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Algebraic geometric codes and their applications - Gil Cohen
 
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Computer Science/Discrete Mathematics Seminar Topic: Algebraic geometric codes and their applications Speaker: Gil Cohen Affiliation: Princeton University For more videos, visit http://video.ias.edu
Cryptographic Problems in Algebraic Geometry Lecture
 
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AGNES is a series of weekend workshops in algebraic geometry. One of our goals is to introduce graduate students to a broad spectrum of current research in algebraic geometry. AGNES is held twice a year at participating universities in the Northeast. Lecture presented by Kristin Lauter.
Views: 1607 Brown University
Cryptography for Everyone: John Voight at TEDxUVM
 
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(NOTE: This new upload has improved audio; the initial upload had 267 views) JOHN VOIGHT John Voight is an assistant professor of mathematics and computer science. His research interests include computational and algorithmic aspects of number theory and arithmetic algebraic geometry, with applications in cryptography and coding theory. About TEDx In the spirit of ideas worth spreading, TEDx is a program of local, self-organized events that bring people together to share a TED-like experience. At a TEDx event, TEDTalks video and live speakers combine to spark deep discussion and connection in a small group. These local, self-organized events are branded TEDx, where x = independently organized TED event. The TED Conference provides general guidance for the TEDx program, but individual TEDx events are self-organized.* (*Subject to certain rules and regulations)
Views: 2159 TEDx Talks
Tanja Lange - Code-Based Cryptography
 
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Title: Code-Based Cryptography Speaker: Tanja Lange (Technische Universiteit Eindhoven) 2016 Post-Quantum Cryptography Winter School https://pqcrypto2016.jp/winter/
Views: 1389 PQCrypto 2016
Cryptography: From Mathematical Magic to Secure Communication
 
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Dan Boneh, Stanford University Theoretically Speaking Series http://simons.berkeley.edu/events/theoretically-speaking-dan-boneh Theoretically Speaking is produced by the Simons Institute for the Theory of Computing, with sponsorship from the Mathematical Sciences Research Institute (MSRI) and Berkeley City College. These presentations are supported in part by an award from the Simons Foundation.
Views: 14387 Simons Institute
The Math Needed for Computer Science
 
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►Support the Channel Patreon: https://patreon.com/majorprep PayPal: https://www.paypal.me/majorprep 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. Join Facebook Group: https://www.facebook.com/groups/majorprep/ Follow MajorPrep on Twitter: https://twitter.com/MajorPrep1 ►Check out the MajorPrep Amazon Store: https://www.amazon.com/shop/majorprep *************************************************** ► 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: 251250 MajorPrep
Alena Pirutka: Algebraic cycles on varieties over finite fields
 
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Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area Let X be a projective variety over a field k. Chow groups are defined as the quotient of a free group generated by irreducible subvarieties (of fixed dimension) by some equivalence relation (called rational equivalence). These groups carry many information on X but are in general very difficult to study. On the other hand, one can associate to X several cohomology groups which are "linear" objects and hence are rather simple to understand. One then construct maps called "cycle class maps" from Chow groups to several cohomological theories. In this talk, we focus on the case of a variety X over a finite field. In this case, Tate conjecture claims the surjectivity of the cycle class map with rational coefficients; this conjecture is still widely open. In case of integral coefficients, we speak about the integral version of the conjecture and we know several counterexamples for the surjectivity. In this talk, we present a survey of some well-known results on this subject and discuss other properties of algebraic cycles which are either proved or expected to be true. We also discuss several involved methods. Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' » the May 18, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
What is Modular Arithmetic - Introduction to Modular Arithmetic - Cryptography - Lesson 2
 
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Modular Arithmetic is a fundamental component of cryptography. In this video, I explain the basics of modular arithmetic with a few simple examples. Learn Math Tutorials Bookstore http://amzn.to/1HdY8vm Donate - http://bit.ly/19AHMvX
Views: 143403 Learn Math Tutorials
Alexander Vardy - What's New and Exciting in Algebraic and Combinatorial Coding Theory?
 
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2006 ISIT Plenary Talk What's New and Exciting in Algebraic and Combinatorial Coding Theory? Alexander Vardy University of California San Diego We will survey the field of algebraic and combinatorial coding theory, in an attempt to answer the question in the title. In particular, we shall revisit classical problems that are yet unsolved, review promising advances in the past decade, elaborate upon recent connections to other areas, and speculate what may lie ahead for the field.
Competitive Programming LIVE - Number Theory Revision Webinar
 
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Join Complete Course - https://online.codingblocks.com/courses/competitive-programming-course-online Use Code - FIFACB to get flat 1000 OFF. Join Complete Course - https://online.codingblocks.com/courses/competitive-programming-course-online Use Code - FIFACB to get flat 1000 OFF. In this webinar, Prateek Bhayia discussed about Inclusion Exclusion Principle using Bitmasking, Number Theory Concepts like Fermats Theorem, Extended Euclidean Thm, Multiplicative Modulo Inverse, Totient and Chinese Remainder Theorem. Join the complete course to the all the tutorials. :)
Views: 1980 Coding Blocks
Marc Hindry: Brauer-Siegel theorem and analogues for varieties over global fields
 
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Abstract: The classical Brauer-Siegel theorem can be seen as one of the first instances of description of asymptotical arithmetic: it states that, for a family of number fields Ki, under mild conditions (e.g. bounded degree), the product of the regulator by the class number behaves asymptotically like the square root of the discriminant. This can be reformulated as saying that the Brauer-Siegel ratio log(hR)/ logD‾‾√ has limit 1. Even if some of the fundamental problems like the existence or non-existence of Siegel zeroes remains unsolved, several generalisations and analog have been developed: Tsfasman-Vladuts, Kunyavskii-Tsfasman, Lebacque-Zykin, Hindry-Pacheco and lately Griffon. These analogues deal with number fields for which the limit is different from 1 or with elliptic curves and abelian varieties either for a fixed variety and varying field or over a fixed field with a family of varieties. Recording during the thematic meeting : "Arithmetic, Geometry, Cryptography and Coding Theory" the June 20, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area
Algebraic Geometric Codes (1 of 5)
 
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Peter Beelen, Techical University of Denmark, Denmark Clase 1 (1 de agosto de 2011). ELGA 2011. Escuela CIMPA-ICTP-UNESCO-MICINN-Santaló de Geometría Algebraica y Aplicaciones. Buenos Aires, Agosto 1-5, 2011.
Views: 249 Difusión DM
1.1.2 Intro to Proofs: Part 1
 
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MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 36677 MIT OpenCourseWare
The Mathematics of Lattices II
 
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Vinod Vaikuntanathan, Massachusetts Institute of Technology Cryptography Boot Camp http://simons.berkeley.edu/talks/vinod-vaikuntanathan-2015-05-18b
Views: 2886 Simons Institute
14th ALGA meeting - Ethan Cotterill (UFF)
 
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14th ALGA meeting - Commutative Algebra and Algebraic Geometry Ethan Cotterill (UFF) Algebraic Geometric Codes on Kummer Extensions Página do Programa: http://www.impa.br/opencms/en/eventos/store_2017/evento_1704 Download dos Vídeos: http://video.impa.br/index.php?page=14th-alga-meeting For twenty years, the ALGA meetings have been bringing together the Brazilian community of Commutative Algebra and Algebraic Geometry, and its foreign collaborators. They have been fundamental for the consolidation and strengthening of the research group. The 14th edition of ALGA celebrates its 20th anniversary. The program includes invited lectures and sessions of "Presentations by Young Researchers". Young researchers and Ph.D. students interested in making a presentation can submit a proposal through the registration form below. IMPA - Instituto de Matemática Pura e Aplicada © http://www.impa.br | http://video.impa.br
Ernst-Ulrich Gekeler: Algebraic curves with many rational points over non-prime finite fields
 
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Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area We construct curves over finite fields with properties similar to those of classical elliptic or Drinfeld modular curves (as far as elliptic points, cusps, ramification, ... are concerned), but whose coverings have Galois groups of type GL(r) over finite rings (r≥3) instead of GL(2). In the case where the finite field is non-prime, there results an abundance of series or towers with a large ratio "number of rational points/genus". The construction relies on higher-rank Drinfeld modular varieties and the supersingular trick and uses mainly rigid-analytic techniques. Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' the May 19, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
Geometry and Number Theory By Kevin Charles Atienza | Indian Programming Camp 2016
 
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You may download the slides referred in the video here: https://docs.google.com/presentation/d/1242hfrxTJ1PpHlKymZHExis9PeH5OBi9UtZL8cKX04M/edit?usp=sharing The lecture was conducted on the Day 3 of the training camp. More details about the series of lectures and assignments given on Day 3 can be found here: https://blog.codechef.com/2016/07/17/snackdown-training-camp-day-3/
Views: 8013 CodeChef
Applied Number Theory
 
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Learn more at: http://www.springer.com/978-3-319-22320-9. First book that covers all four areas: cryptography, coding theory, quasi-Monte Carlo methods, pseudo-random numbers. Contains material for courses on number theory, cryptography, coding theory and quasi-Monte Carlo methods. Builds a bridge from basic number theory to recent research in applied number theory.
Views: 122 SpringerVideos
Quantum Computing for Computer Scientists
 
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This talk discards hand-wavy pop-science metaphors and answers a simple question: from a computer science perspective, how can a quantum computer outperform a classical computer? Attendees will learn the following: - Representing computation with basic linear algebra (matrices and vectors) - The computational workings of qbits, superposition, and quantum logic gates - Solving the Deutsch oracle problem: the simplest problem where a quantum computer outperforms classical methods - Bonus topics: quantum entanglement and teleportation The talk concludes with a live demonstration of quantum entanglement on a real-world quantum computer, and a demo of the Deutsch oracle problem implemented in Q# with the Microsoft Quantum Development Kit. This talk assumes no prerequisite knowledge, although comfort with basic linear algebra (matrices, vectors, matrix multiplication) will ease understanding. See more at https://www.microsoft.com/en-us/research/video/quantum-computing-computer-scientists/
Views: 132389 Microsoft Research
Algebra I Research/Work
 
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Amanda Ysasi, Algebra I teacher from Harts Bluff ISD, shares her experiences with using ELM in her Algebra I class.
Views: 647 engage2learn
COLLOQUIUM: Foundations of Lattice-based Cryptography (November 2017)
 
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Speaker: Divesh Aggarwal, Centre for Quantum Technologies, NUS Abstract: Lattice-based cryptosystems are perhaps the most promising candidates for post-quantum cryptography as they have strong security proofs based on worst-case hardness of computational lattice problems and are efficient to implement due to their parallelizable structure. Attempts to solve lattice problems by quantum algorithms have been made since Shor’s discovery of the quantum factoring algorithm in the mid-1990s, but have so far met with little success if any at all. The main difficulty is that the periodicity finding technique, which is used in Shor’s factoring algorithm and related quantum algorithms, does not seem to be applicable to lattice problems. In this talk, I will survey some of the main developments in lattice cryptography over the last decade or so. The main focus will be on the Learning With Errors (LWE) and the Short Integer Solution (SIS) problems, their ring-based variants, their provable hardness under the intractability assumptions of lattice problems and their cryptographic applications.
Field theory (mathematics) | Wikipedia audio article
 
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This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Field_(mathematics) 00:02:01 1 Definition 00:02:50 1.1 Classic definition 00:02:54 1.2 Alternative definition 00:03:50 2 Examples 00:04:09 2.1 Rational numbers 00:04:29 2.2 Real and complex numbers 00:05:12 2.3 Constructible numbers 00:05:37 2.4 A field with four elements 00:05:47 3 Elementary notions 00:06:48 3.1 Consequences of the definition 00:06:52 3.2 The additive and the multiplicative group of a field 00:07:01 3.3 Characteristic 00:11:22 3.4 Subfields and prime fields 00:12:09 4 Finite fields 00:13:16 5 History 00:15:07 6 Constructing fields 00:15:52 6.1 Constructing fields from rings 00:16:05 6.1.1 Field of fractions 00:16:56 6.1.2 Residue fields 00:17:13 6.2 Constructing fields within a bigger field 00:17:24 6.3 Field extensions 00:17:51 6.3.1 Algebraic extensions 00:18:02 6.3.2 Transcendence bases 00:18:17 6.4 Closure operations 00:19:52 7 Fields with additional structure 00:21:44 7.1 Ordered fields 00:22:30 7.2 Topological fields 00:23:25 7.2.1 Local fields 00:24:13 7.3 Differential fields 00:24:50 8 Galois theory 00:25:35 9 Invariants of fields 00:26:00 9.1 Model theory of fields 00:26:17 9.2 The absolute Galois group 00:27:04 9.3 K-theory 00:28:27 10 Applications 00:31:49 10.1 Linear algebra and commutative algebra 00:31:59 10.2 Finite fields: cryptography and coding theory 00:33:20 10.3 Geometry: field of functions 00:35:47 10.4 Number theory: global fields 00:36:50 11 Related notions 00:37:44 11.1 Division rings 00:38:48 12 Notes 00:39:25 13 References 00:39:42 Algebraic extensions 00:42:28 Transcendence bases 00:43:55 Closure operations 00:46:22 Fields with additional structure 00:46:43 Ordered fields 00:47:53 x2 NaN:NaN:NaN xn NaN:NaN:NaN Topological fields NaN:NaN:NaN Local fields NaN:NaN:NaN Differential fields NaN:NaN:NaN Galois theory NaN:NaN:NaN X5 − 4X + 2 (and E NaN:NaN:NaN Invariants of fields NaN:NaN:NaN Model theory of fields NaN:NaN:NaN The absolute Galois group NaN:NaN:NaN H2(F, Gm). NaN:NaN:NaN K-theory NaN:NaN:NaN F×. Matsumoto's theorem shows that K2(F) agrees with K2M(F). In higher degrees, K-theory diverges from Milnor K-theory and remains hard to compute in general. NaN:NaN:NaN Applications NaN:NaN:NaN === Linear algebra and commutative algebra NaN:NaN:NaN bhas a unique solution x in F, namely x NaN:NaN:NaN Finite fields: cryptography and coding theory NaN:NaN:NaN x3 + ax + b.Finite fields are also used in coding theory and combinatorics. NaN:NaN:NaN Geometry: field of functions NaN:NaN:NaN Number theory: global fields NaN:NaN:NaN Related notions NaN:NaN:NaN Division rings Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago. Learning by listening is a great way to: - increases imagination and understanding - improves your listening skills - improves your own spoken accent - learn while on the move - reduce eye strain Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone. Listen on Google Assistant through Extra Audio: https://assistant.google.com/services/invoke/uid/0000001a130b3f91 Other Wikipedia audio articles at: https://www.youtube.com/results?search_query=wikipedia+tts Upload your own Wikipedia articles through: https://github.com/nodef/wikipedia-tts Speaking Rate: 0.8818678708892833 Voice name: en-US-Wavenet-D "I cannot teach anybody anything, I can only make them think." - Socrates SUMMARY ======= In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure, which is widely used in algebra, number theory and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as fields of rational functions, algebraic function fields, algebraic number fields, and p-adic fields are commonly used and studied in mathematics, particularly in number theory and algebraic geometry. Most cryptographic protocols rely on finite fields, i.e., fields with finitely many elements. The relation of two fields is expressed by the notion of a field extension. Galois theory, initiated by Évariste Galois in the 1830s, is devoted to understanding the symmetries of field extensions. Among other results, this theory shows that angle trisection and squaring the circle can not be done with a compass and straightedge. Moreover, it shows that quintic equations are algebraically unsolvable. Fields serve as foundational notion ...
Views: 3 wikipedia tts
Lattices with Symmetry
 
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Alice Silverberg, UC Irvine The Mathematics of Modern Cryptography http://simons.berkeley.edu/talks/alice-silverberg-2015-07-09
Views: 256 Simons Institute
Coding theory
 
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Coding theory is the study of the properties of codes and their fitness for a specific application. Codes are used for data compression, cryptography, error-correction and more recently also for network coding. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction of errors in the transmitted data. This video is targeted to blind users. Attribution: Article text available under CC-BY-SA Creative Commons image source in video
Views: 316 Audiopedia
Introduction to Geometric (Clifford) Algebra.
 
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Introduction to Geometric (Clifford) algebra. Interpretation of products of unit vectors, rules for reducing products of unit vectors, and the axioms that justify those rules.
Views: 3099 Peeter Joot
Field (mathematics) | Wikipedia audio article
 
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This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Field_(mathematics) 00:01:55 1 Definition 00:02:42 1.1 Classic definition 00:02:46 1.2 Alternative definition 00:03:39 2 Examples 00:03:56 2.1 Rational numbers 00:04:15 2.2 Real and complex numbers 00:04:56 2.3 Constructible numbers 00:05:20 2.4 A field with four elements 00:05:30 3 Elementary notions 00:06:27 3.1 Consequences of the definition 00:06:31 3.2 The additive and the multiplicative group of a field 00:06:41 3.3 Characteristic 00:10:35 3.4 Subfields and prime fields 00:11:19 4 Finite fields 00:12:23 5 History 00:14:09 6 Constructing fields 00:14:52 6.1 Constructing fields from rings 00:15:04 6.1.1 Field of fractions 00:15:52 6.1.2 Residue fields 00:16:08 6.2 Constructing fields within a bigger field 00:16:19 6.3 Field extensions 00:16:45 6.3.1 Algebraic extensions 00:16:56 6.3.2 Transcendence bases 00:17:11 6.4 Closure operations 00:18:41 7 Fields with additional structure 00:20:27 7.1 Ordered fields 00:21:11 7.2 Topological fields 00:22:04 7.2.1 Local fields 00:22:50 7.3 Differential fields 00:23:26 8 Galois theory 00:24:10 9 Invariants of fields 00:24:34 9.1 Model theory of fields 00:24:50 9.2 The absolute Galois group 00:25:37 9.3 K-theory 00:26:54 10 Applications 00:30:06 10.1 Linear algebra and commutative algebra 00:30:16 10.2 Finite fields: cryptography and coding theory 00:31:33 10.3 Geometry: field of functions 00:33:50 10.4 Number theory: global fields 00:34:50 11 Related notions 00:35:41 11.1 Division rings 00:36:42 12 Notes 00:37:17 13 References 00:37:34 Algebraic extensions 00:40:09 Transcendence bases 00:41:31 Closure operations 00:43:51 Fields with additional structure 00:44:11 Ordered fields 00:45:17 x2 NaN:NaN:NaN xn NaN:NaN:NaN Topological fields NaN:NaN:NaN Local fields NaN:NaN:NaN Differential fields NaN:NaN:NaN Galois theory NaN:NaN:NaN X5 − 4X + 2 (and E NaN:NaN:NaN Invariants of fields NaN:NaN:NaN Model theory of fields NaN:NaN:NaN The absolute Galois group NaN:NaN:NaN H2(F, Gm). NaN:NaN:NaN K-theory NaN:NaN:NaN F×. Matsumoto's theorem shows that K2(F) agrees with K2M(F). In higher degrees, K-theory diverges from Milnor K-theory and remains hard to compute in general. NaN:NaN:NaN Applications NaN:NaN:NaN === Linear algebra and commutative algebra NaN:NaN:NaN bhas a unique solution x in F, namely x NaN:NaN:NaN Finite fields: cryptography and coding theory NaN:NaN:NaN x3 + ax + b.Finite fields are also used in coding theory and combinatorics. NaN:NaN:NaN Geometry: field of functions NaN:NaN:NaN Number theory: global fields NaN:NaN:NaN Related notions NaN:NaN:NaN Division rings Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago. Learning by listening is a great way to: - increases imagination and understanding - improves your listening skills - improves your own spoken accent - learn while on the move - reduce eye strain Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone. Listen on Google Assistant through Extra Audio: https://assistant.google.com/services/invoke/uid/0000001a130b3f91 Other Wikipedia audio articles at: https://www.youtube.com/results?search_query=wikipedia+tts Upload your own Wikipedia articles through: https://github.com/nodef/wikipedia-tts Speaking Rate: 0.9588288041795844 Voice name: en-US-Wavenet-E "I cannot teach anybody anything, I can only make them think." - Socrates SUMMARY ======= In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure, which is widely used in algebra, number theory and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as fields of rational functions, algebraic function fields, algebraic number fields, and p-adic fields are commonly used and studied in mathematics, particularly in number theory and algebraic geometry. Most cryptographic protocols rely on finite fields, i.e., fields with finitely many elements. The relation of two fields is expressed by the notion of a field extension. Galois theory, initiated by Évariste Galois in the 1830s, is devoted to understanding the symmetries of field extensions. Among other results, this theory shows that angle trisection and squaring the circle can not be done with a compass and straightedge. Moreover, it shows that quintic equations are algebraically unsolvable. Fields serve as foundational notion ...
Views: 1 wikipedia tts
Felipe Voloch:  Maps between curves and diophantine obstructions
 
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Abstract: Given two algebraic curves X, Y over a finite field we might want to know if there is a rational map from Y to X. This has been looked at from a number of perspectives and we will look at it from the point of view of diophantine geometry by viewing the set of maps as X(K) where K is the function field of Y. We will review some of the known obstructions to the existence of rational points on curves over global fields, apply them to this situation and present some results and conjectures that arise. Recording during the thematic meeting : "Arithmetic, Geometry, Cryptography and Coding Theory" the June 20, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area
Group Multiplication Tables | Cayley Tables  (Abstract Algebra)
 
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When learning about groups, it’s helpful to look at group multiplication tables. Sometimes called Cayley Tables, these tell you everything you need to know to analyze and work with small groups. It’s even possible to use these tables to systematically find all groups of small order! 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: 124409 Socratica
Cryptography research group
 
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This video explores the Cryptography research group at the University of Bristol through an interview with the head of the group, Prof. Nigel Smart.
Aurore Guillevic: Computing discrete logarithms in GF(pn): practical improvement of ...
 
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Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area This talk will focus on the last step of the number field sive algorithm used to compute discrete logarithms in finite fields. We consider here non-prime finite fields of very small extension degree: 1≤n≤6. These cases are interesting in pairing-based cryptography: the pairing output is an element in such a finite field. The discrete logarithm in that finite field must be hard enough to prevent from attacks in a given time (e.g. 10 years). Within the CATREL project we aim to compute DL records in finite fields of moderate size (e.g. in GF(pn) of global size from 600 to 800 bits) to estimate more tightly the hardness of DL in fields of cryptographic size (2048 bits at the moment). The best algorithm known to compute discrete logarithms in large finite fields (with small n) is the number field sieve (NFS) [...] Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' the May 20, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
Coding Theory Lecture
 
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Teaser of my lecture on subspace codes and grassmannian codes held in Silpakorn University in Thailand last November 23.
Views: 34 Virgilio Sison
Lattice (group)
 
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In mathematics, especially in geometry and group theory, a lattice in is a discrete subgroup of which spans the real vector space . Every lattice in can be generated from a basis for the vector space by forming all linear combinations with integer coefficients. A lattice may be viewed as a regular tiling of a space by a primitive cell. Lattices have many significant applications in pure mathematics, particularly in connection to Lie algebras, number theory and group theory. They also arise in applied mathematics in connection with coding theory, in cryptography because of conjectured computational hardness of several lattice problems, and are used in various ways in the physical sciences. For instance, in materials science and solid-state physics, a lattice is a synonym for the "frame work" of a crystalline structure, a 3-dimensional array of regularly spaced points coinciding with the atom or molecule positions in a crystal. More generally, lattice models are studied in physics, often by the techniques of computational physics. This video is targeted to blind users. Attribution: Article text available under CC-BY-SA Creative Commons image source in video
Views: 558 Audiopedia
AG hopes to implement Code Adam in all Guam establishments
 
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Visit our website: www.pacificnewscenter.com
Views: 48 pncnews
Local Correction of Codes and Euclidean Incidence Geometry - Avi Wigderson
 
01:03:06
Avi Wigderson Institute for Advanced Study March 5, 2012 A classical theorem in Euclidean geometry asserts that if a set of points has the property that every line through two of them contains a third point, then they must all be on the same line. We prove several approximate versions of this theorem (and related ones), which are motivated from questions about locally correctable codes and matrix rigidity. The proofs use an interesting combination of combinatorial, algebraic and analytic tools. Joint work with Boaz Barak, Zeev Dvir and Amir Yehudayoff For more videos, visit http://video.ias.edu
Nexus trimester - Alex Sprintson (Texas A&M)
 
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Secure and Reliable Codes for Cooperative Data Exchange Alex Sprintson (Texas A&M) February 09, 2016 Abstract: In many practical settings, a group of clients needs to exchange data over a shared broadcast channel. The goal of cooperative data exchange problem is to find a schedule and an encoding scheme that minimize the total number of transmissions. We focus a wide range of practical settings in which the communication is performed in the presence of unreliable clients as well as in the presence of active and passive adversaries. In such settings, the problem of finding an efficient code is computationally intractable (NP-hard). Accordingly, we present approximation schemes with provable performance guarantees. We also focus on the design of coding schemes that achieve weak security, i.e., prevent the adversary from being able to obtain information about any individual file in the system. The weak security is a low-overhead light-weight approach for protecting users’ data. In contrast to traditional information-theoretic and cryptographic tools, it does not require an exchange of secure keys and does not reduce the capacity of the network. We conjecture that it is possible to linearly transform a Vandermonde matrix to obtain a weakly secure code over a small field. This conjecture admits a number of reformulations that lead to interesting conjectures in algebraic geometry, abstract algebra and number theory.
A Theoretical Approach to Semantic Coding and Hashing
 
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Sanjeev Arora, Princeton University https://simons.berkeley.edu/talks/sanjeev-arora-2016-11-15 Learning, Algorithm Design and Beyond Worst-Case Analysis
Views: 628 Simons Institute
Knots and topology
 
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Daniel Waite, a researcher from the College of Science and Engineering, presents his research in three minutes for the University of Glasgow Three Minute Thesis Competition, College of Science and Engineering heat. http://www.gla.ac.uk/services/rsio/researcherdevelopment/threeminutethesiscompetition/
Introduction to Grobner Bases - Prof. Bernd Sturmfels
 
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Using Grobner bases to perform Gaussian elimination on non-linear systems, apply the Euclidean algorithm to multivariate systems and run the Simplex algorithm in a minimisation problem.
Views: 3676 logicmonkeyuk
Marco Streng: Generators for the group of modular units for Γ1(N) over the rationals
 
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Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area The modular curve Y1(N) parametrises pairs (E,P), where E is an elliptic curve and P is a point of order N on E, up to isomorphism. A unit on the affine curve Y1(N) is a holomorphic function that is nowhere zero and I will mention some applications of the group of units in the talk. The main result is a way of generating generators (sic) of this group using a recurrence relation. The generators are essentially the defining equations of Y1(N) for n[is less than](N+3)/2. This result proves a conjecture of Maarten Derickx and Mark van Hoeij. Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' the May 18, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
Randomness Extraction: A Survey - David Zuckerman
 
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David Zuckerman University of Texas at Austin; Institute for Advanced Study February 7, 2012 A randomness extractor is an efficient algorithm which extracts high-quality randomness from a low-quality random source. Randomness extractors have important applications in a wide variety of areas, including pseudorandomness, cryptography, expander graphs, coding theory, and inapproximability. In this talk, we survey the field of randomness extraction and discuss connections with other areas. For more videos, visit http://video.ias.edu
PotW: Making Polynomials Prime [Number Theory]
 
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If this video is confusing, be sure to check out our blog for the full solution transcript! https://centerofmathematics.blogspot.com/2018/06/problem-of-week-6-12-18-making.html
Andrew Sutherland: Computing the image of Galois representations attached to elliptic curves
 
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Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area Let E be an elliptic curve over a number field K. For each integer n[greater than]1 the action of the absolute Galois group GK:=Gal(K/K) on the n-torsion subgroup E[n] induces a Galois representation ρE,n:GK→ Aut(E[n])⋍GL2(ℤ/nℤ). The representations ρE,n form a compatible system, and after taking inverse limits one obtains an adelic representation ρE:GK→GL2(ℤ̂ ). If E/K does not have CM, then Serre's open image theorem implies that the image of ρE has finite index in GL2(ℤ̂ ); in particular, ρE,ℓ is surjective for all but finitely many primes ℓ. I will present an algorithm that, given an elliptic curve E/K without CM, determines the image of ρE,ℓ in GL2(ℤ/ℓℤ) up to local conjugacy for every prime ℓ for which ρE,ℓ is non-surjective. Assuming the generalized Riemann hypothesis, the algorithm runs in time that is polynomial in the bit-size of the coefficients of an integral Weierstrass model for E. I will then describe a probabilistic algorithm that uses this information to compute the index of ρE in GL2(ℤ̂ ). Recording during the thematic meeting: ''Arithmetics, geometry, cryptography and coding theory'' the May 18, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent

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