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Computer science majors have to learn a different kind of math compared to MOST other majors (with the exception of math majors, plus computer and software engineers). This kind of math is important especially for those looking to go into research in fields like computer science, A.I., or even pure mathematics.
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MajorPrep

This video covers the math major including applied math vs pure math, courses you'll take, and careers you can go into. The math major in undergrad involves a lot of the same classes whether you go into applied math or pure math include Calculus, linear algebra, differential equations, proofs, abstract algebra, real analysis, and more. But you will be able to take electives in pure or applied math concepts.
Pure math is about using math to solve problems in math. Then applied math is about using math to solve problems outside of math (such as physics, engineering, finance, chemistry, biology, etc). Many pure math students end up getting their PhD so they can work in academia on research. Overall math students can go into a variety of fields including engineering, software development, teaching, finance, and more.
Applied Math Courses: https://www.youtube.com/watch?v=mRxsfgilBKY
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MajorPrep

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

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Introduction to Cryptography by Christof Paar

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For this question, we'll need to use Newton’s Law of Cooling. This law states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings (provided this difference is not too large).
Q. At 10:07 pm, you find a secret agent murdered. Next to him is a martini that got shaken before the secret agent could stir it. Room temperature is 70 °F. The martini warms from 60 °F to 61 °F in the 2 minutes from 10:07 pm to 10:09 pm. If the secret agent’s martinis are always served at 40 °F, what was the time of death?

Views: 140
Study Force

What is AVALANCHE EFFECT? What does AVALANCHE EFFECT mean? AVALANCHE EFFECT meaning - AVALANCHE EFFECT definition - AVALANCHE EFFECT explanation.
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Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
In cryptography, the avalanche effect is the desirable property of cryptographic algorithms, typically block ciphers and cryptographic hash functions, wherein if an input is changed slightly (for example, flipping a single bit), the output changes significantly (e.g., half the output bits flip). In the case of high-quality block ciphers, such a small change in either the key or the plaintext should cause a drastic change in the ciphertext. The actual term was first used by Horst Feistel, although the concept dates back to at least Shannon's diffusion.
If a block cipher or cryptographic hash function does not exhibit the avalanche effect to a significant degree, then it has poor randomization, and thus a cryptanalyst can make predictions about the input, being given only the output. This may be sufficient to partially or completely break the algorithm. Thus, the avalanche effect is a desirable condition from the point of view of the designer of the cryptographic algorithm or device.
Constructing a cipher or hash to exhibit a substantial avalanche effect is one of the primary design objectives, and mathematically the construction takes advantage of butterfly effect. This is why most block ciphers are product ciphers. It is also why hash functions have large data blocks. Both of these features allow small changes to propagate rapidly through iterations of the algorithm, such that every bit of the output should depend on every bit of the input before the algorithm terminates.
The strict avalanche criterion (SAC) is a formalization of the avalanche effect. It is satisfied if, whenever a single input bit is complemented, each of the output bits changes with a 50% probability. The SAC builds on the concepts of completeness and avalanche and was introduced by Webster and Tavares in 1985.
Higher-order generalizations of SAC involve multiple input bits. Boolean functions which satisfy the highest order SAC are always bent functions, also called maximally nonlinear functions, also called "perfect nonlinear" functions.

Views: 1456
The Audiopedia

Talk by Stian Fauskanger; Igor Semaev presented at Crypto 2017 rump session.

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TheIACR

Speaker: Satish Shankar
This talk will introduce the essential concepts from cryptography necessary to build AI systems that use sensitive data and yet protect our privacy. Specifically, we will cover concepts from secure multi-party computation (MPC) and how they can be used to build machine learning algorithms.
Why does this matter? This matters because we as a society are struggling to balance the benefits of data driven systems and the privacy risks they create. Building any machine learning or analytics model necessitates the collection of data. If this data is sensitive or personal, it inevitably turns into an honeypot for hackers. At a societal level, we are responding to this issue by introducing more regulation such as the GDPR.
Instead of regulations, it is possible to use cryptography to protect our data and still analyse it: This talk show how.
About: Shankar leads the machine learning and AI efforts for Manulife’s innovation labs. He works on quantitative investment and insurance, drawing on a wide range of fields from machine learning, natural language processing, differential privacy, encryption, and more.
He is particularly interested in the intersection of blockchains, distributed systems and privacy in machine learning.
Event Page: https://www.meetup.com/Singapore-Python-User-Group/events/249344900/
Produced by Engineers.SG
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Engineers.SG

Prof. Leslie Lamport is an American computer scientist. A graduate of the Bronx High School of Science, he received a B.S. in mathematics from the Massachusetts Institute of Technology in 1960, and M.A. and Ph.D. degrees in mathematics from Brandeis University, respectively in 1963 and 1972.[1] His dissertation was about singularities in analytic partial differential equations.[2] Lamport is best known for his seminal work in distributed systems and as the initial developer of the document preparation system LaTeX.[3]
Professionally, Lamport worked as a computer scientist at Massachusetts Computer Associates, SRI International, Digital Equipment Corporation, and Compaq. In 2001 he joined Microsoft Research at Mountain View, California.

Views: 13638
Technion

What is XSL ATTACK? What does XSL ATTACK mean? XSL ATTACK meaning - XSL ATTACK definition - XSL ATTACK explanation.
Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
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In cryptography, the eXtended Sparse Linearization (XSL) attack is a method of cryptanalysis for block ciphers. The attack was first published in 2002 by researchers Nicolas Courtois and Josef Pieprzyk. It has caused some controversy as it was claimed to have the potential to break the Advanced Encryption Standard (AES) cipher, also known as Rijndael, faster than an exhaustive search. Since AES is already widely used in commerce and government for the transmission of secret information, finding a technique that can shorten the amount of time it takes to retrieve the secret message without having the key could have wide implications.
The method has a high work-factor, which unless lessened, means the technique does not reduce the effort to break AES in comparison to an exhaustive search. Therefore, it does not affect the real-world security of block ciphers in the near future. Nonetheless, the attack has caused some experts to express greater unease at the algebraic simplicity of the current AES.
In overview, the XSL attack relies on first analyzing the internals of a cipher and deriving a system of quadratic simultaneous equations. These systems of equations are typically very large, for example 8,000 equations with 1,600 variables for the 128-bit AES. Several methods for solving such systems are known. In the XSL attack, a specialized algorithm, termed eXtended Sparse Linearization, is then applied to solve these equations and recover the key.
The attack is notable for requiring only a handful of known plaintexts to perform; previous methods of cryptanalysis, such as linear and differential cryptanalysis, often require unrealistically large numbers of known or chosen plaintexts.
Solving multivariate quadratic equations (MQ) over a finite set of numbers is an NP-hard problem (in the general case) with several applications in cryptography. The XSL attack requires an efficient algorithm for tackling MQ. In 1999, Kipnis and Shamir showed that a particular public key algorithm, known as the Hidden Field Equations scheme (HFE), could be reduced to an overdetermined system of quadratic equations (more equations than unknowns). One technique for solving such systems is linearization, which involves replacing each quadratic term with an independent variable and solving the resultant linear system using an algorithm such as Gaussian elimination. To succeed, linearization requires enough linearly independent equations (approximately as many as the number of terms). However, for the cryptanalysis of HFE there were too few equations, so Kipnis and Shamir proposed re-linearization, a technique where extra non-linear equations are added after linearization, and the resultant system is solved by a second application of linearization. Re-linearization proved general enough to be applicable to other schemes.
In 2000, Courtois et al. proposed an improved algorithm for MQ known as XL (for eXtended Linearization), which increases the number of equations by multiplying them with all monomials of a certain degree. Complexity estimates showed that the XL attack would not work against the equations derived from block ciphers such as AES. However, the systems of equations produced had a special structure, and the XSL algorithm was developed as a refinement of XL which could take advantage of this structure. In XSL, the equations are multiplied only by carefully selected monomials, and several variants have been proposed.
Research into the efficiency of XL and its derivative algorithms remains ongoing (Yang and Chen, 2004).
Courtois and Pieprzyk (2002) observed that AES (Rijndael) and partially also Serpent could be expressed as a system of quadratic equations. The variables represent not just the plaintext, ciphertext and key bits, but also various intermediate values within the algorithm. The S-box of AES appears to be especially vulnerable to this type of analysis, as it is based on the algebraically simple inverse function. ...

Views: 380
The Audiopedia

What is CUBE ATTACK? What does CUBE ATTACK mean? CUBE ATTACK meaning - CUBE ATTACK definition - CUBE ATTACK explanation.
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The cube attack is a method of cryptanalysis applicable to a wide variety of symmetric-key algorithms, published by Itai Dinur and Adi Shamir in a September 2008 preprint. A revised version of this preprint was placed online in January 2009, and the paper has also been accepted for presentation at Eurocrypt 2009.
A cipher is vulnerable if an output bit can be represented as a sufficiently low degree polynomial over GF(2) of key and input bits; in particular, this describes many stream ciphers based on LFSRs. DES and AES are believed to be immune to this attack. It works by summing an output bit value for all possible values of a subset of public input bits, chosen such that the resulting sum is a linear combination of secret bits; repeated application of this technique gives a set of linear relations between secret bits that can be solved to discover these bits. The authors show that if the cipher resembles a random polynomial of sufficiently low degree then such sets of public input bits will exist with high probability, and can be discovered in a precomputation phase by "black box probing" of the relationship between input and output for various choices of public and secret input bits making no use of any other information about the construction of the cipher.
The paper presents a practical attack, which the authors have implemented and tested, on a stream cipher on which no previous known attack would be effective. Its state is a 10,000 bit LFSR with a secret dense feedback polynomial, which is filtered by an array of 1000 secret 8-bit to 1-bit S-boxes, whose input is based on secret taps into the LFSR state and whose output is XORed together. Each bit in the LFSR is initialized by a different secret dense quadratic polynomial in 10, 000 key and IV bits. The LFSR is clocked a large and secret number of times without producing any outputs, and then only the first output bit for any given IV is made available to the attacker. After a short preprocessing phase in which the attacker can query output bits for a variety of key and IV combinations, only 230 bit operations are required to discover the key for this cipher.
The authors also claim an attack on a version of Trivium reduced to 735 initialization rounds with complexity 230, and conjecture that these techniques may extend to breaking 1100 of Trivium's 1152 initialization rounds and "maybe even the original cipher". As of December 2008 this is the best attack known against Trivium.
The attack is, however, embroiled in two separate controversies. Firstly, Daniel J. Bernstein disputes the assertion that no previous attack on the 10,000-bit LFSR-based stream cipher existed, and claims that the attack on reduced-round Trivium "doesn't give any real reason to think that (the full) Trivium can be attacked". He claims that the Cube paper failed to cite an existing paper by Xuejia Lai detailing an attack on ciphers with small-degree polynomials, and that he believes the Cube attack to be merely a reinvention of this existing technique.
Secondly, Dinur and Shamir credit Michael Vielhaber's "Algebraic IV Differential Attack" (AIDA) as a precursor of the Cube attack. Dinur has stated at Eurocrypt 2009 that Cube generalises and improves upon AIDA. However, Vielhaber contends that the cube attack is no more than his attack under another name. It is, however, acknowledged by all parties involved that Cube's use of an efficient linearity test such as the BLR test results in the new attack needing less time than AIDA, although how substantial this particular change is remains in dispute. It is not the only way in which Cube and AIDA differ. Vielhaber claims, for instance, that the linear polynomials in the key bits that are obtained during the attack will be unusually sparse. He has not yet supplied evidence of this, but claims that such evidence will appear in a forthcoming paper by himself entitled "The Algebraic IV Differential Attack: AIDA Attacking the full Trivium". (It is not clear whether this alleged sparsity applies to any ciphers other than Trivium.)

Views: 176
The Audiopedia

A Differention Equation is linear in which the dependent variable and its derivative occur in first degree. dy/dx+P.Y=Q(x) L.D.P. is solved by when its multiplied by exp ∫▒〖p dx〗 because by the multiplication of this term the equation become perfect.
The general solution is given by-

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Guru Kpo

Views: 1543
Internetwork Security

There are two prices that are critical for any investor to know: the current price of the investment he or she owns, or plans to own, and its future selling price. Despite this, investors are constantly reviewing past pricing history and using it to influence their future investment decisions. Some investors won't buy a stock or index that has risen too sharply, because they assume that it's due for a correction, while other investors avoid a falling stock, because they fear that it will continue to deteriorate. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
https://www.amazon.com/MIND-MATH-Learn-Math-Fun-ebook/dp/B017QEIF18

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Garg University

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Internetwork Security

Realistic Information Technology & Software Engineering Interviews: 8 of 28 - Information & Cyber Security, Embedded Systems, and Energy Conservation. For infinite number of professional interviews (Exactly as you experience in professional companies - Technical + HR), visit https://InterviewMax.com.
This interview series covers graduate syllabus and the syllabus of Masters degree to a great extent. For example, the key topics like, Cyber Attacks, Security Goals like Authentication Authorization, Cipher Techniques like Substitution and Transposition, One Time Pad, Modular Arithmetic, GCD, Euclid’s Algorithms, Chinese Remainder Theorem, Discrete Logarithm, Fermat Theorem, Block Ciphers, Stream Ciphers. Secret Splitting and Sharing, Symmetric Key Algorithms like DES AES BLOWFISH, Attacks on DES, Modes of Operations, Linear Cryptanalysis and Differential Cryptanalysis, Public Key Algorithms like RSA, Key Generation and Usage, message digest, key management, Hash Algorithms like SHA-1, MD5, Key Management, key Generations, key Distribution, key Updation, Digital Certificate, Digital Signature, PKI, Diffie-Hellman Key Exchange, One Way Authentication, Mutual Authentication, Kerberos 5.0, Layer Wise Security Concerns, IPSEC, AH and ESP, Tunnel Mode, Transport Mode, Security Associations, SSL, Handshake Protocol, Record Layer Protocol. IKE, Internet Key Exchange Protocol. Intrusion Detection Systems, Anomaly Based, Signature Based, Host Based, Network Based Intrusion Detection Systems, Cybercrime and Information security, Classification of Cybercrimes, The legal perspectives, Americal perceptive, European perspective, Indian perspective, Global perspective, Categories of Cybercrime, Types of Attacks, Social Engineering, Cyberstalking, Cloud Computing and Cybercrime, Tools and methods used in cybercrime, Proxy servers and Anonymizers, Phishing, Password Cracking, Key-loggers and Spywares, Types of Virus, Worms, Dos and DDoS,SQL injection, Cybercrime and Legal perspectives, Cyber laws, The Indian IT Act, Challenges, Amendments, Challenges to the Law, cybercrime Scenario in India, Indian IT Act, Digital Signatures, information security, algorithms for implementing security, Internet Key Exchange Protocol, Applied Cryptography, Cyber Security, Cyber Crimes, Computer Forensics, Network Security, Cryptography, network security, Intrusion Detection Systems, Tools and methods used in cyber crime. For details visit the website http://InterviewMax.com

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InterviewMax

How to solve 6x ≡ 4 (mod 10)
If you want to see how to solve a linear congruence using Euclid's Algorithm, see https://youtu.be/4-HSjLXrfPs

Views: 68442
Maths with Jay

We will look at a collection of mathematical problems suggested by side-channel attacks against public key cryptosystems, and how the techniques inspired by this work relate to a variety of different applications. First, we discuss the cold boot attack, a side-channel attack against disk encryption systems that uses the phenomenon of DRAM remanence to recover encryption keys from a running computer. In the course of the attack, however, there may be errors introduced in the keys that the attacker obtains. It turns out that the structure of the key data in an AES key schedule can allow an attacker to more efficiently recover the private key in the presence of such errors. We extend this idea to a RSA private keys, and show how the structure of RSA private key data can allow an attacker to recover a key in the presence of random errors from 27 of the bits of the original key. Most previous work on RSA key recovery used the lattice-based techniques introduced by Coppersmith for finding low-degree roots of polynomials modulo numbers of unknown factorization. We will show how powerful analogies from algebraic number theory allow us to translate this theorem from the ring of integers to the ring of polynomials and beyond. This sort of intellectual arbitrage allows us to give a faster algorithm for list decoding of Reed-Solomon codes along with a natural extension to multi-point algebraic geometric codes, as well as an algorithm to find small solutions to polynomials over ideals in number fields.

Views: 1207
Microsoft Research

Congruence problems and solutions in hindi.
CONGRUENCE EXAMPLES IN HINDI.
CONGRUENCE https://youtu.be/wGIc43sT1uY
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Mathematics Analysis

[Maths - 2 , First yr Playlist]
https://www.youtube.com/playlist?list=PL5fCG6TOVhr4k0BJjVZLjHn2fxLd6f19j
Unit 1 – Partial Differentiation and its Applications
Partial Derivative of 1st and 2nd order https://youtu.be/QvufScfeRZ0
Partial Derivative of 1st and 2nd Order (P2) https://youtu.be/he2V9LYzKPY
Euler's Theorem - P1 https://youtu.be/kEMgvpodsEA
Euler's Theorem - P2 https://youtu.be/dCEHrjhplrA
Change Of Variables https://youtu.be/3hyciaX4cSQ
Taylor's Theorem for function of two Variables https://youtu.be/4Z0DjTdVXxg
Errors and Approximations https://youtu.be/KmHiVDrvhD8
Jacobians - Easiest Explained P1 https://youtu.be/CaQvxH0eSiU
Jacobians - P2 https://youtu.be/kwbSFcbwhUA
lagrange's method of Undetermined Multipliers https://youtu.be/SFmIHigJugY
Formation of Partial Different Equations https://youtu.be/fXcul6vf2io
Formation of Partial Differential Equation P2 https://youtu.be/TzPYCRodrdo
Unit – 2 Laplace Transform
Laplace Transform – Properties https://youtu.be/6mMjYC0pzm4
Laplace Transform of Basic Functions https://youtu.be/RSitLCnnoxE
Laplace Transform of Derivatives and Integrals https://youtu.be/mtekg3-2bFU
Inverse Laplace Transform - P1 https://youtu.be/A6JU2jUFAao
Inverse Laplace Transform - Numericals P2 https://youtu.be/WPgHGWI7CRU
Convolution Theorem - II https://youtu.be/V8c8Mk4iD34
Convolution Theorem - Numericals II https://youtu.be/Zjc_RZvf7lU
Solving Differential Equations (Application) - https://youtu.be/R2a3IghkZNA
Differential Equation using Laplace Transform P2 https://youtu.be/zYqV--eHXwM
Differential Equations Using Laplace Transform (P 3) https://youtu.be/5BC-Z3wRIG4
Unit – 3 Complex Functions
Complex function Definition , Limit and Continuity https://youtu.be/2r9NlYsBbro
Differentiability Of Complex Function https://youtu.be/eFwjRP75R8o
Cauchy Riemann Equation II Analytic Function #1 https://youtu.be/59u4PnalRCc
Cauchy Riemann Equation II Numericals #2 https://youtu.be/kG1CN8s8XwQ
Cauchy Riemann Equation II Numericals #3 https://youtu.be/o9bMz1XhfcU
Cauchy Riemann Equation in Polar form https://youtu.be/sSPI1z7MYhw
Harmonic Function - Complex Plane #1 https://youtu.be/zkMh3wJzsVc
Harmonic Function - Complex Plane #2 https://youtu.be/9v46vnzxYcQ
Mapping or Transformations Complex plane II Conformal Mapping https://youtu.be/s6LGM14_S8g
Mapping in Complex Plane II Bilinear Mapping #1 https://youtu.be/OCc-rQkpRKA
Bilinear Mapping II Fixed point Problems #2 https://youtu.be/wfutAHZ-XtI
Complex Integration : Line Integral https://youtu.be/4dwMAOTbp04
Cauchy Integral Theorem - With Numericals #1 https://youtu.be/sq3KW-qj5Pk
Cauchy Integral Theorem - With Numericals #2 https://youtu.be/qUfpCJcyiR0
Cauchy Integral Formula : Complex Plane https://youtu.be/TOsJJX7KpEg
Zeros and Singularity ( with Poles ) : Complex Plane https://youtu.be/3sgEFNZQDt0
Taylor's Series #1 https://youtu.be/LBIQud3p6us
Taylor's Series #2 https://youtu.be/Ab9USK1H4Y4
Laurent's Series #1 https://youtu.be/NIxZp_UBQRU
Laurent's Theorem #2 https://youtu.be/_1ZTaRwelCM
Residue of a Complex Function https://youtu.be/dD-lu-22xQk
Cauchy's Residue Theorem https://youtu.be/GWmNyVzIdTo
Integration Round a Unit Circle https://youtu.be/n5TvfomHbxg
Integration Round the Semi- Cirle https://youtu.be/MmC-2UI8VzY
Unit – 4 Integration and Vector Calculus
Double Integral https://youtu.be/OzaboGyXdFk
Change Of Order Of Integration #1 https://youtu.be/lIKF_5WDHjM
Change Of Order Of Integration II Part -2 (Numericals) https://youtu.be/qXnNOs8dvoE
Tripple integration - Engineering Maths https://youtu.be/xoi7LuUrU1o
Scalar and Vector Point Function , Gradient - P1 https://youtu.be/MdlT561A8_8
Scalar and Vector Point Function , Gradient - P2 https://youtu.be/H6w945A6tkk
Divergence and Curl Of Vector Point Function https://youtu.be/KO6A1JdNlKA
Directional Derivative - Vector Calculus https://youtu.be/PX78MrbdKr8
Line Integral - Vector Calculus https://youtu.be/JiQW1TQ5MMs
Surface Integral - Vector Calculus https://youtu.be/K37VbB5Ukxk
Surface integral P2 - Vector Calculus https://youtu.be/KfSbF3MQ0Hs
Volume Integral - Vector Calculus https://youtu.be/hG7h2g36jrQ
Green's Theorem - Engineering Mathematics https://youtu.be/-ljqqb_Vvso
Green's Theorem P2 - Engineering Maths https://youtu.be/ddZYcTb6lrQ
Stokes Theorem - Engineering Maths https://youtu.be/KnChsPboXqc
Stokes Theorem ( More Numerical) https://youtu.be/tQBlDlmtVSM
Gauss Divergence Theorem - Engineering Maths https://youtu.be/tbJ_zgs84aY
Gauss Divergence Theorem P2 II Engineering MATHS https://youtu.be/GhY56OKu7vs

Views: 34116
Study Buddy

Dr. Dan Spielman presents an efficient, randomized algorithm for constructing sparse approximations that only uses a logarithmic factor more edges than optimal. The algorithms follow from the solution of a problem in linear algebra. Dr. Spellman is a Professor of Computer Science, Mathematics and Applied Mathematics at Yale University and Co-Director of the Yale Institute for Network Science.
Dr. Dan Spielman, Professor of Computer Science, Mathematics and Applied Mathematics and Co-Director of the Yale Institute for Network Science
5/8/2014
http://www.cs.washington.edu/

Views: 969
UW Video

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: 19040
nptelhrd

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Euler Theorem | Homogeneous Function|Lecture 68| Diff Calculus & Coordinate Geometry Bangla Tutorial
In mathematics, a homogeneous function is one with multiplicative scaling behaviour: if all its arguments are multiplied by a factor, then its value is multiplied by some power of this factor.
Homogeneous Functions. Homogeneous. To be Homogeneous a function must pass this test: f(zx,zy) = znf(x,y). In other words. Homogeneous is when we can
A homogeneous function has a property that when every variable of such function is replaced by a constant term times the variable, the multiplied constant can
Definition. Multivariate functions that are “homogeneous” of some degree are often used in economic theory. A function is homogeneous of degree k if, when each of its arguments is multiplied by any number t 0, the value of the function is multiplied by tk.A transformation of the variables of a tensor changes the tensor into another whose components are linear homogeneous functions of the components of the original tensor. SEE ALSO: Euler's Homogeneous Function Theorem, Homogeneous Ordinary Differential Equation. CITE THIS AS: Weisstein, Eric W. " Homogeneous Function."Euler's Homogeneous Function Theorem. Contribute to this entry. Let f(x,y) be a homogeneous function of order n so that
M(x, y)=3x2 + xy is a homogeneous function since the sum of the powers of x and y in each term is the same (i.e. x2 is x to power. 2 and xy = x1y1 giving total
then f(x) is homogeneous to degree “k”. In general, a multivariable function f(x1,x2,x3,…) is said to be homogeneous of degree “k” in variables xi(i=1,2,3,…)
A function f( x,y) is said to be homogeneous of degree n if the equation holds for all x,y, and z (for which both sides are defined)
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The generalization of Fermat's theorem is known as Euler's theorem. In general, Euler's theorem states that, “if p and q are relatively prime, then ”, where φ is Euler's totient function for integers. That is, is the number of non-negative numbers that are less than q and relatively prime to q.
Euler's theorem can be proven using concepts from the theory of groups: The residue classes (mod n) that are coprime to n form a group under multiplication (see the article Multiplicative group of integers modulo n for details). The order of that group is where denotes Euler's totient function.
Euler's theorem is a generalization of Fermat's little theorem dealing with powers of integers modulo positive integers. It arises in applications of elementary number theory, including the theoretical underpinning for the RSA cryptosystem. ... where ϕ(n)ϕ(n)\phi(n) is Euler's ...
The generalization of Fermat's theorem is known as Euler's theorem. In general, Euler's theorem states that, “if p and q are relatively prime, then ”, where φ is Euler's totient function for integers. That is, is the number of non-negative numbers that are less than q and relatively prime to q.
The Euler's totient function φ for integer m is defined as the number of positive integers not greater than and coprime to m. ... In one special case the formula is really simple: for prime p, φ(p) = p - 1. This is why the Euler's Theorem is indeed a generalization of Fermat's.
EULER'S THEOREM. KEITH CONRAD. 1. Introduction. Fermat's little theorem is an important property of integers to a prime modulus. Theorem 1.1 (Fermat).
Today I want to show how to generalize this to prove Euler's Totient
euler's theorem engineering mathematics
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FTorial,Bangla,Tutorial,toc,math5,aiub,ssc,physics,math1,euler theorem,degree of homogeneous function,eulers theorem,homogeneous differential equation,homogeneous,homogenous and heterogenous mixture,homogeneous function,homogeneous function euler theorem,homogeneous first order linear differential equations,euler's method,euler's formula,euler's theorem,euler's theorem on homogeneous function,euler's theorem proof,euler method,euler method differential equation

Views: 516
FTorial

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: 7475
nptelhrd

Basic Algebraic Geometry : Varieties, Morphisms, Local Rings, Function Fields and Nonsingularity by Dr. T.E. Venkata Balaji,Department of Mathematics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in

Views: 37493
nptelhrd

Clip 1/6
Speaker: Gerome Miklau · University of Massachusetts, Amherst
Our recent work investigates the properties of a network that can be accurately studied without threatening the privacy of individuals and their connections. We adopt the rigorous condition of differential privacy, and develop algorithms for releasing randomly perturbed statistics about the topology of a sensitive network.
This talk will focus on two basic analysis tasks: the estimation of the degree distribution of a network and the study of small structural patterns that occur in a network (sometimes called motif analysis). We show that the degree distribution of a network can be very accurately estimated by a novel technique in which constraints are applied to the noisy output to improve utility. This technique is of general interest, and can be used to boost the accuracy of differentially private output in other tasks as well. We show that studying motifs is fundamentally harder, but can be done with acceptable
accuracy if the privacy condition is relaxed.
For more information go to the Cerias website (http://bit.ly/dsFCBF)

Views: 215
Christiaan008

The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.
If you would like to buy a poster of this map, they are available here:
North America: https://store.dftba.com/products/map-of-mathematics-poster
Everywhere else: http://www.redbubble.com/people/dominicwalliman/works/25095968-the-map-of-mathematics
I have also made a version available for educational use which you can find here: https://www.flickr.com/photos/[email protected]/32264483720/in/dateposted-public/
To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!
1. The number one is not a prime number. The definition of a prime number is a number can be divided evenly only by 1, or itself. And it must be a whole number GREATER than 1. (This last bit is the bit I forgot).
2. In the trigonometry section I drew cos(theta) = opposite / adjacent. This is the kind of thing you learn in high school and guess what. I got it wrong! Dummy. It should be cos(theta) = adjacent / hypotenuse.
3. My drawing of dice is slightly wrong. Most dice have their opposite sides adding up to 7, so when I drew 3 and 4 next to each other that is incorrect.
4. I said that the Gödel Incompleteness Theorems implied that mathematics is made up by humans, but that is wrong, just ignore that statement. I have learned more about it now, here is a good video explaining it: https://youtu.be/O4ndIDcDSGc
5. In the animation about imaginary numbers I drew the real axis as vertical and the imaginary axis as horizontal which is opposite to the conventional way it is done.
Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience
Here are links to some of the sources I used in this video.
Links:
Summary of mathematics: https://en.wikipedia.org/wiki/Mathematics
Earliest human counting: http://mathtimeline.weebly.com/early-human-counting-tools.html
First use of zero: https://en.wikipedia.org/wiki/0#History http://www.livescience.com/27853-who-invented-zero.html
First use of negative numbers: https://www.quora.com/Who-is-the-inventor-of-negative-numbers
Renaissance science: https://en.wikipedia.org/wiki/History_of_science_in_the_Renaissance
History of complex numbers: http://rossroessler.tripod.com/ https://en.wikipedia.org/wiki/Mathematics
Proof that pi is irrational: https://www.quora.com/How-do-you-prove-that-pi-is-an-irrational-number
and https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Laczkovich.27s_proof
Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.
Frontiers of Space: http://nobrow.net/shop/professor-astro-cats-frontiers-of-space/
Atomic Adventure: http://nobrow.net/shop/professor-astro-cats-atomic-adventure/
Intergalactic Activity Book: http://nobrow.net/shop/professor-astro-cats-intergalactic-activity-book/
Solar System App: http://www.minilabstudios.com/apps/professor-astro-cats-solar-system/
Find me on twitter, instagram, and my website:
http://dominicwalliman.com
https://twitter.com/DominicWalliman
https://www.instagram.com/dominicwalliman
https://www.facebook.com/dominicwalliman

Views: 4294161
Domain of Science

Alain Passelègue of ENS presents his talk "From Cryptomania to Obfustopia Through Secret-key Functional Encryption" at the DIMACS/CEF Workshop on Cryptography and Software Obfuscation event.
http://dimacs.rutgers.edu/Workshops/Obfuscation/
The workshop was held from Tuesday, November 8, 2016 to Wednesday, November 9, 2016 at the Bechtel Conference Center at Stanford University.

Views: 173
Rutgers University

Mathematics! Visit ekeeda.com for online engineering video lectures of degree and diploma maths.

Views: 36
ekeeda seo

Tune in this week to hear thoughts on course structure, both linear and non-linear, from Udacity's Lead Instructor Andy Brown. How can we make sure students are always learning? Let us know your thoughts on course structure in the comments!

Views: 2699
Udacity

An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves by Dr. T.E. Venkata Balaji, Department of Mathematics, IIT Madras. For more details on NPTEL visit http://www.nptel.iitm.ac.in/syllabus/111106044/
Goals: * To find the zeros of the derivative of the Weierstrass phe-function associated to a lattice
* To use the ODE established in the previous lecture to analyze the values of the Weierstrass phe-function at the zeros of its derivative and to show that these values are nonvanishing analytic (holomorphic) functions on the upper half-plane
* To introduce the notion of order for an elliptic function, namely the finite positive integer which is the number of times the function assumes any value in the extended complex plane (Riemann sphere)
Keywords: Upper half-plane, invariants for complex tori, lattice (or) grid in the plane, fundamental parallelogram (or) period parallelogram associated to a lattice, complex torus associated to a lattice, doubly-periodic meromorphic function (or) elliptic function associated to a lattice, Weierstrass phe-function associated to a lattice, ordinary differential equation satisfied by the Weierstrass phe-function, simple zero, pole of order three, isolated double pole, Argument Principle, Residue theorem, order of an elliptic function, automorphic function (or) automorphic form, modular function (or) modular form, congruence mod two subgroup of the unimodular group, even function, odd function

Views: 1804
nptelhrd

Claude Shannon Centennial Symposium
Rackham Building Amphitheatre
University of Michigan, Ann Arbor
Abbas El Gamal, Hitachi America Professor and Fortinet Founders Chair from Stanford University, talks about Information Theoretic Limits for Randomness Generation.
Abbas El Gamal received his B.Sc. Honors degree in Electrical Engineering from Cairo University in 1972, and his M.S. in Statistics and Ph.D. in Electrical Engineering from Stanford University in 1977 and 1978, respectively. From 1978 to 1980, he was an Assistant Professor at USC. He has been on the Stanford faculty since 1981, where he is currently the Hitachi America Professor in the School of Engineering and Fortinet Founders Chair of the Department of Electrical Engineering. From 1997 to 2002, he served as the principal investigator on the Stanford Programmable Digital Camera program. From 2004 to 2009, he was Director of the Information Systems Laboratory. He was a visiting professor and MacKay Fellow at the University of California, Berkeley in Fall 2009-2010, and visited Tsinghua University as member of the Tsinghua Guest Chair Professor Group on Communications and Networking in Spring 2009-2010.
Prof. El Gamal's research contributions have spanned several areas, including network information theory, Field Programmable Gate Array, and digital imaging devices and systems. He has authored or coauthored over 230 papers and holds over 30 patents in these areas. He has coauthored the book Network Information Theory (Cambridge Press 2011). Prof. El Gamal is a member of the National Academy of Engineering and a Fellow of the IEEE. He has received several honors and awards for his research contributions, including the 2016 IEEE Richard W. Hamming Medal, the 2014 Viterbi Lecture, the 2013 Shannon Memorial Lecture, the 2012 Claude E. Shannon Award, the inaugural Padovani Lecture, and the 2004 INFOCOM Paper Award.
Prof. El Gamal has also played key roles in several Silicon Valley companies. In 1984, he founded the LSI Logic Research Lab, which later became the Consumer Product Division. In 1986, he cofounded Actel, where he served in several capacities, including Chief Scientist. In 1990, he co-founded Silicon Architects, where he was Chief Technical Officer and member of the board of directors until Synopsys acquired it in 1995. He was a Vice President of Synopsys from 1995 to 1997. He co-founded Pixim in 1999 (now part of Sony) and Inscopix in 2011 to commercialize imaging technologies developed under the programmable digital camera program. He has also served on the board of directors and advisory boards of several other semiconductor, EDA, and Biotech startups.
http://www-isl.stanford.edu/people/abbas/
For more lectures on demand, please visit the MconneX website:
http://engin.umich.edu/mconnex/lectures

Views: 665
Michigan Engineering

Leadership Stage (Education to Dream Employment) System Project - Cryptanalysis of DES,3DES and AES (EA)
Social Media Connections:-
https://www.facebook.com/thiyagarajakumar.mimetheatre
https://www.linkedin.com/pub/mime-theatre-maestro-thiyagarajakumar-ramaswamy/48/a23/4a6
Leadership Stage QREM School is now one among the world's best professional training institutions in offering the quality Leadership stage IT, Media, Management and arts education. The training programmes at Leadership Stage QREM School, Education to Dream Employment System-prepare the students as Leaders with expertise in QREM' are structurally and functionally a multi-tier programmes giving emphasis to creative learning thus brewing a student as a true professional.
Our Director Thiyagarajakumar Ramaswamy's aims to offering an assured job for students by supplementing their academics with all the needed hot skills as well as soft skills. Students who have challenges like insufficient cut off marks, a gap after completion of course or back papers etc can also benefit out of the 'Leadership Stage Education to Dream Employment System- prepare the students as Leaders with expertise in QREM' programme. This training program envisions assisting candidates to identify their strengths, thus making them equipped and totally ready for a bright career.
It is a skill-based programme honing both soft skills and hot skills. Focuses on multi-platform proficiency. Grounding in theory and endless platforms for application. Bridges the gap between your education and the demands of the Job Market. Backed by 100% total training and development Solutions Company - Leadership Stage QREM School. Offers Excellent Industry Interface .Increases your Job Quotient.
What is 'Leadership stage Education to Dream Employment System-Prepare the students as Leaders with expertise in QREM Program'? Thiyagarajakumar Ramaswamy's 'Leadership Stage prepare the students as Leaders with expertise in QREM' is a concept aimed at moulding industry-ready candidates. As per the record, the number of engineering graduates was 793,321, of whom 497,475 were studying engineering degrees at undergraduate level. Therefore, of the 497,475 engineering undergraduates, around 124,400 (25%) would be considered globally employable. This is definitely a matter of concern and is a prominent factor that leads to unemployment among graduates. It may sound as a paradox that there are large volumes of unfilled vacancies in all leading MNCs. Leadership Stage QREM School --'Leadership Stage Prepare the students as Leaders with expertise in QREM' program is thus a creative solution for such bewildering factors. This is an Education to Employment association, where a student is provided training in all the needed hot skills and soft skills and then offered a real time industry experience.
Leadership Stage QREM School Education to Dream Employment System-offer potential candidates interested in a TOP IT career a structured recruitment program consisting of:- IT Training - Placement for candidates
The business requirements of our clients and partners are always evolving as they continue to maintain competitive advantage in the market. Also, the IT market is continuously changing with the release of new IT functionality and processes. Therefore, it is always challenging for our clients and partners to find the right people with appropriate IT knowledge and practical skill sets.
Our training consists of:
*Introduction to technology * In-depth study of modules * Practical skills for configuring solutions * Best practice methods and processes * Developing personal skills and business acumen
We have successfully trained and developed IT consultants from a diverse range of backgrounds and cultures that are enjoying a challenging and rewarding IT career.
The training will offer you the ability to:
* Apply technical IT skills * Apply problem solving and analytical skills
* Be creative and proactive * Work on actual business problems and challenges
* Produce high standard IT solutions that make a recognizable difference to business organizations * Further develop technical and personal skills
At Leadership Stage QREM School Education to Dream Employment System-, we provide the following services as a part of training:
• Career-oriented training • Highly affordable courses • Interactive learning at learner's convenience Customized curriculum • CV preparation assistance • Interview Preparation Guidance • Placement Services
For more information on our recruitment and training program,pl send your cv to us -- [email protected] /[email protected]/ [email protected]
Cheers....
Thiyagarajakumar Ramaswamy BTech, MBA, MBL, SAP, PMP, PH.D (Mime-Theatre), Ph.d in Quantitative Research, Evaluation and Measurement (QREM) in Education Policy and Leadership
Director
KalaAnantarupah Consultants-Leadership Stage Group

Views: 438
Thiyagarajakumar Ramaswamy

Mechanical Engineering Video lectures for GATE/IES/IAS and PSUs
follow us at http://iesgeneralstudies.com/
or
http://gatemech.com/forum/

Views: 2949
Adapala Academy & IES GS for Exams

Recorded at the Sydney University Secondary Mathematics Alumni Conference 2018

Views: 358
Wootube²

IN THIS VIDEO WE SHALL LEARN, HOW TO SOLVE QUADRATIC EQUATIONS USING FOUR DIFFERENT METHODS
1 INSPECTION METHOD
2 QUADRATIC FORMULA
3 FACTORISATION METHOD
4 COMPLETING SQUARE METHOD.
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This youtube channel includes or likely to include videos on the topics in future "set , relation ,function ,trigonometry,complex numbers ,quadratic equation, mathematical induction, statistics ,linear inequality, permutation and combination, binomial theorems,conic section, sequence and series , limit and continuity ,matrix,determinants, differentiation ,integration area under curves , differential equations ,probability ,vectors,coordinate geometry,linear programming".
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Views: 191
Dhiman Rajesh Dhiman

Let K be an imaginary quadratic field. Conjecturally, one should be able to associate to any cusp form on GL_n(A_K) which is cohomological (for the trivial coefficient system) a Galois representation. This can be achieved using our understanding of the classification of automorphic representations of the quasi-
split unitary group U(n, n), which relies upon the stabilization of the twisted trace formula for GL_n.
A detailed understanding of the local properties of these Galois representations opens up the possibility of proving automorphy lifting theorems. I will describe work in progress of a 10 author collaboration that proves such theorems, using as a starting point very important vanishing theorems for the cohomology of non-compact Shimura varieties which are work in progress of Caraiani--Scholze.
A particular consequence is the Ramanujan conjecture for cohomological cusp forms in the case n = 2. (The 10 authors are Allen, F. Calegari, Caraiani, Gee, Helm, Le Hung, J. Newton, Scholze, Taylor, and myself.)

Views: 2300
Institut des Hautes Études Scientifiques (IHÉS)

Views: 13319
Study Buddy

Views: 143
Sandeep Maash

A talk given at the University of Waterloo on July 12th, 2016. The intended audience was mathematics students without necessarily any prior background in cryptography or elliptic curves.
Apologies for the poor audio quality. Use subtitles if you can't hear.

Views: 2383
David Urbanik

The inverse function theorem states that if the determinant of the differential of a continuously differentiable function at a point is nonzero then the function is locally one-to-one and its inverse is differentiable at the image of that point. An example from analysis I is provided for comparison.
This is part of a series of lectures on Mathematical Analysis II. Topics covered include continuous and differentiable multi-variable functions on Euclidean space, the chain rule, the implicit function theorem, manifolds, tangent spaces, vector fields, the degree and index of a smooth map, the Euler characteristic, metric spaces, the contraction mapping theorem, existence and uniqueness of solutions to ordinary differential equations, and integral equations.
I speak rather slowly, so you may wish to increase the speed of this video.
These videos were created during the 2017 Spring semester at the UConn CETL Lightboard Room.

Views: 91
Arthur Parzygnat

Computer Science/Discrete Mathematics Seminar II
Topic: The singularity of symbolic matrices (Pt.2)
Speaker: Avi Wigderson
Date: Tuesday, February 9
The main object of study of this talk are matrices whose entries are linear forms in a set of formal variables (over some field). The main problem is determining if a given such matrix is invertible or singular (over the appropriate field of rational functions). As it happens, this problem has a dual life; when the underlying variables commute, and when they do not. Most of the talk will be devoted to explaining the many origins, motivations and interrelations of these two problems, in computational complexity, non-commutative algebra, (commutative) invariant theory, quantum information theory, optimization, approximating the permanent and more. I will provide an introduction to the relevant theory in each of these areas which will assume no prior knowledge. I will then describe a recent joint work with Garg, Gurvits and Olivera, giving a deterministic polynomial time algorithm for the non-commutative version (over the rationals), which uses many of the connections above. Strangely, while the problem is completely algebraic, the algorithm is analytic! This algorithm actually computes the non-commutative rank of the symbolic matrix, which turns out to give a factor-2 approximation to the commutative rank. This creates a different natural challenge for deterministic polynomial identity testing (PIT) - obtain a better approximation ratio for the rank.
For more videos, visit http://video.ias.edu

Views: 181
Institute for Advanced Study

Biyani Girls College. Present very good lecture about differential equation by Ms. Megha Sharma.
Please visit http://www.Gurukpo.com for more informative videos.

Views: 1303
Guru Kpo

Example problem using "conditional probability formula" to solve.
In the future this channel will mostly have math problem solving videos. I have a degree in Applied Math and Statistics and instead of letting it go to waste, why not make YouTube videos to help students currently on the grind. The format for all videos will be example/solution.
Note: This is my first playlist of math videos. I reviewed the solutions, however if you spot any mistakes please let me know by email [email protected]
Sorry if I go a little too fast on the videos. Still getting the hang of making them. I hope to get better at making these over time. Thanks for watching.
http://cauchypotato.com/
My bitcoin green address: GU9aQ1ossgQdmD4qXXfGCzhLPuajQ9sweu

Views: 46
Cauchypotato

When the two expressions are connected by 'greater than' or 'less than' sign, we get an inequality. When operating in terms of real numbers, linear inequalities are the ones written in the forms- or ,where is a linear functional in real numbers and b is a constant real number.

Views: 832
Guru Kpo

Daniel Kane
Harvard University
March 15, 2011
We define a polynomial threshold function to be a function of the form f(x) = sgn(p(x)) for p a polynomial. We discuss some recent techniques for dealing with polynomial threshold functions, particular when evaluated on random Gaussians. We show how to use these ideas to produce a pseudo random generator for degree-d polynomial threshold functions of Gaussians with seed length poly(2^d,log(n),epsilon^{-1}) .
For more videos, visit http://video.ias.edu

Views: 805
Institute for Advanced Study

By Pavel Emeliyanenko and Michael Kerber
A web application is presented to compute, plot, and interactively explore planar arrangements induced by algebraic plane curves of arbitrary degree. It produces accurate curve plots and reflects the exact topology for any arrangement, including degenerated cases. Various user interface features allow the interactive exploration of the arrangement structure. This makes the tool useful for demonstrative and educational purposes, especially as it runs without initial installation process.

Views: 781
Pavel Emeliyanenko

Yasufumi Hashimoto of the University of Ryukyus presented a talk titled: Cryptanalysis of the multivariate signature scheme proposed in PQCrypto 2013 at the 2014 PQCrypto conference in October, 2014.
Abstract: In PQCrypto 2013, Yasuda, Takagi and Sakurai proposed a new signature scheme as one of multivariate public key cryptosystems (MPKCs). This scheme (called YTS) is based on the fact that there are two isometry classes of non-degenerate quadratic forms on a vector space with a prescribed dimension. The advantage of YTS is its efficiency . In fact, its signature generation is eight or nine times faster than Rainbow of similar size. For the security, it is known that the direct attack, the IP attack and the min-rank attack are applicable on YTS, and the running times are exponential time for the first and the second attacks and subexponential time for the third attack. In the present paper, we give a new attack on YTS using an approach similar to the diagonalization of a matrix. Our attack works in polynomial time and it actually recovers equivalent secret keys of YTS having 140-bits security against min-rank attack in several minutes.
PQCrypto
2014 Book: http://www.springer.com/computer/security+and+cryptology/book/978-3-319-11658-7
Workshop: https://pqcrypto2014.uwaterloo.ca/
Find out more about IQC!
Website - https://uwaterloo.ca/institute-for-qu...
Facebook - https://www.facebook.com/QuantumIQC
Twitter - https://twitter.com/QuantumIQC

Views: 273
Institute for Quantum Computing