Solutions to some typical exam questions. See my other videos
https://www.youtube.com/channel/UCmtelDcX6c-xSTyX6btx0Cw/.

Views: 37820
Randell Heyman

If you find our videos helpful you can support us by buying something from amazon.
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Elliptic curve cryptography
Elliptic curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.ECC requires smaller keys compared to non-ECC cryptography (based on plain Galois fields) to provide equivalent security.
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https://www.youtube.com/watch?v=UTJ2jxuyL7g

Views: 522
WikiAudio

This is episode one of the Math Behind Bitcoin. In an effort to understand the math behind bitcoin, I try to explain it to you guys. If there are any mistakes or suggestions, please put it in the comment section below. Thanks!
Resources
- https://www.coindesk.com/math-behind-bitcoin/
- https://eng.paxos.com/blockchain-101-foundational-math
- Mastering Bitcoin by Andreas Antonopoulos
- https://www.cryptocoinsnews.com/explaining-the-math-behind-bitcoin/
- https://en.wikipedia.org/wiki/Finite_field

Views: 1134
Kevin Su

Vídeo original: https://youtu.be/iB3HcPgm_FI
Welcome to part four in our series on Elliptic Curve Cryptography. I this episode we dive into the development of the public key. In just 44 lines of code, with no special functions or imports, we produce the elliptic curve public key for use in Bitcoin. Better still, we walk you through it line by line, constant by constant. Nothing makes the process clearer and easier to understand than seeing it in straight forward code. If you've been wondering about the secp256k1 (arguably the most important piece of code in Bitcoin), well then this is the video for you.
This is part 4 of our upcoming series on Elliptic Curves. Because of such strong requests, even though this is part 4, it is the first one we are releasing. In the next few weeks we will release the rest of the series. Enjoy.
Here's the link to our Python code (Python 2.7.6):
https://github.com/wobine/blackboard1...
Here's the private key and the link to the public address that we use. Do you know why it is famous?
Private Key : A0DC65FFCA799873CBEA0AC274015B9526505DAAAED385155425F7337704883E
Public Address on Blockchain.info
https://blockchain.info/address/1JryT...
Here's the private key we use at the end:
42F615A574E9CEB29E1D5BD0FDE55553775A6AF0663D569D0A2E45902E4339DB
Public Address on Blockchain.info
https://blockchain.info/address/16iTd...
Welcome to WBN's Bitcoin 101 Blackboard Series -- a full beginner to expert course in bitcoin. Please like, subscribe, comment or even drop a little jangly in our bitcoin tip jar 1javsf8GNsudLaDue3dXkKzjtGM8NagQe. Thanks, WBN

Views: 6053
Fabio Carpi

Animation of elliptic curve y² = x³ + ax + b, varying Parameter a from -2..1 and b from -1..2. see also http://en.wikipedia.org/wiki/Image:EllipticCurveCatalog.svg

Views: 6366
fuckyoubugger

From http://1anonymous.org
Want to see how the NSA HACKED ECC CRYPTO?
Want to see what the SNOWDEN DOCS and WIKI LEAKS really says about the NSA and the NSA HACK of ECC CRYPTO and NSA BITCOIN.
The special relationship between primes and numbers on the 8 PRIMES SPIRALS is how the NSA has been able to create backdoors and cook ECC SEED KEYS.
The NSA is hiding any info on the 8 PRIME SPIRALS and WIKI is now under NSA CONTROL.
SEE THE PROOF
DO NOT USE ANY ECC CRYPTO IT IS ALL BACK DOORED
WE ARE ANONYMOUS
WE ARE EVERYWHERE
WE ARE LEGION
WE ARE WATCHING
1 ANONYMOUS ORG

Views: 1429
1 Anonymous Org 7

Animation of elliptic curve y² = x³ + ax + b, varying Parameter a from -2..1 and b from -1..2. see also http://en.wikipedia.org/wiki/Image:EllipticCurveCatalog.svg

Views: 1758
fuckyoubugger

In this video I'm explaining what is that Galois Counter Mode that provides Authenticated Encryption with Associated Data (AEAD). You must have heard it combined with AES, and maybe used in TLS, ... This is just a small explanation, you can get more on the NIST specs.
Errata (thanks to Casper Kejlberg-Rasmussen in the comments)
error at 11:21, the last M_H that is applied before going into the TAG should not be there if you compare your drawing to the diagram on https://en.wikipedia.org/wiki/Galois/Counter_Mode.
Be sure to follow me on twitter :) https://twitter.com/lyon01_david
and to subscribe to my blog! http://www.cryptologie.net
Cheers!

Views: 19373
David Wong

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Modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition.The theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections with number theory.
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image source in video
https://www.youtube.com/watch?v=S0BTCAta6gw

Views: 187
WikiAudio

A course on how bitcoin works and how to program bitcoin stuff with the javascript bitcoin library Yours Bitcoin. Taught by Ryan X. Charles, Cofounder & CEO of Yours, and former cryptocurrency engineer of reddit. The third lecture covers elliptic curves and in particular secp256k1, the curve used by bitcoin. This curve is used for public keys and ECDSA, the digital signature algorithm of bitcoin.
https://github.com/yoursnetwork/yours-bitcoin
https://github.com/yoursnetwork/yours-bitcoin-examples
https://www.yours.network
https://www.ryanxcharles.com/
https://twitter.com/ryanxcharles

Views: 779
Yours

This video is a demonstration of some infamous Elliptic curves.
http://en.wikipedia.org/wiki/Elliptic_curve
The parameter "a" running from -3 to 3

Views: 1120
Hazhar Ghaderi

In this video I demonstrate getting the ECDSA Z value from a bitcoin transaction with only one input. I also show the R and S values.
The ECDSA R, S and Z values are used throughout the many layers of bitcoin to validate a transaction, The Z value is also sometimes referred to as the signed message. Transactions that don't contain valid inputs can be safely ignored, and the Z value is one of the properties that is used to check validity.
This video shows me dissecting a very basic transaction with only 1 input and 1 output.
The urls I show in this video are
https://2coin.org/index.html?txid=bf474b96908ba7769120b2e8f2bfcbd2deca80c99b576b4b63bf18fb69e3d242
https://en.bitcoin.it/wiki/Protocol_documentation#tx
https://2coin.org/doublesha256.html

Views: 3512
seanwasere ytbe

For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com

Views: 52162
Introduction to Cryptography by Christof Paar

GCM does AES-256 encryption and, simutaneously, performs message authentication. View this video to understand how it works.

Views: 6132
Vidder, Inc.

What is CRYPTOGRAPHIC SPLITTING? What does CRYPTOGRAPHIC SPLITTING mean? CRYPTOGRAPHIC SPLITTING definition - CRYPTOGRAPHIC SPLITTING explanation.
Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
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Cryptographic splitting, also known as cryptographic bit splitting or cryptographic data splitting, is a technique for securing data over a computer network. The technique involves encrypting data, splitting the encrypted data into smaller data units, distributing those smaller units to different storage locations, and then further encrypting the data at its new location. With this process, the data is protected from security breaches, because even if an intruder is able to retrieve and decrypt one data unit, the information would be useless unless it can be combined with decrypted data units from the other locations.
The technology was filed for patent consideration in June 2003, and the patent was granted in June 2008.
Cryptographic splitting utilizes a combination of different algorithms to provide the data protection. A block of data is first encrypted using the AES-256 government encryption standard. The encrypted bits are then split into different shares and then each share is hashed using the National Security Agency's SHA-256 algorithm.
One application of cryptographic splitting is to provide security for cloud computing. The encrypted data subsets can be stored on different clouds, with the information required to restore the data being held on a private cloud for additional security. Security vendor Security First Corp uses this technology for its Secure Parser Extended (SPx) product line.
In 2009, technology services company Unisys gave a presentation about using cryptographic splitting with storage area networks. By splitting the data into different parts of the storage area network, this technique provided data redundancy in addition to security.
Computer giant IBM has written about using the technology as part of its Cloud Data Encryption Services (ICDES).
The technology has also been written about in the context of more effectively using sensitive corporate information, by entrusting different individuals within a company (trustees) with different parts of the information.

Views: 216
The Audiopedia

This is my video on the modularity theorem for the #breakthroughjuniorchallenge

Views: 2082
Chris Williams

Many years ago I came across a clickable flash animation that explained how the Rijndael cipher works. And even though Rijndael is pure, complex math, the animated visualizations made the whole process so crystal clear that I had to bend down to the floor afterwards to pick up my dropped jaw.
Since then I know how powerful animated visualizations can be, even (or rather especially) for abstract and/or complex topics.
When I started my Go blog, I knew I had to use animations because they are worth a thousand words. I did the same in my Go videos that you can find over here in my channel, and also in my Go course.
This video is a recoding of the flash animation while I click through it. The flash animation is still available at formaestudio.com (link below), but no sane browser would agree to play any flash content anymore, so a video capture is the best we can get. I hope the pace of clicking through the steps is just right for you.
NOTE: The video has no audio part. This is not a bug, the Flash animation simply had no sounds.
The Rijndael Animation (and another Flash program called Rijndael Inspector): http://www.formaestudio.com/rijndaelinspector/
(c) Enrique Zabala. License terms: "Both these programs are free of use." (I guess that publishing a video of the animation is covered by these terms.)
My blog: https://appliedgo.net
My course: https://appliedgo.com/p/mastergo

Views: 28320
AppliedGo

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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========
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https://www.youtube.com/watch?v=LRRT6Pg6LeU

Views: 258
WikiAudio

Between Logjam, FREAK, POODLE, and Heartbleed, TLS hasn't had a good year. TLS is the most commonly deployed cryptographic protocol, but is notoriously difficult to both implement and deploy, resulting in widespread security issues for many of the top services on the Internet. For the past three years, we've been working to improve the global state of TLS deployment through measurement-based approaches, including tracking the impact of Heartbleed and other vulnerabilities. Based on measurement data, we conducted one of the largest-ever mass vulnerability notification campaigns, discovered failures in how Diffie-Hellman has been deployed in practice, and uncovered the Logjam attack against TLS. In this talk, we'll briefly examine what TLS is and how it fails, and present the Logjam attack. We'll also discuss ZMap, the Internet-wide network scanner we use for our research, and show how ZMap helped lead to the discovery of Logjam.

Views: 1573
Duo Security

Cryptography is the practice and study of techniques for secure communication in the presence of third parties . More generally, it is about constructing and analyzing protocols that overcome the influence of adversaries and which are related to various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation. Modern cryptography intersects the disciplines of mathematics, computer science, and electrical engineering. Applications of cryptography include ATM cards, computer passwords, and electronic commerce.
This video targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 243
encyclopediacc

For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com

Views: 71188
Introduction to Cryptography by Christof Paar

A classical approach of constructing elliptic curves that can be used for cryptographic purposes relies on the theory of complex multiplication. A key ingredient in the algorithm is to compute the Hilbert class polynomial P_D for a suitable discriminant D. The polynomial P_D has integer coefficients, and is the minimal polynomial of the modular j-value j(O_D) for the imaginary quadratic order O_D of discriminant D. The polynomial P_D can be computed using complex analytic techniques. In this talk we present a new p-adic algorithm to compute P_D. One of the advantages of working over a p-adic field is that we do not have to worry about rounding errors, and the p-adic algorithm is the first algorithm with a rigorous run time analysis. When implemented carefully, the p-adic algorithm is very fast in practice and easily competes with the complex analytic approach. Many examples will be given.

Views: 76
Microsoft Research

Eleventh IACR Theory of Cryptography Conference TCC 2014
February 24-26, 2014
Amos Beimel and Aner M. Ben-Efraim and Carles Padró and Ilya Tomkin

Views: 1462
Calit2ube

What is GENERIC GROUP MODEL? What does GENERIC GROUP MODEL mean? GENERIC GROUP MODEL meaning - GENERIC GROUP MODEL definition - GENERIC GROUP MODEL explanation.
Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
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The generic group model is an idealised cryptographic model, where the adversary is only given access to a randomly chosen encoding of a group, instead of efficient encodings, such as those used by the finite field or elliptic curve groups used in practice.
The model includes an oracle that executes the group operation. This oracle takes two encodings of group elements as input and outputs an encoding of a third element. If the group should allow for a pairing operation this operation would be modeled as an additional oracle.
One of the main uses of the generic group model is to analyse computational hardness assumptions. An analysis in the generic group model can answer the question: "What is the fastest generic algorithm for breaking a cryptographic hardness assumption". A generic algorithm is an algorithm that only makes use of the group operation, and does not consider the encoding of the group. This question was answered for the discrete logarithm problem by Victor Shoup using the generic group model. Other results in the generic group model are for instance. The model can also be extended to other algebraic structures, such as, e.g., rings.
The generic group model suffers from some of the same problems as the random oracle model. In particular, it has been shown using a similar argument that there exist cryptographic schemes which are provable secure in the generic group model, but which are trivially insecure once the random group encoding is replaced with any efficiently computable instantiation of the encoding function.

Views: 94
The Audiopedia

Cryptography is a systems problem (or) 'Should we deploy TLS'
Given by Matthew Green, Johns Hopkins University

Views: 5734
Dartmouth

Steven J Miller and M. Ram Murty
Williams College
Department of Mathematics and Statistics
Bronfman Science Center, Rm. 202
Williamstown, MA 01267
Email: [email protected]
Manuscript Number: JNT-D-10-00120 R3

Views: 513
JournalNumberTheory

Lehrbuch: Kryptographie verständlich: Ein Lehrbuch für
Studierende und Anwender
https://www.amazon.de/Kryptografie-verständlich-Lehrbuch-Studierende-eXamen-press-ebook/dp/B01M10TWQY/ref=as_li_ss_tl?ie=UTF8&qid=1541146225&sr=8-2&keywords=paar+cryptography&linkCode=sl1&tag=julianhosp-21&linkId=c64f90611a652bf9c5595e9fea0bdcb7&language=en_GB
------------
Hier mein neuestes Buch "Blockchain 2.0 - mehr als nur Bitcoin" - die 100 innovativsten dezentralen Anwendungen abgesehen von Kryptowährungen: https://amzn.to/2wOVICV
Wenn dir das Video gefallen hat, abonniere meinen Kanal, gib einen "Daumen hoch" und teile dieses Video um gemeinsam AT, DE und CH #cryptofit machen :)
► Abonnieren: https://www.youtube.com/subscription_center?add_user=julianhosp
► Kryptowährungen handeln: https://www.binance.com/?ref=11272739
► Hardware Wallet kaufen: http://www.julianhosp.com/hardwallet
► Ruben's Trinkgeld Adressen:
Bitcoin: 3MNWaot64Fr1gRGxv4YzHCKAcoYTLXKxbc
Litecoin: MTaGwg5EhKooonoVjDktroiLqQF6Rvn8uE
---------------
► Komplett NEU? Was ist Blockchain, Bitcoin und Co? Hol dir dieses Buch von mir: https://amzn.to/2kdgipU
► Sei bei unserer Facebook Gruppe dabei: https://www.facebook.com/groups/kryptoganzeinfach/
► Die Kryptoshow (Podcast): http://kryptoshow.libsyn.com
► Meine Webseite: http://www.julianhosp.com
► Hier ist ein VIP Webinar mit Detailschritten und meinem privaten Account: https://www.digistore24.com/product/122531
----------------
Mein Name ist Dr. Julian Hosp oder einfach nur Julian.
In meinen Videos geht es um Bitcoin, Ethereum, Blockchain und Kryptowährungen generell, um Scam, Abzocke und Betrug besonders im Mining keinen Platz zu geben. Ich spreche darüber, wie du schlau investieren kannst und das Ganze rational und simpel angehst. Viel Spaß!
► Folge mir hier und bleibe in Kontakt:
Facebook: https://www.facebook.com/julianhosp/
Twitter: https://twitter.com/julianhosp
Instagram: https://www.instagram.com/julianhosp/
#Julianhosp

Views: 4892
Dr. Julian Hosp

An animated introduction to the Fourier Transform, winding graphs around circles.
Supported by viewers: https://www.patreon.com/3blue1brown
Special thanks to these Patrons: http://3b1b.co/fourier-thanks
Follow-on video about the uncertainty principle: https://youtu.be/MBnnXbOM5S4
Puzzler at the end by Jane Street: https://janestreet.com/3b1b
Interactive made by a viewer inspired by this video:
https://prajwalsouza.github.io/Experiments/Fourier-Transform-Visualization.html
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
Music by Vincent Rubinetti:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown

Views: 2436743
3Blue1Brown

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Discrete logarithm
In mathematics, a discrete logarithm is an integer k solving the equation bk = g, where b and g are elements of a finite group.Discrete logarithms are thus the finite-group-theoretic analogue of ordinary logarithms, which solve the same equation for real numbers b and g, where b is the base of the logarithm and g is the value whose logarithm is being taken.
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Article text available under CC-BY-SA
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https://www.youtube.com/watch?v=2SVqP_0RCHc

Views: 1032
WikiAudio

14th ALGA meeting - Commutative Algebra and Algebraic Geometry
Fabien Pazuki (University of Copenhagen)
Bad reduction of curves with CM jacobianss
Página do Programa: http://www.impa.br/opencms/en/eventos/store_2017/evento_1704
Download dos Vídeos: http://video.impa.br/index.php?page=14th-alga-meeting
For twenty years, the ALGA meetings have been bringing together the Brazilian community of Commutative Algebra and Algebraic Geometry, and its foreign collaborators. They have been fundamental for the consolidation and strengthening of the research group.
The 14th edition of ALGA celebrates its 20th anniversary. The program includes invited lectures and sessions of "Presentations by Young Researchers". Young researchers and Ph.D. students interested in making a presentation can submit a proposal through the registration form below.
IMPA - Instituto de Matemática Pura e Aplicada ©
http://www.impa.br | http://video.impa.br

Views: 165
Instituto de Matemática Pura e Aplicada

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Classical cipher
A cipher is a means of concealing a message, where letters of the message are substituted or transposed for other letters, letter pairs, and sometimes for many letters.In cryptography, a classical cipher is a type of cipher that was used historically but now has fallen, for the most part, into disuse.
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Views: 270
WikiAudio

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/List_of_important_publications_in_mathematics
00:00:49 1 Algebra
00:00:59 1.1 Theory of equations
00:01:08 1.1.1 iBaudhayana Sulba Sutra/i
00:01:57 1.1.2 iThe Nine Chapters on the Mathematical Art/i
00:02:17 1.1.3 iHaidao Suanjing/i
00:02:46 1.1.4 iSunzi Suanjing/i
00:03:07 1.1.5 iAryabhatiya/i
00:03:23 1.1.6 iJigu Suanjing/i
00:04:15 1.1.7 iBrāhmasphuṭasiddhānta/i
00:04:38 1.1.8 iAl-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa'l-muqābala/i
00:05:07 1.2 iLīlāvatī/i, iSiddhānta Shiromani/i and iBijaganita/i
00:05:49 1.2.1 iYigu yanduan/i
00:06:12 1.2.2 iMathematical Treatise in Nine Sections/i
00:06:30 1.2.3 iCeyuan haijing/i
00:07:05 1.2.4 iJade Mirror of the Four Unknowns/i
00:07:25 1.2.5 iArs Magna/i
00:07:46 1.2.6 iVollständige Anleitung zur Algebra/i
00:08:18 1.2.7 iDemonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse/i
00:08:55 1.3 Abstract algebra
00:09:05 1.3.1 Group theory
00:09:27 1.3.1.1 iRéflexions sur la résolution algébrique des équations/i
00:09:43 1.3.2 iArticles Publiés par Galois dans les Annales de Mathématiques/i
00:09:53 1.3.3 iTraité des substitutions et des équations algébriques/i
00:10:08 1.3.4 iTheorie der Transformationsgruppen/i
00:10:26 1.3.5 iSolvability of groups of odd order/i
00:11:10 1.3.6 Homological algebra
00:11:24 1.3.7 iHomological Algebra/i
00:11:53 1.3.8 "Sur Quelques Points d'Algèbre Homologique"
00:12:47 2 Algebraic geometry
00:13:28 2.1 "Theorie der Abelschen Functionen"
00:14:04 2.2 iFaisceaux Algébriques Cohérents/i
00:14:13 2.3 iGéométrie Algébrique et Géométrie Analytique/i
00:14:44 2.4 "Le théorème de Riemann–Roch, d'après A. Grothendieck"
00:15:11 2.5 iÉléments de géométrie algébrique/i
00:15:21 2.6 iSéminaire de géométrie algébrique/i
00:16:33 3 Number theory
00:18:03 3.1 iBrāhmasphuṭasiddhānta/i
00:19:33 3.2 iDe fractionibus continuis dissertatio/i
00:20:25 3.3 iRecherches d'Arithmétique/i
00:21:05 3.4 iDisquisitiones Arithmeticae/i
00:22:26 3.5 "Beweis des Satzes, daß jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält"
00:22:35 3.6 "Über die Anzahl der Primzahlen unter einer gegebenen Grösse"
00:23:21 3.7 iVorlesungen über Zahlentheorie/i
00:23:50 3.8 iZahlbericht/i
00:24:50 3.9 iFourier Analysis in Number Fields and Hecke's Zeta-Functions/i
00:26:34 3.10 "Automorphic Forms on GL(2)"
00:27:25 3.11 "La conjecture de Weil. I."
00:28:39 3.12 "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern"
00:29:30 3.13 "Modular Elliptic Curves and Fermat's Last Theorem"
00:30:11 3.14 iThe geometry and cohomology of some simple Shimura varieties/i
00:30:54 3.15 "Le lemme fondamental pour les algèbres de Lie"
00:31:24 4 Analysis
00:31:48 4.1 iIntroductio in analysin infinitorum/i
00:32:38 4.2 Calculus
00:33:25 4.2.1 iYuktibhāṣā/i
00:34:01 4.2.2 iNova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illi calculi genus/i
00:34:26 4.2.3 iPhilosophiae Naturalis Principia Mathematica/i
00:34:36 4.2.4 iInstitutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum/i
00:36:17 4.2.5 iÜber die Darstellbarkeit einer Function durch eine trigonometrische Reihe/i
00:36:26 4.2.6 iIntégrale, longueur, aire/i
00:37:30 4.3 Complex analysis
00:38:09 4.3.1 iGrundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse/i
00:39:30 4.4 Functional analysis
00:40:41 4.4.1 iThéorie des opérations linéaires/i
00:41:30 4.5 Fourier analysis
00:41:54 4.5.1 iMémoire sur la propagation de la chaleur dans les corps solides/i
00:42:04 4.5.2 iSur la convergence des séries trigonométriques qui servent à représenter une fonction arbitraire entre des limites données/i
00:42:38 4.5.3 iOn convergence and growth of partial sums of Fourier series/i
00:42:47 5 Geometry
00:43:44 5.1 iBaudhayana Sulba Sutra/i
00:43:53 5.2 iEuclid's/i iElements/i
00:45:06 5.3 iThe Nine Chapters on the Mathematical Art/i
00:46:10 5.4 iThe Conics/i
00:46:41 5.5 iSurya Siddhanta/i
00:46:51 5.6 iAryabhatiya/i
00:47:56 5.7 iLa Géométrie/i
00:48:16 5.8 iGrundlagen der Geometrie/i
00:49:15 5.9 iRegular Polytopes/i
00:50:13 5.10 Differential geometry
00:50:51 5.10.1 iRecherches sur la courbure des surfaces/i
00:51:47 5.10.2 iDisquisitiones generales circa superficies curvas/i
00:52:28 5.10.3 iÜber die Hypothesen, welche der Geometrie zu Grunde Liegen/i
00:53:00 5.10.4 iLeçons sur la théorie génerale des surfaces et les applications géométriques du calcul infinitésimal/i
00:53:47 6 Topology
00:54:32 6.1 iAnalysis situs/i
00:54:42 6.2 iL'anneau d'homologie d'une représentation/i, iStructure de l'anneau d'homologie d'une r ...

Views: 19
wikipedia tts

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Cryptography
00:03:38 1 Terminology
00:07:53 2 History of cryptography and cryptanalysis
00:08:55 2.1 Classic cryptography
00:16:37 2.2 Computer era
00:19:13 2.3 Advent of modern cryptography
00:21:54 3 Modern cryptography
00:23:02 3.1 Symmetric-key cryptography
00:23:13 3.2 Public-key cryptography
00:23:28 3.3 Cryptanalysis
00:27:58 3.4 Cryptographic primitives
00:34:01 3.5 Cryptosystems
00:40:06 4 Legal issues
00:41:12 4.1 Prohibitions
00:43:02 4.2 Export controls
00:43:12 4.3 NSA involvement
00:45:45 4.4 Digital rights management
00:48:46 4.5 Forced disclosure of encryption keys
00:50:51 5 See also
00:53:36 6 References
00:55:46 7 Further reading
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:
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Speaking Rate: 0.8357640430680523
Voice name: en-US-Wavenet-D
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
Cryptography or cryptology (from Ancient Greek: κρυπτός, translit. kryptós "hidden, secret"; and γράφειν graphein, "to write", or -λογία -logia, "study", respectively) is the practice and study of techniques for secure communication in the presence of third parties called adversaries. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages; various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, electrical engineering, communication science, and physics. Applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications.
Cryptography prior to the modern age was effectively synonymous with encryption, the conversion of information from a readable state to apparent nonsense. The originator of an encrypted message shares the decoding technique only with intended recipients to preclude access from adversaries. The cryptography literature often uses the names Alice ("A") for the sender, Bob ("B") for the intended recipient, and Eve ("eavesdropper") for the adversary. Since the development of rotor cipher machines in World War I and the advent of computers in World War II, the methods used to carry out cryptology have become increasingly complex and its application more widespread.
Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed around computational hardness assumptions, making such algorithms hard to break in practice by any adversary. It is theoretically possible to break such a system, but it is infeasible to do so by any known practical means. These schemes are therefore termed computationally secure; theoretical advances, e.g., improvements in integer factorization algorithms, and faster computing technology require these solutions to be continually adapted. There exist information-theoretically secure schemes that provably cannot be broken even with unlimited computing power—an example is the one-time pad—but these schemes are more difficult to use in practice than the best theoretically breakable but computationally secure mechanisms.
The growth of cryptographic technology has raised a number of legal issues in the information age. Cryptography's potential for use as a tool for espionage and sedition has led many governments to classify it as a weapon and to limit or even prohibit its use and export. In some jurisdictions where the use of cryptography is legal, laws permit investigators to compel the disclosure of encryption keys for documents relevant to an investigation. Cryptography also plays a major role in digital rights management and copyright infringement of digital media.

Views: 0
wikipedia tts

https://www.instagram.com/prometei.tech/ reassured screamed liter favoring traction wondered reconsider realizing plow nap brain's ebb manifests CVD HDL minutiae ducks They've sufficed proponents waged salvo yearlong Tulane coverage unanimously sarcasm Pundits predictors coffin headlines representative enrolled Asians demographic diehards implausible slashing upped group's balloons publicized uptick bioelectrical impedance predictor LDL carbers pedestrian cuttingsome glean takeaways echoed study's Lydia Bazzano compel directing dogmatic almighty Jake fascinating devoting installment I’ve mmols Wingates foggy acuity tissue's oxidize Phinney synonymous Mistaking intriguing teamed Auburn Wolfe's CPT impede trash Someone's calorically reintroduction reintroduce blunts Paoli transitioned lasted Ketostix conservatively reversals lackluster telltale stroll tantamount deluge chockfull edibles aisle Who's les courgettes serrated peeler spiralizer wonderfully hash browns mandolin dubbed cauliflower's spuds pulverize Brassica wallop Chard sauté cremini shiitake fungi umami portobello stealthily praised dearth smear firepower backlash au naturale pint shrivelled rosy orbs lycopene Nature's lengthwise microwavable parchment scrape benevolent gourd Radish Bok choy Watercress famously sang stoned sweetness tinged tipoff nondigestible plush stellar sniffles pucker Fillets mercury unseasoned marinades ante beloved deli spared lunchmeats Dijon collard fests fattened Cornish hen Gruyere mundane decoupled riff blending pinches mop cultured surging critters tangy horns cow's Brie Ricotta kefir carnivores soaks brilliantly marinate Tempeh earthy mushroomy crumbling casseroles sauerkraut Pinto boast Pepitas o castoffs Sargento stringy bathed humming lofty healthyomega shops supermarkets Pepperettes Hazelnuts Bob's fare Shirataki translucent gelatinous konjac bowlful nondescript rinse blanch Preliminary prediabetes viscous Hazelnut brewed quencher moo cartons sidestep Imbibing infuses exhaustive flapjacks marys ye sipped seltzer contradictory farther swilling interchangeably insulinogenic spur counterintuitive accessing tougher adjusts Mozzarella cucumbers kcals reservoir thriving ongoing chow insisted French's Trimmed Uncured Portabella condensed tamari aminos steamer bubbly Ruthie ours marshmallows dye pumpkins fl Truvia Nutmeg Cloves towels masher lumpy quartered ½ generously pierced family's else's cleanup cooks Kosher slits slit PDF unwrap tossed bowl's ooohs aaaahs mouthwatering Coarse wilt bakes Sprouted crumb crumbs crumble byproducts apiece appreciable granite unconditioned stepmill app Centopani eater groundbreaking world's Evan's insists com's it'd befriending fluke flounder rutabaga turnips distributing rigors regimented hamburgers Animal's flagship Pak negotiable fundamentally depleting plows wishful oversimplified depletes Karbolyn Labrada's shuttling muscles replenished proponent dragging microtraumas pounder resynthesis disposal polymer shuttle Elasti RTD MRP EFA Charge Krill MPS rapamycin hesitate Centopani's diner steakhouse wheelbarrow Overseas border nearest awful refrigeration Stak Iconic XL Beanie Rotisserie precooked breaded standby powered brothers McGrath Antoine Vaillant baggie brainer Nothing's comforting goulash Slurp swole requested dad's bursting rotini parsnips I’ll paprika Worcestershire Caraway saucepot batch Printable Frosting silicone brethren Vincenzo Masone Fritz approached days steal sanitary basa jumbo gallbladder crowns handfuls plums nectarines underconsumed drilled skulls lid poking USDA thickest translates clump cruciferous broil cardamom thankfully occasions roasting dicing drizzling facet pectin midworkout plump insides glorious skimp Tahini Cumin pretzels sing Ramen entrée zing sharpest leftover pinapple Endive chilies clove crumbles vinaigrette Kalamata pitted Oregano Bragg's tonight's Mendelsohn frothy stove fortunate micromanaging achievements NASCAR skimping mussels rabbit seitan grapefruits limes Melons honeydew apricots… chestnuts overanalyzing fistful plateauing stricter fistfuls arrangement honing afforded it'll Fiber's Satiate Yep compiled SOUTHWEST potlucks bevy ROMA SEEDED uncovered BALSAMIC yummy clocks heats PARSNIP resealable rimmed Discard FE COB THINLY spinner BURRITO RINSED GARNISHES STROGANOFF CAMPBELL'S SHERRY dente garnished Dorian coveted GROUNDED hesitation filets tenderloins scours tags grabs fattier semblance beefing thrifty exchanges D's rodeo beeline Quaker swayed canister opts canisters measly sizzling sitcom Kris EZ sec Bathe proverbial anticipate Radar Benchmarks Robergs R Pearson Costill Fink J Pascoe Benedict Zachweija intensities Calder Yaqoob Bowtell Gelly Simeoni Rennie Wang uncompromising Welsh Kage meditative yin coincides iconoclast's sellers efficaciously replicate brand's Vitargo disguise bitterness reluctantly Offerings Hydra underperforming refilming raced biked deadlifted Ironman Matt Pritchard Ironmans swears triathletes Trainee Hey faceless

Views: 83601
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This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Curve
00:01:06 1 History
00:05:03 2 Definition
00:10:13 3 Differentiable curve
00:11:11 4 Length of a curve
00:17:44 5 Differential geometry
00:23:06 6 Algebraic curve
00:24:59 7 See also
00:26:03 8 Notes
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: 0.944525136320136
Voice name: en-AU-Wavenet-C
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight. Thus, a curve is a generalization of a line, in that its curvature need not be zero.Various disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context. However, many of these meanings are special instances of the definition which follows. A curve is a topological space which is locally homeomorphic to a line. In everyday language, this means that a curve is a set of points which, near each of its points, looks like a line, up to a deformation. A simple example of a curve is the parabola, shown to the right. A large number of other curves have been studied in multiple mathematical fields.
A closed curve is a curve that forms a path whose starting point is also its ending point—that is, a path from any of its points to the same point.
Closely related meanings include the graph of a function (for example, Phillips curve) and a two-dimensional graph.

Views: 3
wikipedia tts

https://www.instagram.com/prometei.tech/ reassured screamed liter favoring traction wondered reconsider realizing plow nap brain's ebb manifests CVD HDL minutiae ducks They've sufficed proponents waged salvo yearlong Tulane coverage unanimously sarcasm Pundits predictors coffin headlines representative enrolled Asians demographic diehards implausible slashing upped group's balloons publicized uptick bioelectrical impedance predictor LDL carbers pedestrian cuttingsome glean takeaways echoed study's Lydia Bazzano compel directing dogmatic almighty Jake fascinating devoting installment I’ve mmols Wingates foggy acuity tissue's oxidize Phinney synonymous Mistaking intriguing teamed Auburn Wolfe's CPT impede trash Someone's calorically reintroduction reintroduce blunts Paoli transitioned lasted Ketostix conservatively reversals lackluster telltale stroll tantamount deluge chockfull edibles aisle Who's les courgettes serrated peeler spiralizer wonderfully hash browns mandolin dubbed cauliflower's spuds pulverize Brassica wallop Chard sauté cremini shiitake fungi umami portobello stealthily praised dearth smear firepower backlash au naturale pint shrivelled rosy orbs lycopene Nature's lengthwise microwavable parchment scrape benevolent gourd Radish Bok choy Watercress famously sang stoned sweetness tinged tipoff nondigestible plush stellar sniffles pucker Fillets mercury unseasoned marinades ante beloved deli spared lunchmeats Dijon collard fests fattened Cornish hen Gruyere mundane decoupled riff blending pinches mop cultured surging critters tangy horns cow's Brie Ricotta kefir carnivores soaks brilliantly marinate Tempeh earthy mushroomy crumbling casseroles sauerkraut Pinto boast Pepitas o castoffs Sargento stringy bathed humming lofty healthyomega shops supermarkets Pepperettes Hazelnuts Bob's fare Shirataki translucent gelatinous konjac bowlful nondescript rinse blanch Preliminary prediabetes viscous Hazelnut brewed quencher moo cartons sidestep Imbibing infuses exhaustive flapjacks marys ye sipped seltzer contradictory farther swilling interchangeably insulinogenic spur counterintuitive accessing tougher adjusts Mozzarella cucumbers kcals reservoir thriving ongoing chow insisted French's Trimmed Uncured Portabella condensed tamari aminos steamer bubbly Ruthie ours marshmallows dye pumpkins fl Truvia Nutmeg Cloves towels masher lumpy quartered ½ generously pierced family's else's cleanup cooks Kosher slits slit PDF unwrap tossed bowl's ooohs aaaahs mouthwatering Coarse wilt bakes Sprouted crumb crumbs crumble byproducts apiece appreciable granite unconditioned stepmill app Centopani eater groundbreaking world's Evan's insists com's it'd befriending fluke flounder rutabaga turnips distributing rigors regimented hamburgers Animal's flagship Pak negotiable fundamentally depleting plows wishful oversimplified depletes Karbolyn Labrada's shuttling muscles replenished proponent dragging microtraumas pounder resynthesis disposal polymer shuttle Elasti RTD MRP EFA Charge Krill MPS rapamycin hesitate Centopani's diner steakhouse wheelbarrow Overseas border nearest awful refrigeration Stak Iconic XL Beanie Rotisserie precooked breaded standby powered brothers McGrath Antoine Vaillant baggie brainer Nothing's comforting goulash Slurp swole requested dad's bursting rotini parsnips I’ll paprika Worcestershire Caraway saucepot batch Printable Frosting silicone brethren Vincenzo Masone Fritz approached days steal sanitary basa jumbo gallbladder crowns handfuls plums nectarines underconsumed drilled skulls lid poking USDA thickest translates clump cruciferous broil cardamom thankfully occasions roasting dicing drizzling facet pectin midworkout plump insides glorious skimp Tahini Cumin pretzels sing Ramen entrée zing sharpest leftover pinapple Endive chilies clove crumbles vinaigrette Kalamata pitted Oregano Bragg's tonight's Mendelsohn frothy stove fortunate micromanaging achievements NASCAR skimping mussels rabbit seitan grapefruits limes Melons honeydew apricots… chestnuts overanalyzing fistful plateauing stricter fistfuls arrangement honing afforded it'll Fiber's Satiate Yep compiled SOUTHWEST potlucks bevy ROMA SEEDED uncovered BALSAMIC yummy clocks heats PARSNIP resealable rimmed Discard FE COB THINLY spinner BURRITO RINSED GARNISHES STROGANOFF CAMPBELL'S SHERRY dente garnished Dorian coveted GROUNDED hesitation filets tenderloins scours tags grabs fattier semblance beefing thrifty exchanges D's rodeo beeline Quaker swayed canister opts canisters measly sizzling sitcom Kris EZ sec Bathe proverbial anticipate Radar Benchmarks Robergs R Pearson Costill Fink J Pascoe Benedict Zachweija intensities Calder Yaqoob Bowtell Gelly Simeoni Rennie Wang uncompromising Welsh Kage meditative yin coincides iconoclast's sellers efficaciously replicate brand's Vitargo disguise bitterness reluctantly Offerings Hydra underperforming refilming raced biked deadlifted Ironman Matt Pritchard Ironmans swears triathletes Trainee Hey faceless

Views: 54445
ПРОКАЧКА

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/History_of_mathematics
00:04:37 1 Prehistoric
00:07:45 2 Babylonian
00:13:09 3 Egyptian
00:15:38 4 Greek
00:30:28 5 Roman
00:35:28 6 Chinese
00:44:11 7 Indian
00:51:23 8 Islamic empire
00:58:41 9 Maya
00:59:50 10 Medieval European
01:05:46 11 Renaissance
01:10:29 12 Mathematics during the Scientific Revolution
01:10:41 12.1 17th century
01:13:34 12.2 18th century
01:15:08 13 Modern
01:15:17 13.1 19th century
01:21:05 13.2 20th century
01:31:21 13.3 21st century
01:32:11 14 Future
01:32:48 15 See also
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: 0.75313900926134
Voice name: en-US-Wavenet-B
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, together with Ancient Egypt and Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the field of astronomy and to formulate calendars and record time.
The most ancient mathematical texts available are from Mesopotamia and Egypt - Plimpton 322 (Babylonian c. 1900 BC), the Rhind Mathematical Papyrus (Egyptian c. 2000–1800 BC) and the Moscow Mathematical Papyrus (Egyptian c. 1890 BC). All of these texts mention the so-called Pythagorean triples and so, by inference, the Pythagorean theorem, seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a "demonstrative discipline" begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek μάθημα (mathema), meaning "subject of instruction". Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics. Although they made virtually no contributions to theoretical mathematics, the ancient Romans used applied mathematics in surveying, structural engineering, mechanical engineering, bookkeeping, creation of lunar and solar calendars, and even arts and crafts. Chinese mathematics made early contributions, including a place value system and the first use of negative numbers. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics through the work of Muḥammad ibn Mūsā al-Khwārizmī. Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations. Contemporaneous with but independent of these traditions were the mathematics developed by the Maya civilization of Mexico and Central America, where the concept of zero was given a standard symbol in Maya numerals.
Many Greek and Arabic texts on mathematics were translated into Latin from the 12th century onward, leading to further development of mathematics in Medieval Europe. From ancient times through the Middle Ages, periods of mathematical discovery were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 15th century, new mathematical developments, interacting with new scientific discoveries, were made at an increasing pace that continues through the present day. This includes the groundbreaking work of both Isaac Newton and Gottfried Wilhelm Leibniz in the development of infinitesimal calculus during the course of the 17th century. At the end of the 19th century the International Congress of Mathematicians was founded a ...

Views: 23
wikipedia tts

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/History_of_mathematics
00:03:27 1 Prehistoric
00:05:49 2 Babylonian
00:09:54 3 Egyptian
00:11:48 4 Greek
00:22:56 5 Roman
00:26:44 6 Chinese
00:33:15 7 Indian
00:38:41 8 Islamic empire
00:44:10 9 Maya
00:45:03 10 Medieval European
00:49:32 11 Renaissance
00:53:05 12 Mathematics during the Scientific Revolution
00:53:16 12.1 17th century
00:55:27 12.2 18th century
00:56:39 13 Modern
00:56:48 13.1 19th century
01:01:09 13.2 20th century
01:08:51 13.3 21st century
01:09:30 14 Future
01:09:59 15 See also
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: 0.9803638922155543
Voice name: en-US-Wavenet-A
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, together with Ancient Egypt and Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the field of astronomy and to formulate calendars and record time.
The most ancient mathematical texts available are from Mesopotamia and Egypt - Plimpton 322 (Babylonian c. 1900 BC), the Rhind Mathematical Papyrus (Egyptian c. 2000–1800 BC) and the Moscow Mathematical Papyrus (Egyptian c. 1890 BC). All of these texts mention the so-called Pythagorean triples and so, by inference, the Pythagorean theorem, seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a "demonstrative discipline" begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek μάθημα (mathema), meaning "subject of instruction". Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics. Although they made virtually no contributions to theoretical mathematics, the ancient Romans used applied mathematics in surveying, structural engineering, mechanical engineering, bookkeeping, creation of lunar and solar calendars, and even arts and crafts. Chinese mathematics made early contributions, including a place value system and the first use of negative numbers. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics through the work of Muḥammad ibn Mūsā al-Khwārizmī. Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations. Contemporaneous with but independent of these traditions were the mathematics developed by the Maya civilization of Mexico and Central America, where the concept of zero was given a standard symbol in Maya numerals.
Many Greek and Arabic texts on mathematics were translated into Latin from the 12th century onward, leading to further development of mathematics in Medieval Europe. From ancient times through the Middle Ages, periods of mathematical discovery were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 15th century, new mathematical developments, interacting with new scientific discoveries, were made at an increasing pace that continues through the present day. This includes the groundbreaking work of both Isaac Newton and Gottfried Wilhelm Leibniz in the development of infinitesimal calculus during the course of the 17th century. At the end of the 19th century the International Congress of Mathematicians was founded ...

Views: 20
wikipedia tts

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 ...

Views: 8
wikipedia tts

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Views: 8209
ПРОКАЧКА

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Undergraduate_Texts_in_Mathematics
00:00:42 List of books
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.
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"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size.
The books in this series tend to be written at a more elementary level than the similar Graduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and difficulty level.
There is no Springer-Verlag numbering of the books like in the Graduate Texts in Mathematics series.
The books are numbered here by year of publication.

Views: 15
wikipedia tts

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

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Number_theory
00:01:39 1 History
00:01:48 1.1 Origins
00:01:56 1.1.1 Dawn of arithmetic
00:06:49 1.1.2 Classical Greece and the early Hellenistic period
00:10:09 1.1.3 Diophantus
00:14:18 1.1.4 Āryabhaṭa, Brahmagupta, Bhāskara
00:16:20 1.1.5 Arithmetic in the Islamic golden age
00:17:07 1.1.6 Western Europe in the Middle Ages
00:17:50 1.2 Early modern number theory
00:18:00 1.2.1 Fermat
00:22:36 1.2.2 Euler
00:25:47 1.2.3 Lagrange, Legendre, and Gauss
00:28:37 1.3 Maturity and division into subfields
00:30:30 2 Main subdivisions
00:30:39 2.1 Elementary tools
00:31:42 2.2 Analytic number theory
00:33:38 2.3 Algebraic number theory
00:38:56 2.4 Diophantine geometry
00:45:03 3 Recent approaches and subfields
00:45:38 3.1 Probabilistic number theory
00:47:16 3.2 Arithmetic combinatorics
00:49:50 3.3 Computations in number theory
00:52:57 4 Applications
00:53:55 5 Prizes
00:54:16 6 See also
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:
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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.
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"There is only one good, knowledge, and one evil, ignorance."
- Socrates
SUMMARY
=======
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers).
Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, for example, as approximated by the latter (Diophantine approximation).
The older term for number theory is arithmetic. By the early twentieth century, it had been superseded by "number theory". (The word "arithmetic" is used by the general public to mean "elementary calculations"; it has also acquired other meanings in mathematical logic, as in Peano arithmetic, and computer science, as in floating point arithmetic.) The use of the term arithmetic for number theory regained some ground in the second half of the 20th century, arguably in part due to French influence. In particular, arithmetical is preferred as an adjective to number-theoretic.

Views: 11
wikipedia tts

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Quantum_mechanics
00:02:03 1 History
00:10:41 2 Mathematical formulations
00:20:43 3 Mathematically equivalent formulations of quantum mechanics
00:22:31 4 Interactions with other scientific theories
00:27:08 4.1 Quantum mechanics and classical physics
00:29:45 4.2 Copenhagen interpretation of quantum versus classical kinematics
00:33:26 4.3 General relativity and quantum mechanics
00:35:01 4.4 Attempts at a unified field theory
00:38:02 5 Philosophical implications
00:44:12 6 Applications
00:45:26 6.1 Electronics
00:46:55 6.2 Cryptography
00:47:47 6.3 Quantum computing
00:48:42 6.4 Macroscale quantum effects
00:49:35 6.5 Quantum theory
00:50:37 7 Examples
00:50:46 7.1 Free particle
00:52:35 7.2 Particle in a box
00:56:01 7.3 Finite potential well
00:56:18 7.4 Rectangular potential barrier
00:56:44 7.5 Harmonic oscillator
00:56:50 7.6 Step potential
00:59:28 8 See also
00:59:48 9 Notes
01:00:24 10 References
01:00:49 11 Further reading
01:04:00 12 External links
01:06:34 See also
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.
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https://github.com/nodef/wikipedia-tts
"There is only one good, knowledge, and one evil, ignorance."
- Socrates
SUMMARY
=======
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.Classical physics, the physics existing before quantum mechanics, describes nature at ordinary (macroscopic) scale. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.
Quantum mechanics differs from classical physics in that energy, momentum, angular momentum and other quantities of a bound system are restricted to discrete values (quantization); objects have characteristics of both particles and waves (wave-particle duality); and there are limits to the precision with which quantities can be measured (uncertainty principle).Quantum mechanics gradually arose from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and from the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. Early quantum theory was profoundly re-conceived in the mid-1920s by Erwin Schrödinger, Werner Heisenberg, Max Born and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle.
Important applications of quantum theory include quantum chemistry, quantum optics, quantum computing, superconducting magnets, light-emitting diodes, and the laser, the transistor and semiconductors such as the microprocessor, medical and research imaging such as magnetic resonance imaging and electron microscopy. Explanations for many biological and physical phenomena are rooted in the nature of the chemical bond, most notably the macro-molecule DNA.

Views: 8
wikipedia tts

This is an audio version of the Wikipedia Article:
Quantum mechanics
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:
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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
=======
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.Classical physics, the physics existing before quantum mechanics, describes nature at ordinary (macroscopic) scale. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.
Quantum mechanics differs from classical physics in that energy, momentum, angular momentum and other quantities of a bound system are restricted to discrete values (quantization); objects have characteristics of both particles and waves (wave-particle duality); and there are limits to the precision with which quantities can be measured (uncertainty principle).Quantum mechanics gradually arose from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and from the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. Early quantum theory was profoundly re-conceived in the mid-1920s by Erwin Schrödinger, Werner Heisenberg, Max Born and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle.
Important applications of quantum theory include quantum chemistry, quantum optics, quantum computing, superconducting magnets, light-emitting diodes, and the laser, the transistor and semiconductors such as the microprocessor, medical and research imaging such as magnetic resonance imaging and electron microscopy. Explanations for many biological and physical phenomena are rooted in the nature of the chemical bond, most notably the macro-molecule DNA.

Views: 18
wikipedia tts

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.
A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours; in 12-hour time, there is no "15 o'clock". Likewise, if the clock starts at 12:00 (noon) and 21 hours elapse, then the time will be 9:00 the next day, rather than 33:00. Since the hour number starts over after it reaches 12, this is arithmetic modulo 12. 12 is congruent not only to 12 itself, but also to 0, so the time called "12:00" could also be called "0:00", since 12 is congruent to 0 modulo 12.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 612
Audiopedia

Factoring a number using pollard rho
http://www.awright2009.com/factor.c
Edit: Just realized people might want a windows version. Had it in my email a long time ago (Professor didnt seem to believe in me or Linux) I believe this is compiled for conroe based intel machine's, but better than nothing.
http://www.awright2009.com/factor.zip
I'll put the source and binary on my http://github.com/akw0088/factor in a bit (had to repull the windows binary from email as the university servers went down)

Views: 3355
akw0088

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Source:http://en.wikipedia.org/wiki/History_of_mathematics
The study of mathematics as a subject in its own right begins in the 6th century
BC with the Pythagoreans, who coined the term "mathematics" from the ancient
Greek μάθημα (mathema), meaning "subject of instruction". Greek mathematics
greatly refined the methods (especially through the introduction of deductive
reasoning and mathematical rigor in proofs) and expanded the subject matter of
mathematics. Chinese mathematics made early contributions, including a place
value system. The Hindu-Arabic numeral system and the rules for the use of
its operations, in use throughout the world today, likely evolved over the
course of the first millennium AD in India and was transmitted to the west via
Islamic mathematics. Islamic mathematics, in turn, developed and expanded
the mathematics known to these civilizations. Many Greek and Arabic texts on
mathematics were then translated into Latin, which led to further development of
mathematics in medieval Europe.

Views: 6877
Wikivoicemedia

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Glossary_of_areas_of_mathematics
00:00:09 A
00:10:55 B
00:11:43 C
00:23:36 D
00:26:35 E
00:30:01 F
00:32:12 G
00:36:57 H
00:38:40 I
00:40:29 J
00:40:37 K
00:42:10 L
00:44:09 M
00:46:45 N
00:48:45 O
00:50:02 P
00:52:20 Q
00:52:59 R
00:56:17 S
01:01:29 T
01:03:46 U
01:04:34 V
01:05:36 W
01:05:53 X
01:06:02 Y
01:06:10 Z
01:06:19 See also
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:
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Speaking Rate: 0.7678575093241932
Voice name: en-AU-Wavenet-A
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
This is a glossary of terms that are or have been considered areas of study in mathematics.

Views: 3
wikipedia tts

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Group_theory
00:01:10 1 Main classes of groups
00:01:34 1.1 Permutation groups
00:02:42 1.2 Matrix groups
00:03:20 1.3 Transformation groups
00:04:13 1.4 Abstract groups
00:06:05 1.5 Groups with additional structure
00:08:21 2 Branches of group theory
00:08:30 2.1 Finite group theory
00:09:52 2.2 Representation of groups
00:11:55 2.3 Lie theory
00:13:00 2.4 Combinatorial and geometric group theory
00:16:37 3 Connection of groups and symmetry
00:19:10 4 Applications of group theory
00:19:42 4.1 Galois theory
00:20:35 4.2 Algebraic topology
00:21:42 4.3 Algebraic geometry and cryptography
00:22:58 4.4 Algebraic number theory
00:23:40 4.5 Harmonic analysis
00:24:04 4.6 Combinatorics
00:24:24 4.7 Music
00:24:41 4.8 Physics
00:25:21 4.9 Chemistry and materials science
00:27:30 4.10 Statistical mechanics
00:27:43 5 History
00:27:53 6 See also
00:28:08 7 Notes
00:30:20 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.
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"There is only one good, knowledge, and one evil, ignorance."
- Socrates
SUMMARY
=======
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.
Various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.
One of the most important mathematical achievements of the 20th century was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 1980, that culminated in a complete classification of finite simple groups.

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