“Introduction to Elliptic Curves,” by Álvaro Lozano-Robledo. This is an overview of the theory of elliptic curves, discussing the Mordell-Weil theorem, how to compute the torsion subgroup of an elliptic curve, the 2-descent algorithm, and what is currently known about rank and torsion subgroups of elliptic curves.
This is a video from CTNT, the Connecticut Summer School in Number Theory that took place at UConn during August 8th - 14th, 2016, organized by Keith Conrad, Amanda Folsom, Alvaro Lozano-Robledo, and Liang Xiao. For more information, see
http://ctnt-summer.math.uconn.edu/

Views: 3180
UConn Mathematics

“Introduction to Elliptic Curves,” by Álvaro Lozano-Robledo. This is an overview of the theory of elliptic curves, discussing the Mordell-Weil theorem, how to compute the torsion subgroup of an elliptic curve, the 2-descent algorithm, and what is currently known about rank and torsion subgroups of elliptic curves.
This is a video from CTNT, the Connecticut Summer School in Number Theory that took place at UConn during August 8th - 14th, 2016, organized by Keith Conrad, Amanda Folsom, Alvaro Lozano-Robledo, and Liang Xiao. For more information, see
http://ctnt-summer.math.uconn.edu/

Views: 743
UConn Mathematics

“Introduction to Elliptic Curves,” by Álvaro Lozano-Robledo. This is an overview of the theory of elliptic curves, discussing the Mordell-Weil theorem, how to compute the torsion subgroup of an elliptic curve, the 2-descent algorithm, and what is currently known about rank and torsion subgroups of elliptic curves.
This is a video from CTNT, the Connecticut Summer School in Number Theory that took place at UConn during August 8th - 14th, 2016, organized by Keith Conrad, Amanda Folsom, Alvaro Lozano-Robledo, and Liang Xiao. For more information, see
http://ctnt-summer.math.uconn.edu/

Views: 611
UConn Mathematics

Views: 404
UConn Mathematics

Elliptic curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. One of the main benefits in comparison with non-ECC cryptography is the same level of security provided by keys of smaller size.
Elliptic curves are applicable for encryption, digital signatures, pseudo-random generators and other tasks. They are also used in several integer factorization algorithms that have applications in cryptography, such as Lenstra elliptic curve factorization.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 2863
Audiopedia

Views: 389
UConn Mathematics

Math 706 Section 5.3
The Jacobi Symbol

Views: 2000
Todd Cochrane

slides for this lecture: http://swc-alpha.math.arizona.edu/video/2018/2018CoatesLecture1Slides.pdf
lecture notes: http://swc.math.arizona.edu/aws/2018/2018CoatesNotes.pdf
CLASSICAL ALGEBRAIC IWASAWA THEORY.
JOHN COATES
If one wants to learn Iwasawa theory, the starting point has to be the basic
material covered in §1 - §8 of Iwasawa’s paper [1]. The aim of these lectures will
be to give a concise account of this work, concentrating on proving one of the
main results of the paper, which is the so called weak Leopoldt conjecture for the
cyclotomic Zp-extension of any number field, i.e. that the p-adic defect of Leopoldt
is always bounded as one goes up the cyclotomic Zp-extension. The course will also
include a brief introduction to the notion of the Iwasawa algebra of Zp, and the
structure theory of modules for this Iwasawa algebra. The background required for
the lectures will be basic algebraic number theory, including a knowledge of the
main facts of abelian global class field theory.
References
[1] K. Iwasawa On Zl-extensions of algebraic number fields, Ann. of Math. 98 (1973), 246-
326.
[2] J. Coates Infinite descent on elliptic curves with complex multiplication, in Arithmetic
and Geometry, Progress in Mathematics 35 (1983), Birkhauser, 107-137.
http://swc.math.arizona.edu/index.html

Views: 988
Graduate Mathematics

How to write a program to encrypt a message in Mathematica, using linear algebra.

Views: 175
vigvig

Dmitry Orlov
March 10, 2015
Workshop on Chow groups, motives and derived categories
More videos on http://video.ias.edu

Views: 138
Institute for Advanced Study

Here's Fermat's original proof. See the drawing that was too large to fit into margin
.https://www.youtube.com/watch?v=wFyX5uqyLLA&t=157s
I am looking for someone to helpo write proof of beawl conj3ecture. there is a 1 $1,000,000 prize.
This proof has been verified by a former professor of mathematics at Harvard. I am presenting this video in order to get any possible objections.
http://en.wikipedia.org/wiki/Square_root_of_2 Here is one use of irreducible fractions to prove square root of 2 is irrational.
October 23, 2013 The view count is now over 1200. No person has come forth with a counter proof in the last 200 views. So my proof must be correct. Sept. 23, 2013I was waiting until the view count reached 1000 to make this statement, but the statement at 960 view count (September 28, 2013) spurred me to make it now. No one has been able to disprove the Theorem and there has been attempts to disprove the proof that were incorrect. So, I am making the challenge that the proof is correct. There have been a number of people that have read the proof but have been afraid of saying the proof is correct. That includes Sean Gomes. Even the mathematicians at Chapman University have been silent on the veracity of the proof. David B. Moore has tried several times to get faculty to respond, with no success. You can call him at 714-516-4590 to verify this for yourself.
Ferrmat's Dilemma The problem with this proof is that it may be possible for the larger denominator that makes the presumed smallest ratio for the rational number, in front of the term (x^n-1 + y^n-1), divides into this term perfectly. So which number is the real ratio? Is the proof really dependent on the language used? This question is what prompted Fermat to go on to prove the case for n=4, I am sure.
August 16, 2013 Dear reader
Look at what Sean Gomes has written about you
"Youtube is not a system for peer review. That is like asking a deaf man to distinguish mozart from cannibal corpse."
All you have to do to prove him wrong is to invoke social media intelligence. retweet this link or post on facebook, etc.
This is a solution using infinite descent along with Diophantine equations, a technique used by Fermat in many other theorems. This probably is the proof that he thought of, and it only uses very simple math.
I prayed to God for the answer for the proof. He has delivered once again. This time I am remembering that he did it.
July 17, 2013
My friend, Mike Slack, mentioned that I misused the term 'infinite descent in the proof. I did go back and check and the term was misused. Fortunately, infinite descent is not used in the proof. In thinking back on this mistake, I think I was seeing how Fermat started looking at this as a possible path to proof with infinite descent and discovered that the square of factor was double that of the calculated rational ratio, like I did.Thanks to Mike, I am able to explain this inconsistency.
If you get smarter like I did, here is a video on how to do it.
http://youtu.be/Dn0awOfrgBk
I am attempting another impossible task, creating a space elevator. Here is a link to the contest I am in.
http://contest.techbriefs.com/2013/entries/aerospace-and-defense/3823

Views: 10125
michael weir

What is EPHEMERAL KEY? What does EPHEMERAL KEY mean? EPHEMERAL KEY meaning - EPHEMERAL KEY definition - EPHEMERAL KEY explanation.
Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
SUBSCRIBE to our Google Earth flights channel - https://www.youtube.com/channel/UC6UuCPh7GrXznZi0Hz2YQnQ
A cryptographic key is called ephemeral if it is generated for each execution of a key establishment process. In some cases ephemeral keys are used more than once, within a single session (e.g., in broadcast applications) where the sender generates only one ephemeral key pair per message and the private key is combined separately with each recipient's public key. Contrast with a static key.
Private ephemeral key agreement key: Private ephemeral key agreement keys are the private keys of asymmetric key pairs that are used only once to establish one or more keys (e.g., key wrapping keys, data encryption keys, or MAC keys) and, optionally, other keying material (e.g., Initialization Vectors).
Public ephemeral key agreement key: Public ephemeral key agreement keys are the public keys of asymmetric key pairs that are used in a single key establishment transaction to establish one or more keys (e.g., key wrapping keys, data encryption keys, or MAC keys) and, optionally, other keying material (e.g., Initialization Vectors).

Views: 1112
The Audiopedia

A High-Speed FPGA Implementation of an RSD-Based ECC Processor
2015 VLSI Project Training
Contact: IIS TECHNOLOGIES
ph:9952077540,landline:044 42637391
mail:[email protected]
www.iistechnologies.in

Views: 171
IIS Technologies

FLT Proof is given in simple way which can be easily followed by UG students as well.

Views: 3423
Sadasivan Haridasan

slides for this lecture: http://swc-alpha.math.arizona.edu/video/2018/2018CoatesLecture3Slides.pdf
lecture notes: http://swc.math.arizona.edu/aws/2018/2018CoatesNotes.pdf
CLASSICAL ALGEBRAIC IWASAWA THEORY.
JOHN COATES
If one wants to learn Iwasawa theory, the starting point has to be the basic
material covered in §1 - §8 of Iwasawa’s paper [1]. The aim of these lectures will
be to give a concise account of this work, concentrating on proving one of the
main results of the paper, which is the so called weak Leopoldt conjecture for the
cyclotomic Zp-extension of any number field, i.e. that the p-adic defect of Leopoldt
is always bounded as one goes up the cyclotomic Zp-extension. The course will also
include a brief introduction to the notion of the Iwasawa algebra of Zp, and the
structure theory of modules for this Iwasawa algebra. The background required for
the lectures will be basic algebraic number theory, including a knowledge of the
main facts of abelian global class field theory.
References
[1] K. Iwasawa On Zl-extensions of algebraic number fields, Ann. of Math. 98 (1973), 246-
326.
[2] J. Coates Infinite descent on elliptic curves with complex multiplication, in Arithmetic
and Geometry, Progress in Mathematics 35 (1983), Birkhauser, 107-137.
http://swc.math.arizona.edu/index.html

Views: 92
Graduate Mathematics

Launchpad Accelerator Engineer Bootcamp 2018 → http://bit.ly/2G1w5py
Ananth Raghunathan is a computer scientist broadly interested in cryptography, security, and
machine learning. At Google, he works in the security and privacy research team in Google Brain
on differential privacy, applied crypto, and topics at the intersection of security and machine
learning.
About Launchpad Accelerator:
Launchpad Accelerator is an acceleration program for the world’s top startups. Founders work closely with Google and Alphabet product teams and experts to solve specific technical challenges and optimize their businesses for growth with machine learning. Accelerator Startups are selected to be a part of the four month product acceleration program. Each startup is paired with a Google product manager to accelerate their product development, working alongside Google’s ML research and development teams. Learn more at → https://goo.gl/qFTrKD
About Accelerator’s Engineering Bootcamp:
Accelerator’s Engineering Bootcamp brings together each startup’s project team for a four-day event in San Francisco to learn best practices in experimenting, building, and implementing advanced tech within their startup. The teams are composed of Founders and VPs along with developers, data scientists, and product managers.
Watch more in this playlist → http://bit.ly/2G1w5py
Subscribe to Launchpad to learn all about startups → http://bit.ly/Launchpad9

Views: 145
Google Developers Launchpad

Math 313: Introduction to Number Theory: Lecture 23: April 14, 2017: Method of Descent for Fermat and Introduction to p-adics

Views: 131
Steven Miller

Go to http://fly.thruhere.net to download the game and play online for free.

Views: 8406
sir fleshmorph

The Solitude of Prime Numbers (Music from the Film and Inspired By the Book)

Views: 4368
MissMachine

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:
- 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
"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

I interview Keith Hunter regarding his latest research on Megalithic monuments and how they are linked to secret military bases.
his website: http://www.occultphysics.com/
KERRY CASSIDY
http://projectcamelot.tv

Views: 19224
Project Camelot