Introduction to Euler's Totient Function!
Euler's totient function φ(n) is an important function in number theory. Here we go over the basics of the definition of the totient function as well as the value for prime numbers and powers of prime numbers! Modular Arithmetic playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJ
From playlist Modular Arithmetic
Totient Function - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
Injective, Surjective and Bijective Functions (continued)
This video is the second part of an introduction to the basic concepts of functions. It looks at the different ways of representing injective, surjective and bijective functions. Along the way I describe a neat way to arrive at the graphical representation of a function.
From playlist Foundational Math
What is an Injective Function? Definition and Explanation
An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez
From playlist Functions
906,150,257 and the Pólya conjecture (MegaFavNumbers)
#MegaFavNumbers "Most numbers have an odd number of prime factors!" ...or do they...? Ben chats about the large counterexample to Polya's conjecture, for Matt Parker and James Grime's MegaFavNumbers project. Ben is @SparksMaths on twitter and at http://www.bensparks.co.uk on the web
From playlist MegaFavNumbers
Definition of a Surjective Function and a Function that is NOT Surjective
We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht
From playlist Injective, Surjective, and Bijective Functions
(New Version Available) Inverse Functions
New Version: https://youtu.be/q6y0ToEhT1E Define an inverse function. Determine if a function as an inverse function. Determine inverse functions. http://mathispower4u.wordpress.com/
From playlist Exponential and Logarithmic Expressions and Equations
Definition of an Injective Function and Sample Proof
We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil
From playlist Injective, Surjective, and Bijective Functions
Ex 1: Find the Inverse of a Function
This video provides two examples of how to determine the inverse function of a one-to-one function. A graph is used to verify the inverse function was found correctly. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Determining Inverse Functions
Discrete Structures: Multiplicative Inverse; Greatest Common Divisor; Euler's Totient Function
Decrypting the linear cipher leaves us with a fundamental problem: dividing two integers yields a fraction, which is difficult to work with. Learn about new concepts: the greatest common divisor (GCD), the multiplicative inverse, and Euler's totient function. These will allow us to decrypt
From playlist Discrete Structures, Spring 2022
Explicit Formula for Euler's Totient Function!
Totient of p^a: https://youtu.be/NgZ33qr5WHM?t=210 Product formula: https://youtu.be/qpYqvNBQZ4g Euler's totient function involves counting how many numbers are coprime to n. In fact, we can calculate this value directly as long as we know the prime factors! This makes many theorems in n
From playlist Modular Arithmetic
AKPotW: A Lack of Primitive Roots [Number Theory]
If this video is confusing, be sure to check out our blog for the full solution transcript! https://centerofmathematics.blogspot.com/2018/05/advanced-knowledge-problem-of-week-5-3.html
From playlist Center of Math: Problems of the Week
Asymmetric Key Cryptography: The RSA Algorithm by Hand
This video demonstrates the underlying principles of the RSA cryptosystem. It shows how the public and private asymmetric keys can be calculated from a pair of prime numbers. It also shows how to encrypt a message using the public key, and decrypt it using the private key. For ease, the
From playlist Cryptography
Proof that the Totient Function is Multiplicative
Coprime numbers mod n: https://youtu.be/SslPWR2N5jA Chinese remainder theorem: https://www.youtube.com/playlist?list=PL22w63XsKjqyg3TEfDGsWoMQgWMUMjYhl Surjection and bijection: https://youtu.be/kt5eABzTVGQ Explanation of why Euler's totient function of a product of coprime numbers is e
From playlist Modular Arithmetic
This video explains what a mathematical function is and how it defines a relationship between two sets, the domain and the range. It also introduces three important categories of function: injective, surjective and bijective.
From playlist Foundational Math
Discrete Structures: Public Key Cryptography; RSA
See that little "lock" icon in your browser's address bar? What does that mean? Learn about the RSA algorithm, how it helps solve the key-exchange problem, and how your browser uses these algorithms to protect your privacy.
From playlist Discrete Structures, Spring 2022
GT12. Aut(Z/n) and Fermat's Little Theorem
Abstract Algebra: We show that Aut(Z/n) is isomorphic to (Z/n)*, the group of units in Z/n. In turn, we show that the units consist of all m in Z/n with gcd(m,n)=1. Using (Z/n)*, we define the Euler totient function and state and prove Fermat's Little Theorem: if p is a prime, then, for
From playlist Abstract Algebra
Discrete Structures: Digital certificates and implementing RSA
Our last session on RSA and public key cryptography. We'll learn about digital certificates and see how to implement the core RSA algorithms in Python.
From playlist Discrete Structures, Spring 2022
Dirichlet Eta Function - Integral Representation
Today, we use an integral to derive one of the integral representations for the Dirichlet eta function. This representation is very similar to the Riemann zeta function, which explains why their respective infinite series definition is quite similar (with the eta function being an alte rna
From playlist Integrals