Cyclic groups are the building blocks of abelian groups. There are finite and infinite cyclic groups. In this video we will define cyclic groups, give a list of all cyclic groups, talk about the name “cyclic,” and see why they are so essential in abstract algebra.
If you’d like to help us make videos more quickly, you can support us on Patreon at
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We also welcome Bitcoin donations! Our Bitcoin address is:
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**************
We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
http://amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
http://www.jmilne.org/math/CourseNotes/index.html
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Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison

Views: 140781
Socratica

Learn and understand GF and various operations on elements using polynomial representation

Views: 12820
DrVikasThada

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

Views: 37763
Randell Heyman

Multiplication and addition tables for GF(2^3), concept of generator in GF and operations using generator.

Views: 5509
DrVikasThada

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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Views: 160359
MajorPrep

Additive and Multiplicative Inverse of elements in Galois Field.
link to my channel-
https://www.youtube.com/user/lalitkvashishtha
link to data structure and algorithm playlist -
https://www.youtube.com/watch?v=GbOW74e4xZE&list=PLLvKknWU7N4y_eGpQdg1Y-hORO7cxtoLU
link to information theory and coding techniques playlist -
https://www.youtube.com/watch?v=2qJ_mcjKYtk&list=PLLvKknWU7N4yDkIlN4YE-sXfFD4trDf6W
link to compiler design playlist -
https://www.youtube.com/watch?v=uAVkjTbB7Yc&list=PLLvKknWU7N4zpJWLqk7DXK26JwTB-gFmZ

Views: 27453
Lalit Vashishtha

Coding Theory by Dr. Andrew Thangaraj, Department of Electronics & Communication Engineering, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 26113
nptelhrd

Groups of Permutations
- Also, A could be empty, since the empty function on the empty set is the identity permutation of that set, so S_emptyset is the trivial group.

Views: 155485
LadislauFernandes

2018 Program for Women and Mathematics
Topic: Mathematics in Cryptography II
Speaker: Toni Bluher
Affiliation: National Security Agency
Date: May 21, 2018
For more videos, please visit http://video.ias.edu

Views: 199
Institute for Advanced Study

In this video I discuss irreducible polynomials and tests for irreducibility. Note that this video is intended for students in abstract algebra and is not appropriate for high-school or early college level algebra courses.

Views: 35885
James Hamblin

How to check whether the given polynomial is irreducible or not.
link to my channel-
https://www.youtube.com/user/lalitkvashishtha
link to data structure and algorithm playlist -
https://www.youtube.com/watch?v=GbOW74e4xZE&list=PLLvKknWU7N4y_eGpQdg1Y-hORO7cxtoLU
link to information theory and coding techniques playlist -
https://www.youtube.com/watch?v=2qJ_mcjKYtk&list=PLLvKknWU7N4yDkIlN4YE-sXfFD4trDf6W
link to compiler design playlist -
https://www.youtube.com/watch?v=uAVkjTbB7Yc&list=PLLvKknWU7N4zpJWLqk7DXK26JwTB-gFmZ

Views: 18083
Lalit Vashishtha

Chapter 14 (Formerly Chapter 5: Cryptography) of "Elementary Abstract Algebra: Examples and Applications. To find the textbook, "Algebraic Structures and Applications", please visit the page:
abstractalgebra.altervista.org

Views: 209
coachmath3

Learn the definition of a ring, one of the central objects in abstract algebra. We give several examples to illustrate this concept including matrices and polynomials.
If you’d like to help us make videos more quickly, you can support us on Patreon at
https://www.patreon.com/socratica
We also welcome Bitcoin donations! Our Bitcoin address is:
1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9
Thank you!!
**************
We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
http://amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
http://www.jmilne.org/math/CourseNotes/index.html
**************
Be sure to subscribe so you don't miss new lessons from Socratica:
http://bit.ly/1ixuu9W
You can also follow Socratica on:
- Twitter: @socratica
- Instagram: @SocraticaStudios
- Facebook: @SocraticaStudios
********
Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison

Views: 123836
Socratica

Learn more math and science with brilliant.org, https://brilliant.org/blackpenredpen/ ,
first 200 people to sign up will get 20% off your subscription, and you can also support my channel! Thank you!
Read more about CRT: https://brilliant.org/wiki/chinese-remainder-theorem/
Solution to the question: https://brilliant.org/problems/thursday-birthday/
a classic modular arithmetic problem, solving system of congruences, must know number theory basic,
blackpenredpen,
math for fun,
https://blackpenredpen.com/bprplive, https://twitter.com/blackpenredpen,
[email protected]

Views: 47789
blackpenredpen

In this video we only focus on the mathematical solution for software_update from the 34c3 CTF.
sage script:
https://gist.github.com/LiveOverflow/104adacc8af7895a4c14cea4a5236ecc
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All links with "*" are affiliate links.
LiveOverflow / Security Flag GmbH is part of the Amazon Affiliate Partner Programm.
#CTF #Cryptography

Views: 22093
LiveOverflow

This video is useful for students of BTech/BE/Engineering/ BSc/MSc Mathematics students. Also for students preparing IIT-JAM, GATE, CSIR-NET and other exams.

Views: 484587
Bhagwan Singh Vishwakarma

Views: 9042
Internetwork Security

This video is useful for students of BTech/BE/Engineering/ BSc/MSc Mathematics students. Also for students preparing IIT-JAM, GATE, CSIR-NET and other exams.

Views: 216249
Bhagwan Singh Vishwakarma

Fermat's Little Theorem was observed by Fermat and proven by Euler, who generalized the theorem significantly. This theorem aids in dividing extremely large numbers and can aid in testing numbers to see if they are prime. For more advanced students, this theorem can be easily proven using basic group theory.
Prerequisites: To follow this video, you will want to first learn the basics of congruences.
If you found this video helpful, please share it with your friends!
You might like the other videos in our Number Theory Playlist:
https://www.youtube.com/watch?v=VLFjOP7iFI0&list=PLi01XoE8jYojnxiwwAPRqEH19rx_mtcV_
Don't forget to Subscribe to our channels so you'll hear about our newest videos:
http://www.youtube.com/subscription_center?add_user=SocraticaStudios
Subject: Number Theory
Teacher: Michael Harrison
Artist: Katrina de Dios

Views: 148184
Socratica

Ring Theory: As an application of maximal ideals and residue fields, we give explicit constructions of fields with 4 and 8 elements. A key step is to find irreducible polynomials (quadratic and cubic).

Views: 8699
MathDoctorBob

This video is useful for students of BSc/MSc Mathematics students. Also for students preparing IIT-JAM, GATE, CSIR-NET and other exams.

Views: 165001
Bhagwan Singh Vishwakarma

Learn the definition of a group - one of the most fundamental ideas from abstract algebra.
If you found this video helpful, please give it a "thumbs up" and share it with your friends!
To see more videos on Abstract Algebra, please watch our playlist:
https://www.youtube.com/watch?v=QudbrUcVPxk&list=PLi01XoE8jYoi3SgnnGorR_XOW3IcK-TP6
If you’d like to help us make videos more quickly, you can support us on Patreon at
https://www.patreon.com/socratica
We also welcome Bitcoin donations! Our Bitcoin address is:
1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9
Thank you!!
**************
We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
http://amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
http://www.jmilne.org/math/CourseNotes/index.html
**************
Be sure to subscribe so you don't miss new lessons from Socratica:
http://bit.ly/1ixuu9W
You can also follow Socratica on:
- Twitter: @socratica
- Instagram: @SocraticaStudios
- Facebook: @SocraticaStudios
********
Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison

Views: 206011
Socratica

This tutorial demonstrates how the euclidian algorithm can be used to find the greatest common denominator of two large numbers.
Learn Math Tutorials Bookstore http://amzn.to/1HdY8vm
Donate http://bit.ly/19AHMvX
STILL NEED MORE HELP?
Connect one-on-one with a Math Tutor. Click the link below:
https://trk.justanswer.com/aff_c?offer_id=2&aff_id=8012&url_id=232
:)

Views: 322720
Learn Math Tutorials

Field Theory 1, Extension Fields
Please check my list on Abstract Algebra
http://www.youtube.com/playlist?list=PLWbnIo7XnOkw7zZu6u3si3at21r534qIM

Views: 9824
LadislauFernandes

This video shows you how to calculate the order of integers and how to find primitive roots.

Views: 15727
Cathy Frey

Views: 18824
Internetwork Security

How e to the pi i can be made more intuitive with some perspectives from group theory, and why exactly e^(pi i) = -1.
Apply to work at Emerald Cloud Lab:
- Application software engineer: http://3b1b.co/ecl-app-se
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Special thanks to the following Patrons: http://3b1b.co/epii-thanks
There's a slight mistake at 13:33, where the angle should be arctan(1/2) = 26.565 degrees, not 30 degrees. Arg! If anyone asks, I was just...er...rounding to the nearest 10's.
For those looking to read more into group theory, I'm a fan of Keith Conrads expository papers: http://www.math.uconn.edu/~kconrad/blurbs/
------------------
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 about 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: 888906
3Blue1Brown

Addition and multiplication of Ring of polynomials over Modulo m.
How to solve addition and multiplication of Ring of polynomial over Modulo.
#RingOfPolynomials #additionMultiplication #modulo #ringtheory
Please subscribe the channel for updates and support us.

Views: 547
Mathematics Analysis

MajorPrep Merch Store: https://teespring.com/stores/majorprep
Join Facebook Group: https://www.facebook.com/groups/majorprep/
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This video goes over some of the extra math classes you can take if you get a math minor. Some of these include...
Graph Theory
Vector Analysis
Topology
Numerical Analysis
Real Analysis
Complex Analysis
Abstract Algebra
Differential Geometry
etc
If you want the full list of classes I show in this video you can click the link below.
Full List of Required Math Classes: http://catalog.calpoly.edu/collegesandprograms/collegeofsciencemathematics/mathematics/mathematicsminor/
Cutting a Mobius Strip in Half (more detailed explanation): https://www.youtube.com/watch?v=XlQOipIVFPk
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► For more information on math, science, and engineering majors, check us out at https://majorprep.com
Best Ways to Contact Me: Facebook, twitter, or email ([email protected])

Views: 203037
MajorPrep

https://annamalaimaths.wordpress.com/

Views: 130
Annamalai N

Google Tech Talk
1/8/13
Presented by Nigel P. Smart
ABSTRACT
Multi-Party Computation (MPC) allows, in theory, a set of parties to compute any function on their secret input without revealing anything bar the output of the function. For many years this has been a restricted to a theoretical tool in cryptography. However, in the past five years amazing strides have been made in turning theory into practice. In this talk I will present the latest, practical, protocol called SPDZ (Speedz), which achieves much of its performance advantage from the use of Fully Homomorphic Encryption as a sub-procedure. No prior knowledge of MPC will be assumed.
Speaker Info
University of Bristol, U.K.

Views: 9630
GoogleTechTalks

This video is useful for students of BTech/BE/Engineering/ BSc/MSc Mathematics students. Also for students preparing IIT-JAM, GATE, CSIR-NET and other exams.

Views: 104669
Bhagwan Singh Vishwakarma

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: 60780
Maths with Jay

this video is useful for Bsc maths student and msc maths student and other exams...we upload daily one video so tell us which topic yu want NEXT.......check our channel, we have uploaded many videos ......
do LIKE,SHARE,COMMENT,SUBSCRIBE
galois theory part-1 - https://youtu.be/7mAt9q2ofIw
galois theory part-2 - https://youtu.be/jMdO_nbBqI4
solvable n nilpotent groups - https://youtu.be/Q8Z1IIAne4Q
thanks for watching
understanding mathematics

Views: 423
Understanding Mathematics

We give a large number of defintions
Ref: Part III notes(Burt)

Views: 746
Harpreet Bedi

Modules and Homomorphisms

Views: 13375
Introduction to Commutative Algebra

So you first converted between bases, but now there's variables in the way. What a bummer. Learn how to solve for the variable.

Views: 153632
Mike McCraith

Siavosh Benabbas, Rosario Gennaro, and Yevgeniy Vahlis
University of Toronto, Canada; IBM Research, USA; and Columbia University, USA
Abstract. We study the problem of computing on large datasets that are stored on an untrusted server. We follow the approach of amortized verifiable computation introduced by Gennaro, Gentry, and Parno in CRYPTO 2010. We present the first practical verifiable computation scheme for high degree polynomial functions. Such functions can be used, for example, to make predictions based on polynomials tted to a large number of sample points in an experiment. In addition to the many noncryptographic applications of delegating high degree polynomials, we use our veriable computation scheme to obtain new solutions for verifiable keyword search, and proofs of retrievability. Our constructions are based on the DDH assumption and its variants, and achieve adaptive security, which was left as an open problem by Gennaro et al (albeit for general functionalities).
Our second result is a primitive which we call a verifiable database (VDB). Here, a weak client outsources a large table to an untrusted server, and makes retrieval and update queries. For each query, the server provides a response and a proof that the response was computed correctly. The goal is to minimize the resources required by the client. This is made particularly challenging if the number of update queries is unbounded. We present a VDB scheme based on the hardness of the subgroup membership problem in composite order bilinear groups.

Views: 425
TheIACR

Views: 4161
Project Rhea

Views: 2700
Harpreet Bedi

SPEAKER: Francois Rodier TITLE: Asymptotic nonlinearity of Boolean functions ABSTRACT: The nonlinearity of Boolean functions on the space Fm2 is important in cryptography. It is used to measure the strength of cryptosystems when facing linear attacks. In the case low degree of approximation attacks, we examine the nonlinearity of order r of a Boolean function, which equals the number of necessary substitutions in its truth table needed to change it into a function of degree at most r. Studies aimed at the distribution of Boolean functions according to the r-th order nonlinearity. Asymptotically, a lower bound is established in the higher order cases for almost all Boolean functions, whereas a concentration point is shown in the first and second order nonlinearity case. In the case of vectorial Boolean functions, a concentration point is shown in the first order nonlinearity case. SPEAKER: Sorina Ionica TITLE: Pairing-based methods for genus 2 curve jacobians with maximal endomorphism ring ABSTRACT: Algorithms for constructing jacobians of genus 2 curves with nice cryptographic properties involve the computation of Igusa class polynomials for CM quartic fields. The CRT method used to compute these polynomials needs to find first a jacobian with maximal endomorphism ring over a finite field, and then enumerates all others jacobians having maximal endomorphism ring using horizontal isogenies. For $\ell 2$, we use Galois cohomology and the Tate pairing to compute the action of the Frobenius on the $\ell$-torsion. In view of application to Igusa class polynomials computation, we deduce an algorithm to verify whether the jacobian of a genus 2 curve has locally maximal endomorphism ring at $\ell$. Moreover, we derive a method to construct horizontal isogenies starting from a jacobian with maximal endomorphism ring.

Views: 69
Microsoft Research

This video shows you the method to look for the primitive roots which are useful in to be used in cryptosystem of Discrete Logarithm.

Views: 28451
Steven Wong

Addition and multiplication table of gf(2), gf(3), gf(5), gf(7).
link to my channel-
https://www.youtube.com/user/lalitkvashishtha
link to data structure and algorithm playlist -
https://www.youtube.com/watch?v=GbOW74e4xZE&list=PLLvKknWU7N4y_eGpQdg1Y-hORO7cxtoLU
link to information theory and coding techniques playlist -
https://www.youtube.com/watch?v=2qJ_mcjKYtk&list=PLLvKknWU7N4yDkIlN4YE-sXfFD4trDf6W
link to compiler design playlist -
https://www.youtube.com/watch?v=uAVkjTbB7Yc&list=PLLvKknWU7N4zpJWLqk7DXK26JwTB-gFmZ

Views: 6442
Lalit Vashishtha