mini-talks inspired by Atkin's papers on recognizing primes (1982, 'On a primality test of Solovay and Strassen'; 1995, 'Intelligent primality test offer'), proving primes to be prime (1993, 'Elliptic curves and primality proving'), factoring integers into primes (1993, 'Finding suitable curves for the elliptic curve method of factorization'), and enumerating primes (2004, 'Prime sieves using binary quadratic forms').

Views: 1643
Microsoft Research

The AKS Test has been a major break-through in the search for Prime Numbers.
More links & stuff in full description below ↓↓↓
See the previous video about Fermat's Prime Test at: http://youtu.be/jbiaz_aHHUQ
The video features Dr James Grime - http://singingbanana.com
The AKS Test paper: http://bit.ly/primetest
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
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Videos by Brady Haran
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Views: 652481
Numberphile

Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 7653
nptelhrd

If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Monte Carlo algorithm
In computing, a Monte Carlo algorithm is a randomized algorithm whose running time is deterministic, but whose output may be incorrect with a certain (typically small) probability.The related class of Las Vegas algorithms are also randomized, but in a different way: they take an amount of time that varies randomly, but always produce the correct answer.
-Video is targeted to blind users
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Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=Q2-FH36LuT0

Views: 7498
WikiAudio

Full article: https://opensource.com/life/16/10/top-5-october-28
*Top 5 articles of the week*
5. 12 open source games for Android
https://opensource.com/life/16/10/12-open-source-games-android
4. Python file-management tricks for digital artists
https://opensource.com/life/16/10/python-file-management-tricks-digital-artists
3. MySQL and database programming for beginners
https://opensource.com/life/16/10/all-things-open-interview-dave-stokes
2. Distributing encryption software may break the law
https://opensource.com/law/16/10/distributing-encryption-software-may-break-law
1. 3 open source time management tools
https://opensource.com/life/16/10/tools-time-management

Views: 310
Opensource.com

-- Created using PowToon -- Free sign up at http://www.powtoon.com/youtube/ -- Create animated videos and animated presentations for free. PowToon is a free tool that allows you to develop cool animated clips and animated presentations for your website, office meeting, sales pitch, nonprofit fundraiser, product launch, video resume, or anything else you could use an animated explainer video. PowToon's animation templates help you create animated presentations and animated explainer videos from scratch. Anyone can produce awesome animations quickly with PowToon, without the cost or hassle other professional animation services require.

Views: 819
Toures Tiu

A History of Primes
Manindra Agrawal, American Academy of Arts and Sciences, October 2002
The Clay Mathematics Institute (CMI) 2002 Annual Meeting took place on Wednesday, October 30, 2002, from 2:30 to 5:30 PM, at the American Academy of Arts & Sciences in Cambridge, Massachusetts. The Annual Meeting brought together an international assembly of mathematicians to celebrate the universality of mathematical thought. This meeting provided a public forum for discussion among leading mathematicians and scientists, and it strengthened relations between mathematicians, the public, and the scientific research community.
The meeting began with the presentation of the 2002 Clay Research Award to Oded Schramm (for his work on the Loewner equation) and to Manindra Agrawal (for his work on primality testing). CMI President Arthur Jaffe and Directors Landon Clay and Lavinia Clay gave the awards. This Research Award recognizes major recent breakthroughs in two mathematical directions, and represents the pinnacle of recognition of research achievement by CMI. Each prizewinner becomes a Clay Research Scholar, and receives a bronze model of the CMI logo, an elegant sculpture "Figureight Knot Complement vii/ CMI" by sculptor Helaman Ferguson. Former winners are: Andrew Wiles, Laurent Lafforgue, Alain Connes, Stanislav Smirnov and Edward Witten.
Two talks followed the awards ceremony. Manindra Agrawal of the Indian Institute of Technology surprised all experts in August 2002 by solving an ancient problem (working with two undergraduate students). They showed that one could determine the primality of a number in polynomial time. This was the first talk in the United States by the inventor of the new method. Vladimir Voevodsky from the Institute of Advanced Study gave the second talk. He spoke about the mathematical breakthroughs that led to his receiving the Fields Medal in August 2002.
"We have a very impressive set of ground-breaking mathematicians at this year's meeting as award winners and speakers. The meeting certainly will inspire young mathematicians who attend, as well as all those who read about it or view the meeting on the web," said Arthur Jaffe, President of the Clay Mathematics Institute. "Agrawal will discuss his exciting discovery - the ASK algorithm for primality testing, and Voevodsky will explain his novel approach to the mathematical modeling of shapes known as "motivic homotopy theory."
http://www.claymath.org/annual_meeting/2002_Annual_Meeting/

Views: 13469
PoincareDuality

The second method for testing whether alpha is a primitive root mod p. Description of primitive roots is in the Primitive Roots pt. 1 video.
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 26175
Theoretically

Step by step instructions on how to use The Chinese Remainder Theorem to solve a system of linear congruence.
Visit Our Channel :- https://www.youtube.com/channel/UCxikHwpro-DB02ix-NovvtQ
In this lecture we have taught about what how to solve multiplicative cipher method.
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Views: 55465
Quick Trixx

Some Prime Functions I created over the past year or so with some patterns I've noticed and a few functions I've derived. Still lots of work to be done, exciting stuff!

Views: 941
Albert Renshaw

In number theory, integer factorization or prime factorization is the decomposition of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer.
When the numbers are very large, no efficient, non-quantum integer factorization algorithm is known; an effort by several researchers concluded in 2009, factoring a 232-digit number (RSA-768), utilizing hundreds of machines over a span of two years. However, it has not been proven that no efficient algorithm exists. The presumed difficulty of this problem is at the heart of widely used algorithms in cryptography such as RSA. Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing.
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Views: 3818
Audiopedia

Views: 76
STUDY AND YOU

A brief description of the "Basic Principle" and how it can be used to test for primality.

Views: 237
Theoretically

Not Without the Rest by Twin Musicom is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)
Artist: http://www.twinmusicom.org/
I created this video with the YouTube Video Editor (https://www.youtube.com/editor)

Views: 115
Nathaniel Seagren

For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com.
The book chapter "Introduction" for this video is also available for free at the website (click "Sample Chapter").

Views: 454875
Introduction to Cryptography by Christof Paar

Fundamentals of Computer Network Security
This specialization in intended for IT professionals, computer programmers, managers, IT security professionals who like to move up ladder, who are seeking to develop network system security skills. Through four courses, we will cover the Design and Analyze Secure Networked Systems, Develop Secure Programs with Basic Cryptography and Crypto API, Hacking and Patching Web Applications, Perform Penetration Testing, and Secure Networked Systems with Firewall and IDS, which will prepare you to perform tasks as Cyber Security Engineer, IT Security Analyst, and Cyber Security Analyst.
course 2 Basic Cryptography and Programming with Crypto API:
About this course: In this MOOC, we will learn the basic concepts and principles of cryptography, apply basic cryptoanalysis to decrypt messages encrypted with mono-alphabetic substitution cipher, and discuss the strongest encryption technique of the one-time-pad and related quantum key distribution systems. We will also learn the efficient symmetric key cryptography algorithms for encrypting data, discuss the DES and AES standards, study the criteria for selecting AES standard, present the block cipher operating modes and discuss how they can prevent and detect the block swapping attacks, and examine how to defend against replay attacks. We will learn the Diffie-Hellman Symmetric Key Exchange Protocol to generate a symmetric key for two parties to communicate over insecure channel. We will learn the modular arithmetic and the Euler Totient Theorem to appreciate the RSA Asymmetric Crypto Algorithm, and use OpenSSL utility to realize the basic operations of RSA Crypto Algorithm. Armed with these knowledge, we learn how to use PHP Crypto API to write secure programs for encrypting and decrypting documents and for signing and verify documents. We then apply these techniques to enhance the registration process of a web site which ensures the account created is actually requested by the owner of the email account.
Asymmetric Key Cryptography
In this module we will learn the modular arithmetic, the Euler Totient Theorm, the RSA Asymmetric Crypto Algorithm, use OpenSSL to realize the basic operations of RSA Crypto Algorithm, and Diffie-Hellman Symmetric Key Exchange Protocol to derive session keys.
Learning Objectives
• Use Diffi-Hellman algorithm for Key Exchange
• Apply RSA with OpenSSL for signing and encryption
• Describe RSA Asymmetric Crypto Algorithm
Subscribe at: https://www.coursera.org

Views: 124
intrigano

This work provides a systematic analysis of primality testing under adversarial conditions, where the numbers being tested for primality are not generated randomly, but instead provided by a possibly malicious party.
Read this paper in the ACM Digital Library:
https://dl.acm.org/citation.cfm?id=3243787

Views: 142
Association for Computing Machinery (ACM)

How to decrypt the vigenere cipher on Maple software.
Note: at 1:03 when I said "original text" I was referring to the ciphertext.

Views: 3166
Theoretically

Fundamental concepts of prime numbers are discussed. Fermat's & Euler's Theorems are explained. Testing for primality is Analyzed. Chinese Remainder Theorem is presented.

Views: 1100
Scholartica Channel

Learn how to use algorithm for solving modular linear equation with two clearly explained examples

Views: 883
DrVikasThada

Russell Impagliazzo, UC San Diego
Fine-Grained Complexity and Algorithm Design Boot Camp
http://simons.berkeley.edu/talks/russell-impagliazzo-2015-09-03

Views: 393
Simons Institute

In this paper, we introduce a primitive known as Verifiable Oblivious Transfer. It is similar to oblivious transfer except that the sender is committed to its input. We then generate protocols for Generalized Oblivious Transfer by secret sharing using the Verifiable Oblivious Transfer primitive based on previous work. The protocols are universally composable. The GOT protocol is used to instantiate Batch Single-Choice Cut-And-Choose OT which in conjunction with a modification to the main protocol of [LP11], achieves constant round secure function evaluation based on Yao's Garbled Circuit. In addition, the idea of GOT is used in conjunction with linear secret sharing and commitments to instantiate a primitive known as Multi-Sender K-Out-of-N OT. This primitive is the most important building block of the optimization of the IPS compiler presented in [LOP11]. In contrast to their specific computational assumptions, our protocols only require black-box Verifiable OT. In addition, the GOT protocols can be used to execute Priced Oblivious Transfer.

Views: 128
Microsoft Research

In this youtube channel we are going to teach you the basic concepts of Cryptography and Network Security.
In this video we have discussed about how to find Inverse using Fermant's Little Theorem.
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Programming Interview, Software Interview, Data Structure, Algorithm, modular multiplicative inverse, multiplicative inverse, modular arithmetic, fermats theorem, euler's totient, Euler's Totient Function, Fermat's Little Theorem, Modular Multiplicative Inverse | Fermat's Theorem | Euler's Totient, yt:crop=16:11,
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Views: 11547
Quick Trixx

Previous video: https://youtu.be/uPh6IUhiFUo
Next video: https://youtu.be/wD7paOvy-3Q

Views: 797
Leandro Junes

As A Man Think, So Is He...

Here's a test for determining the primality of a number that's similar to Proth's Theorem (1878). It lays hidden, except when the base "b" is co-prime to the number 3. You'll have to brush up on a few number theory ideas to enjoy it! Enjoy! William Bouris www.oddperfectnumbers.com

Views: 213
William Bouris

Title was changed from "Universal Constructions and Robust Combiners for Indistinguishability Obfuscation and Witness Encryption", by Prabhanjan Ananth and Aayush Jain and Moni Naor and Amit Sahai and Eylon Yogev, Crypto 2016. See http://www.iacr.org/cryptodb/data/paper.php?pubkey=27649

Views: 458
TheIACR

http://demonstrations.wolfram.com/Pseudoprime/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Fermat's little theorem (FLT) states that for any prime number p and coprime base a, a^p=a (mod p). If this congruence fails, then p cannot be prime. Using FLT as a primality test seems promising because it distinguishes primes from nonprimes...
Contributed by: Ed Pegg Jr

Views: 1333
wolframmathematica

ECC2K-130 is the smallest unsolved Certicom discrete-logarithm challenge. Certicom originally stated that breaking ECC2K-130 was 'infeasible' and would require 2700000000 machine days. This talk reports on an ongoing joint project by researchers from 12 different universities to break ECC2K-130. The project has increased our knowledge of the mathematical speedups for attacking elliptic-curve cryptosystems, has led to a new representation for finite fields in 'optimal polynomial bases', and has led to a better understanding of the randomness of pseudorandom walks used in Pollard's rho method. The project has produced optimized implementations of a highly tuned iteration function for different platforms ranging from standard CPUs to customized FPGA clusters. These optimizations have moved the ECC2K-130 computation to the range of feasibility. The computation would finish in only two years using 1595 standard PCs, or 1231 PlayStation 3 game consoles, or 534 GTX 295 graphics cards, or 308 XC3S5000 FPGAs, or any combination of the above. We are now actively performing the computations. See our twitter page for updates.

Views: 286
Microsoft Research

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime, because the only ways of writing it as a product, or , involve 5 itself. However, 6 is composite, because it is the product of two numbers that are both smaller than 6. Primes are central in number theory, because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple, but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast, but has a small chance of error, and the AKS primality test, which always produces the correc...
http://www.wikividi.com
____________________________________
Shortcuts to chapters:
00:02:45 Definition and examples
00:05:10 History
00:09:11 Primality of one
00:11:05 Unique factorization
____________________________________
Copyright WikiVidi.
Licensed under Creative Commons.
Wikipedia link: https://en.wikipedia.org/wiki/Prime_number

Views: 36
WikiVidi Documentaries

How to factories any number with the help of Fermat method.
Fermat's method to solve numericals.
NUMBER THEORY.
Fermat's little theorem.

Views: 463
Mathematics Analysis

Speaks about his early life, family, education, and research word leading up to the Turing Award and his work after.
More information:
http://amturing.acm.org/award_winners/rabin_9681074.cfm

Views: 776
Association for Computing Machinery (ACM)

Chinese Remainder Theorem (in Basic Number Theory)
Statement of the theorem and how to use it to solve for some x (mod m*n) given x = a (mod m) and x = b (mod n).
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 2791
Theoretically

PCI DSS Encryption: Secure your data, complying with PCI DSS Encryption rules. Vormetric : data security simplified
http://enterprise-encryption.vormetric.com/eva4-pcidss-singleStep-landingpage.html
Visit this link to download free whitepapers.
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This whitepaper outlines how Vormetric addresses PCI DSS compliance; it addresses Vormetric's position relative to the Payment Card Industry Security Standards Council's (PCI SSC) guidance on point-to-point encryption solutions. The whitepaper also features case studies of PCI DSS regulated companies leveraging Vormetric for PCI DSS compliance and maps PCI DSS requirements to Vormetric Data Security capabilities.
Vormetric Data Security helps organizations meet PCI DSS compliance demands with a transparent data security approach for diverse IT environments that requires minimal administrative support and does not undermine performance.
Follow CTOBuddy on Facebook : https://www.facebook.com/pages/CTOBuddy/163641553830817?ref=hl

Views: 378
CTOBuddy

Interviewed about what has influenced him, his life, his research work, and his accomplishments since receiving the Turing Award.
More information:
http://amturing.acm.org/award_winners/adleman_7308544.cfm

Views: 1706
Association for Computing Machinery (ACM)

Public-key cryptography, also known as asymmetric cryptography, is a class of cryptographic algorithms which require two separate keys, one of which is secret (or private) and one of which is public. Although different, the two parts of this key pair are mathematically linked. The public key is used to encrypt plaintext or to verify a digital signature; whereas the private key is used to decrypt ciphertext or to create a digital signature. The term "asymmetric" stems from the use of different keys to perform these opposite functions, each the inverse of the other -- as contrasted with conventional ("symmetric") cryptography which relies on the same key to perform both.
Public-key algorithms are based on mathematical problems which currently admit no efficient solution that are inherent in certain integer factorization, discrete logarithm, and elliptic curve relationships. It is computationally easy for a user to generate their own public and private key-pair and to use them for encryption and decryption. The strength lies in the fact that it is "impossible" (computationally infeasible) for a properly generated private key to be determined from its corresponding public key. Thus the public key may be published without compromising security, whereas the private key must not be revealed to anyone not authorized to read messages or perform digital signatures. Public key algorithms, unlike symmetric key algorithms, do not require a secure initial exchange of one (or more) secret keys between the parties.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 774
Audiopedia

Public-key cryptography, also known as asymmetric cryptography, is a class of cryptographic algorithms which require two separate keys, one of which is secret and one of which is public. Although different, the two parts of this key pair are mathematically linked. The public key is used to encrypt plaintext or to verify a digital signature; whereas the private key is used to decrypt ciphertext or to create a digital signature. The term "asymmetric" stems from the use of different keys to perform these opposite functions, each the inverse of the other -- as contrasted with conventional cryptography which relies on the same key to perform both.
This video targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Public domain image source in video

Views: 2101
encyclopediacc

Views: 4651
comai comai

En menos de 5 minutos el Test de ARTEAGA depura el 79% de numeros de Mersenne que son compuestos, estando en el 21% restante, la mitad de los primos de Mersenne es decir desde (2^2)-1 hasta (2^11213)-1 rapido verdad? siendo que es el primer desarrollo del test de primalidad.

Views: 287
Victor Arteaga

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/List_of_important_publications_in_theoretical_computer_science
00:00:31 1 Computability
00:00:40 1.1 iCutland's /iComputability: An Introduction to Recursive Function Theoryi (Cambridge)/i
00:01:58 1.2 iDecidability of second order theories and automata on infinite trees/i
00:02:32 1.3 iFinite automata and their decision problems/i
00:03:05 1.4 iIntroduction to Automata Theory, Languages, and Computation/i
00:03:30 1.5 iOn certain formal properties of grammars/i
00:04:11 1.6 iOn computable numbers, with an application to the Entscheidungsproblem/i
00:05:18 1.7 iRekursive Funktionen/i
00:05:58 1.8 iRepresentation of Events in Nerve Nets and Finite Automata/i
00:06:41 2 Computational complexity theory
00:06:52 2.1 iArora & Barak's /iComputational Complexityi and Goldreich's /iComputational Complexityi (both Cambridge)/i
00:08:13 2.2 iA machine-independent theory of the complexity of recursive functions/i
00:08:51 2.3 iAlgebraic methods for interactive proof systems/i
00:09:32 2.4 iThe complexity of theorem proving procedures/i
00:10:32 2.5 iComputers and Intractability: A Guide to the Theory of NP-Completeness/i
00:11:17 2.6 iDegree of difficulty of computing a function and a partial ordering of recursive sets/i
00:11:52 2.7 iHow good is the simplex method?/i
00:12:48 2.8 iHow to construct random functions/i
00:13:27 2.9 iIP = PSPACE/i
00:13:41 2.10 iReducibility among combinatorial problems/i
00:14:37 2.11 iThe Knowledge Complexity of Interactive Proof Systems/i
00:15:09 2.12 iA letter from Gödel to von Neumann/i
00:15:45 2.13 iOn the computational complexity of algorithms/i
00:16:09 2.14 iPaths, trees, and flowers/i
00:16:51 2.15 iTheory and applications of trapdoor functions/i
00:17:33 2.16 iComputational Complexity/i
00:18:25 2.17 iInteractive proofs and the hardness of approximating cliques/i
00:18:53 2.18 iProbabilistic checking of proofs: a new characterization of NP/i
00:19:31 2.19 iProof verification and the hardness of approximation problems/i
00:20:07 2.20 iThe Intrinsic Computational Difficulty of Functions/i
00:20:57 3 Algorithms
00:21:30 3.1 "A machine program for theorem proving"
00:21:40 3.2 "A machine-oriented logic based on the resolution principle"
00:22:24 3.3 "The traveling-salesman problem and minimum spanning trees"
00:23:05 3.4 "A polynomial algorithm in linear programming"
00:23:51 3.5 "Probabilistic algorithm for testing primality"
00:24:45 3.6 "Optimization by simulated annealing"
00:25:24 3.7 iThe Art of Computer Programming/i
00:26:20 3.8 iAlgorithms + Data Structures = Programs/i
00:26:56 3.9 iThe Design and Analysis of Computer Algorithms/i
00:27:23 3.10 iHow to Solve It By Computer/i
00:27:53 3.11 iAlgorithms/i
00:28:26 3.12 iIntroduction to Algorithms/i
00:28:56 4 Algorithmic information theory
00:29:37 4.1 "On Tables of Random Numbers"
00:29:47 4.2 "A formal theory of inductive inference"
00:30:46 4.3 "Algorithmic information theory"
00:31:31 5 Information theory
00:32:16 5.1 "A mathematical theory of communication"
00:32:25 5.2 "Error detecting and error correcting codes"
00:32:57 5.3 "A method for the construction of minimum redundancy codes"
00:33:43 5.4 "A universal algorithm for sequential data compression"
00:34:19 5.5 iElements of Information Theory/i
00:35:04 6 Formal verification
00:35:32 6.1 Assigning Meaning to Programs
00:35:41 6.2 An Axiomatic Basis for Computer Programming
00:36:33 6.3 Guarded Commands, Nondeterminacy and Formal Derivation of Programs
00:37:19 6.4 iProving Assertions about Parallel Programs/i
00:38:19 6.5 iAn Axiomatic Proof Technique for Parallel Programs I/i
00:38:45 6.6 iA Discipline of Programming/i
00:39:28 6.7 iDenotational Semantics/i
00:39:59 6.8 The Temporal Logic of Programs
00:40:28 6.9 iCharacterizing correctness properties of parallel programs using fixpoints (1980)/i
00:41:06 6.10 iCommunicating Sequential Processes (1978)/i
00:41:39 6.11 iA Calculus of Communicating Systems/i
00:42:10 6.12 iSoftware Development: A Rigorous Approach/i
00:42:42 6.13 iThe Science of Programming/i
00:43:24 6.14 iCommunicating Sequential Processes (1985)/i
00:44:24 6.15 iLinear logic (1987)/i
00:45:00 6.16 iA Calculus of Mobile Processes (1989)/i
00:45:47 6.17 iThe Z Notation: A Reference Manual/i
00:46:25 6.18 iCommunication and Concurrency/i
00:47:03 6.19 ia Practical Theory of Programming/i
00:47:29 7 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 ...

Views: 6
wikipedia tts

Hello friends, this is (probably) high level Dota 2 play with Blue Span. Please be respectful in chat and we will be friends thank you.
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POP https://goo.gl/h83npA
NINTENDO https://bit.ly/2HSXVoW
PERMANENT STREAM LINK TO BOOKMARK: https://gaming.youtube.com/c/BlueSpan/live
LIKE US? JOIN US AT OUR DISCORD https://discord.gg/2nhPhsN
Chat Rules:
1: No racism/hate/harassing.
2: Don't advertise your channel / beg for subscribers or shout outs.
3: English ONLY.
4: No backseat gaming (i.e. telling Blue Span what to do).
Things I like: compliments, donations, encouragement and support, and friendly and nice people :-)
Not looking for friend list adds or parties sry.
PC SPECS:
i7-8700K
16GB DDR4 2666 MHZ RAM
GTX 1080 TI
512GB SAMSUNG 850 PRO SSD
GEAR:
LOGITECH G502 MOUSE
RAZER BLACKWIDOW 2016
LOGITECH C922 CAMERA
BLUE YETI MICROPHONE
SENNHEISER CX 686 G / BOSE QC 35-2
ALIENWARE AW2518H 240HZ MONITOR
TOBII EYE TRACKER 4C
Follow my social media! Instant notifications for LIVE STREAMS/VIDS, ask me anything any time!
Facebook: https://www.facebook.com/bluespandota
Twitter: https://twitter.com/bluespangaming
Instagram: http://www.instagram.com/bluespangaming
Twitch: http://www.twitch.tv/bluespantwitch
Dotabuff: http://www.dotabuff.com/players/80467654
#Dota2 #Live #Youtube #Discord #BlueSpan

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Blue Span