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Ments meravellosesMents meravellosesÉvariste Galois: matemàtiques i revolució️ En aquest episodi de Ments Meravelloses, ens endinsem en la breu però revolucionària vida d’Évariste Galois, un geni matemàtic que, amb només 20 anys, va establir les bases de la teoria de grups i va canviar per sempre el camp de l'àlgebra. Amb l'ajuda del catedràtic Luis Dieulefait, expert en teoria de nombres, explorarem com Galois va enfrontar una vida plena de fracassos acadèmics, agitació política i un destí tràgic que acabaria amb un misteriós duel. Uneix-te a nosaltres en aquest viatge per la vida de Galois, un personatge extraordinari en la intersecció en...2024-11-1546 minSteady LadsSteady LadsTruth Terminal Was More Fun When $GOAT Was Pumping w/ Galois CapitalThe Lads are joined by Kevin Zhou (aka @Galois_Capital) for his first podcast appearance in a long while, and they've got a boat-load to chat about. It's the final days before the US election, $GOAT is down—and though it's more fun when the price is going up—we're making our own fun here. In Episode #67 we cover: 00:00 Coming Up on Steady Lads… 01:18 Kevin's Luna Battle 05:38 What's Kevin Been Up To? 09:52 Celestia Unlock 18:51 Blockchain Week In Dubai 22:11 Final Days Before...2024-11-0150 minGeschichten aus der MathematikGeschichten aus der MathematikÉvariste Galois und das tödliche DuellMit gerade einmal 20 Jahren stirbt der französische Mathematiker Évariste Galois an den Folgen eines Pistolenduells — nicht ohne vorher noch schnell die Algebra zu revolutionieren. Die Idee für diesen Podcast ist am MIP.labor entstanden, der Ideenwerkstatt für Wissenschaftsjournalismus zu Mathematik, Informatik und Physik an der Freien Universität Berlin, ermöglicht durch die Klaus Tschira Stiftung. >> Artikel zum Nachlesen: https://detektor.fm/wissen/geschichten-aus-der-mathematik-evariste-galois2024-06-0530 mindetektor.fm | Wissendetektor.fm | WissenÉvariste Galois und das tödliche DuellMit gerade einmal 20 Jahren stirbt der französische Mathematiker Évariste Galois an den Folgen eines Pistolenduells — nicht ohne vorher noch schnell die Algebra zu revolutionieren. Die Idee für diesen Podcast ist am MIP.labor entstanden, der Ideenwerkstatt für Wissenschaftsjournalismus zu Mathematik, Informatik und Physik an der Freien Universität Berlin, ermöglicht durch die Klaus Tschira Stiftung. >> Artikel zum Nachlesen: https://detektor.fm/wissen/geschichten-aus-der-mathematik-evariste-galois2024-06-0530 minASecuritySite PodcastASecuritySite PodcastCryptography Fundamentals 4: Finite Fields (aka Galois Fields)I will bet you, that you have a memory of school where you had the “pleasure” or, most likely, the “nightmare” of performing long addition or long subtraction, and where you had carry overs between columns. The units carried over in the tens, the tens into the hundreds, and so on. And, then, you encountered long multiplication with those ever growing list of numbers.  And, please forgive me, you progressed to long division, and you had that divisor dividing into your number and with the bar along the top, and where you put your result, and which those pes...2023-07-2119 minGeschichten aus der GeschichteGeschichten aus der GeschichteGAG408: Das kurze und tragische Leben des Évariste GaloisEine Geschichte über einen mathematischen Visionär Wir springen in dieser Folge ins Frankreich des frühen 19. Jahrhunderts. Dort wird im Jahr 1811 ein Junge geboren, der im Laufe seines kurzen Lebens die moderne Mathematik nachhaltig prägen wird. Die entsprechende Anerkennung wird ihm dafür aber im Laufe seines kurzen und tragischen Lebens nicht zuteil. Wir sprechen in dieser Folge über Évariste Galois, Begründer der später nach ihm benannten Galoistheorie, dessen tragisches Leben unter mysteriösen Umständen viel zu früh endete. Die erwähnten Bücher sind "Évariste Galois: 1811-1832" von Laura Toti Riga...2023-07-1959 minInterchain.FMInterchain.FMGalois - How Galois Capital Made the Big $LUNA Short, is One of a Few Crypto Hedge Funds Who Came out on Top✨About Galois✨ Galois Capital is a long-standing crypto hedge fund run by a Bitcoin OG, Kevin Zhou. He goes over his highly controversial takes about Ethereum moving to PoS, base layer neutrality, his framework for reasoning about different classes of tokens, and where he believes the space is headed should there be an OFAC chain and permissionless chain paradigm.______________ 💟 SUPPORT iFM If you enjoy this content, please give it a thumbs up and consider subscribing to my channel. If you use Osmosis, Umee, and/or Comdex, you can support...2023-04-172h 05Maths en têteMaths en têteLa dernière nuit d'Evariste Galois🎙️ Vous voulez entendre parler d'un héros romantique, écroché vif, passionné, révolutionnaire ?  Sur Maths en tête, on parle aujourd'hui d'Evariste Galois, le petit prince de la géométrie algébrique. #maths #galois #vulgarisation Pour retrouver mon travail : 📽️ sur YouTube : https://www.youtube.com/channel/UCpbU7mXDloketKRA92AcW7Q?view_as=subscriber  💼 sur mon site :  www.mathsentete.fr  Les sources viennent d'ici : Google Doc  Musiques : Pada & Hyperbol et https://artlist.io/ Contact : morganprof...2022-11-2310 minBuilding Better SystemsBuilding Better SystemsEpisode #22: Eric Daimler — Guaranteeing the Integrity of Data Models with Category TheoryIn this episode, we're joined by Eric Daimler, CEO & co-founder of Conexus AI, Inc, an MIT spin out. We discuss the Conexus software platform, which is built on top of breakthroughs in the mathematics of Category Theory, and how it guarantees the integrity of universal data models. Eric shares real-world examples of applying this approach to various complex industries, such as transportation and logistics, avionics, and energy.Listen to this episode wherever you listen to podcasts. Eric Daimler: https://www.linkedin.com/in/ericdaimler/ Joey Dodds: https://www.linkedin.com/in/joey-dodds-4b462a4...2022-08-1037 minBuilding Better SystemsBuilding Better SystemsEpisode #21: Nikhil Swamy — Fully In Bed With Dependent TypesToday we're joined by Nikhil Swamy, Senior Principal Researcher in the RiSE group at Microsoft Research. We are very excited to hear about what he's been working on. In particular, we're going discuss a language that he's co-created and continually develops called F* (pronounced F star). F* is a dependently typed language that you can both program and prove things about the programs that you write. We'll talk about what makes that language special and unique from other similar languages, as well as some of the applications of F*. Watch all our episodes on the B...2022-06-1048 minThe Parsec PodcastThe Parsec PodcastGalois at the GatesKevin Zhou from Galois Capital, the fabled terra bear, comes on to discuss the collapse of UST and the events of one of the wildest weeks in crypto history.We discussedInitial depeg on curve, how Galois reacted/positionedThe compounding of negative factors led to an accelerated failureGame theory of the decisions made during the collapseLFG reserves and if a alternative collateral structure would have helpedRoman historyLinksLFG ThreadGalois Twitterparsecdisclosure: this is an educational podcast nothing said on here by hosts or guests is financial advice DYOR - on parsec...2022-05-1846 minThe Blockcrunch PodcastThe Blockcrunch PodcastThe Crypto Big Short: How I Predicted the $50B Luna Collapse - Kevin Zhou, Galois Capital, Ep. 197Last week, $60B in value was wiped from crypto in a few days. Not many saw the collapse of Luna coming - even fewer had the guts to bet on it. Since the start of the year, Galois Capital has been openly calling out for the impending fall of Luna and endured the barrage of hate comments until 8th May 2022 - the day that Luna started death spiraling. Kevin Zhou from Galois Capital shares with us: Why he was convinced LUNA would implode How he timed his short trade The 4 high conviction trades Galois...2022-05-171h 02Building Better SystemsBuilding Better SystemsEpisode #20: Ankush Desai — P: The Modeling Language That CouldJoey and Shpat talk with Ankush Desai, a Senior Applied Scientist at AWS and one of the primary developers behind the P language. They dig into uses for P, bug finding, and what it takes for formal methods researchers to build useful tools for applied engineers. Watch all our episodes on the Building Better Systems youtube channel.Ankush Desai: https://www.linkedin.com/in/ankush-desai/ Joey Dodds: https://galois.com/team/joey-dodds/Shpat Morina: https://galois.com/team/shpat-morina/ Galois, Inc.: https://galois.com/ Contact us: podcast@galo...2022-04-2846 minBuilding Better SystemsBuilding Better Systems#19: Steve Weis — Security Shouldn't Be the Last Check BoxIn this episode, we talk with Steve Weis, a Senior Staff Security Engineer at Databricks with extensive knowledge of security, cryptography, and software engineering. Steve shares his experience working for large companies like Google and Facebook and how their security needs differ from start-ups and companies trying to scale. He talks about why he thinks companies should share more about how they design their infrastructure and how they can develop a “security mindset” so even non-security-related roles can contribute to building secure systems. Watch all our episodes on the Building Better Systems youtube channel.Steve Weis...2022-04-1441 minBuilding Better SystemsBuilding Better Systems#18: Jordan Kyriakidis — Helping People Write More Useful RequirementsIn episode #18, we chat with Jordan Kyriakidis, co-founder and CEO of QRA Corp. QRA is developing QVScribe, a product that helps engineers write requirements and analyze those requirements to gauge whether they are framed well and capture the writer's intent.We discuss the impact of writing good, early-stage design requirements, how they impact your system, how to write better requirements, the state of natural language processing, and machine learning for this use case. We also talk about applying those in situations where you need explainability and where ambiguity is unacceptable.Watch all our episodes on...2022-03-0947 minBuilding Better SystemsBuilding Better Systems#17: Iain Whiteside — The Twists and Turns of Validating Neural Networks for Autonomous Driving (Part 2)In this two-part episode, we speak with Iain Whiteside about the challenges and some of the more novel solutions to make autonomous vehicles safer and easier to program. In part 1, we discuss how Ian and his team formalize and check the different actions and situations that a car finds itself in while on the road. In part 2, we discuss how you might validate the accuracy of neural networks that sense the world, and how to mitigate issues that might arise.Watch all our episodes on the Building Better Systems youtube channel.Iain Whiteside: https://www...2022-02-0928 minBuilding Better SystemsBuilding Better Systems#16: Iain Whiteside – Autonomous Driving: Reasoning About the Rules of the Road (Part 1)In this two-part episode, we speak with Iain Whiteside about the challenges and some of the more novel solutions to make autonomous vehicles safer and easier to program. In part 1, we discuss how Ian and his team formalize and check the different actions and situations that a car finds itself in while on the road. In part 2, we discuss how you might validate the accuracy of neural networks that sense the world, and how to mitigate issues that might arise.Watch all our episodes on the Building Better Systems youtube channel.Iain Whiteside: https://www...2022-02-0956 minBuilding Better SystemsBuilding Better Systems#15: Dr. Kathleen Fisher – Sparking the New Age of Formal Verification at DARPAIn this episode, we chat with Dr. Kathleen Fisher, who was chair of the Computer Science department at Tufts University at the time of the interview. We talk about Kathleen’s experience in applying formal methods and PL theory to solve significant practical problems throughout her career. Equally important, we discuss how it came to be that she is practically a pro at golf!Watch all our episodes on the Building Better Systems youtube channel.Dr. Kathleen Fisher: https://www.darpa.mil/staff/dr-kathleen-fisher HACMS: https://www.darpa.mil/program/high-assurance-cyber-military-systems PADS: https://pad...2022-01-1055 minBuilding Better SystemsBuilding Better Systems#14: Leo de Moura — Combining the Worlds of Automated and Interactive Theorem Proving In LeanIn this episode, we talk with Leo de Moura, a principal researcher at Microsoft Research. We’ll dive into his work on Lean, how goals for Lean have evolved, and who can use it. We also discuss how Leo was able to implement such a system without being a programming languages expert.Watch all our episodes on the Building Better Systems youtube channel.Joey Dodds: https://galois.com/team/joey-dodds/ Shpat Morina: https://galois.com/team/shpat-morina/  Leo de Moura: https://www.microsoft.com/en-us/research/people/leonardo/Galois, Inc...2021-12-0345 minCiencia y HumorCiencia y Humor25 de Octubre del 2021 efemerides nace Evariste Galois matemáticoTal día como hoy (25 de Octubre) de 1811 nace Évariste Galois, fue un matemático francés.https://lacienciadejaun.com/blogs/efemerides-cientificas/25-de-octubre-de-1811-nace-evariste-galois-fue-un-matematico-francesSi te gusta nuestro contenido, coméntalo y compártelo con tus amigos , familia, conocidos, redes... y visita nuestra página https://lacienciadejaun.comSi te gusta mas todavía , puedes seguir en nuestras redes sociales;Facebook-- https://www.facebook.com/lacienciadejaunPinterest -- https://www.pinterest.es/lacienciadejaunInstagram -- https://www.instagram.com/lacienciadejaun/Twitter -- https://twitter.com/lacienciadejaun¡Siguenos!Y si...2021-10-2505 minCiencia y HumorCiencia y Humor25 de Octubre del 2021 efemerides nace Evariste Galois matemáticoTal día como hoy (25 de Octubre) de 1811 nace Évariste Galois, fue un matemático francés. https://lacienciadejaun.com/blogs/efemerides-cientificas/25-de-octubre-de-1811-nace-evariste-galois-fue-un-matematico-frances Si te gusta nuestro contenido, coméntalo y compártelo con tus amigos , familia, conocidos, redes... y visita nuestra página https://lacienciadejaun.com Si te gusta mas todavía , puedes seguir en nuestras redes sociales; Facebook-- https://www.facebook.com/lacienciadejaun Pinterest -- https://www.pinterest.es/lacienciadejaun Instagram -- https://www.instagram.com/lacienciadejaun/ Twitter -- https://twitter.com/lacienciadejaun ¡Siguenos! Y si te encanta , también puedes apoyarlo cómo patrono en https://www.patreon...2021-10-2505 minBuilding Better SystemsBuilding Better Systems#13: Rod Chapman – It's Either Automated or It's WrongRod Chapman explains his recent verification of TweetNACL using SPARK/ADA. We discuss how every aspect of his proofs are automated, how the correctness proofs actually enabled better performance after compilation, and higher confidence in some otherwise risky-seeming optimizations.Watch all our episodes on the Building Better Systems youtube channel.Joey Dodds: https://galois.com/team/joey-dodds/ Shpat Morina: https://galois.com/team/shpat-morina/  Rod Chapman: linkedin.com/in/rod-chapman-7b60266https://github.com/rod-chapman/SPARKNaClGalois, Inc.: https://galois.com/Contact us: podcast@galois.co...2021-09-2444 minO MUNDO DOS PLÁSTICOSO MUNDO DOS PLÁSTICOSO problema do plástico nos maresEpisódio da turma do 7 A, Feito por Tiago Peoraro, Cristiano Portela, Felipe dos Santos, Lucas Caroba e Davi Sampaio.2021-08-2703 minO MUNDO DOS PLÁSTICOSO MUNDO DOS PLÁSTICOSPlástico, por que é tão ruim?Episódio criado pela aluna Mariana Morais 7º ano C.2021-08-2701 minO MUNDO DOS PLÁSTICOSO MUNDO DOS PLÁSTICOSO problema do plástico no mundoO plástico é muito presente em qualquer espaço que usamos no nosso dia a dia, mesmo tende um custo benefício muito alto, ele é muito prejudicial ao meio ambiente, tendo causado muitos problemas, que se não forem resolvidos até 2050, o mundo estará perdido. Aprenda como fazer sua parte e o motivo pelo qual é tão perigoso. E se você gostar não esqueça de compartilhar! Espero que gostem!!! Joana Chaves Chiaretto Guerra 7 b2021-08-2701 minBuilding Better SystemsBuilding Better Systems#12: Alex Malozemoff & Marc Rosen – Censorship Circumvention with ROCKY BalboaWe chat with Alex Malozemoff and Marc Rosen about a recently published paper on a novel system for censorship circumvention, and it's corresponding implementation. The paper authors also include James Parker.Watch all our episodes on the Building Better Systems youtube channel.Joey Dodds: https://galois.com/team/joey-dodds/ Shpat Morina: https://galois.com/team/shpat-morina/  Alex Malozemoff: https://galois.com/team/alex-malozemoff/Marc Rosen: https://galois.com/team/marc-rosen/ Paper referenced: Balboa: Bobbing and Weaving Around Network Censorship: https://arxiv.org/abs/2104.05871 2021-08-1230 minBuilding Better SystemsBuilding Better Systems#11: Alastair Reid – Meeting Developers Where They AreAlastair Reid describes Google's efforts to bring formal methods to developers so that they can be useful today. We cover a recent publication describing their approach, Alastair's project to document all of the papers he read for a year, and a prototype tool that they've been building to demonstrate formal verification tools in rust.Watch all our episodes on the Building Better Systems youtube channel.Joey Dodds: https://galois.com/team/joey-dodds/ Shpat Morina: https://galois.com/team/shpat-morina/  Alastair Reid's paper project: https://alastairreid.github.io/RelatedWork/papers/Ru...2021-07-2336 minO MUNDO DOS PLÁSTICOSO MUNDO DOS PLÁSTICOSA Criação Do PlásticoEpisódio criado por: Rodolfo de Araújo - 7° ano B.2021-06-2901 minLearning by WilliamLearning by WilliamWhat is Abstract Algebra? - Rings, Fields, Modules, Lattices, Vector Spaces, Algebras, and Galois TheoryReferences: Galois Theory - Wikipedia https://en.wikipedia.org/wiki/Galois_theory Commutative Ring - Wikipedia https://en.wikipedia.org/wiki/Commutative_ring Commutative Algebra - Wikipedia https://en.wikipedia.org/wiki/Commutative_algebra Commutative Property - Wikipedia https://en.wikipedia.org/wiki/Commutative_property Noncommutative Ring - Wikipedia https://en.wikipedia.org/wiki/Noncommutative_ring Glossary of Ring Theory - Wikipedia https://en.wikipedia.org/wiki/Glossary_of_ring_theory Field...2021-06-2636 minO MUNDO DOS PLÁSTICOSO MUNDO DOS PLÁSTICOSDe onde vem e o que são plásticosmeu nome é Matheus Queiroz Oliveira sou estudante do colégio galois na turma 7B 2021-06-2202 minO MUNDO DOS PLÁSTICOSO MUNDO DOS PLÁSTICOSLinverd Eco MarketNesse episódio as alunas Mariana Ferreira, Helena Rubin, Juliana Castelo e Cecília Moura do 7ºano C do colégio Galois, vão falar sobre o Linveard Eco Market o primeiro supermercado do mundo 100% sem plástico2021-06-2101 minBuilding Better SystemsBuilding Better Systems#10: Gregory Malecha – Formal Methods and Systems Programmers Working TogetherGregory Malecha talks with Joey and Shpat about Bedrock, a startup bringing systems engineers together with formal methods engineers to build some of the most secure and correct systems in the world. Watch all our episodes on the Building Better Systems youtube channel.Joey Dodds: https://galois.com/team/joey-dodds/ Shpat Morina: https://galois.com/team/shpat-morina/  Gregory Malecha: https://www.linkedin.com/in/gregory-malecha-91a71469/https://gmalecha.github.io/Formal Methods for the  Informal Engineer: https://fmie2021.github.io/agenda.html Galois, Inc.: https://galoi...2021-06-1143 minO MUNDO DOS PLÁSTICOSO MUNDO DOS PLÁSTICOSComo o plástico pode ser a pior coisa para a humanidadeBernardo Janiques de Matos Córdova 7B2021-05-2401 minBuilding Better SystemsBuilding Better Systems#9: Tycho Andersen – Commit Log SpelunkingTycho Andersen shares lessons that Linux kernel developers have learned from decades of open-source interactions. We discuss how the open-source community works together to make the Linux kernel better for everyone, and also what it's like to work debugging the kernel.Watch all our episodes on the Building Better Systems Youtube channel.Joey Dodds: https://galois.com/team/joey-dodds/ Shpat Morina: https://galois.com/team/shpat-morina/  Tycho Andersen: https://tycho.pizza/Galois, Inc.: https://galois.com/ Contact us: podcast@galois.com 2021-05-1342 minO MUNDO DOS PLÁSTICOSO MUNDO DOS PLÁSTICOSO MUNDO DOS PLÁSTICOS (Trailer)2021-04-2600 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第28回 (p50-51) 3.2.1 Algebraic Number Theory (ⅳ) Kummer’s ideal numbers録音状態が非常に悪くなっています。 レポート https://akasakas.cool/wp-content/uploads/2021/04/第28回3.2.1-Algebraic-Number-TheoryⅳKummer’s-ideal-numbers-20190923勉強会.pdf 3 History of Ring Theory 3.2 Commutative ring theory 3.2.1 Algebraic Number Theory (ⅳ) Kummer’s ideal numbers  --- Send in a voice message: https://anchor.fm/tecum/message2021-04-2211 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第27回 (p49-50) 3.2.1 Algebraic Number Theory (ⅲ)Binary quadratic formsレポート https://akasakas.cool/wp-content/uploads/2021/04/第27回3.2.1-Algebraic-Number-TheoryⅲBinary-quadratic-forms-20190918勉強会.pdf 3 History of Ring Theory 3.2 Commutative ring theory 3.2.1 Algebraic Number Theory (ⅲ)Binary quadratic forms --- Send in a voice message: https://anchor.fm/tecum/message2021-04-2219 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第26回 (p49) 3.2.1 Algebraic Number Theory (ii) Reciprocity laws https://akasakas.cool/wp-content/uploads/2021/04/第26回3.2.1-Algebraic-Number-Theoryii-Reciprocity-laws20190911勉強会.pdf 3 History of Ring Theory 3.2 Commutative ring theory 3.2.1 Algebraic Number Theory (ii) Reciprocity laws --- Send in a voice message: https://anchor.fm/tecum/message2021-04-2217 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第25回（p47-48）3.2.1 Algebraic Number Theory (ⅰ)Fermat's Last Theorem https://akasakas.cool/wp-content/uploads/2021/04/第25回3.2.1-Algebraic-Number-Theory-ⅰFermats-Last-Theorem-20190828.pdf 3 History of Ring Theory 3.2 Commutative ring theory 3.2.1 Algebraic Number Theory (ⅰ)Fermat's Last Theorem --- Send in a voice message: https://anchor.fm/tecum/message2021-04-2228 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第24回（p45-47）3.1.3-Structureレポート https://akasakas.cool/wp-content/uploads/2021/04/第24回3.1.3-Structure2019082128.pdf --- Send in a voice message: https://anchor.fm/tecum/message2021-04-2223 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第23回（p43-45）3.1.2 Classificationレポート https://akasakas.cool/wp-content/uploads/2021/04/第23回3.1.2-Classification20190821.pdf --- Send in a voice message: https://anchor.fm/tecum/message2021-04-2232 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第22回(p42-43)　3.1.1 Examples of Hypercomplex Number Systemsレポート https://akasakas.cool/wp-content/uploads/2021/04/第22回3.1.1-Examples-of-Hypercomplex-Number-Systems20190814.pdf --- Send in a voice message: https://anchor.fm/tecum/message2021-04-2225 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第21回(p41-42)　3 History of Ring Theory　3.1 Noncommutative ring theoryレポート　https://akasakas.cool/wp-content/uploads/2021/04/第21回3History-of-Ring-Theory20190731.pdf --- Send in a voice message: https://anchor.fm/tecum/message2021-04-2223 minBuilding Better SystemsBuilding Better Systems#8: Eric Davis – Building Better Data ModelsDr. Eric Davis walks us through what it means for a data model to be trustworthy, what common pitfalls predictive models run into, reproducibility issues, and what can be done. We chat about how subject area experts are expected to be many things: statisticians, computer scientists, and mathematicians, and how that can sometimes lead to mistakes. We also look at the COVID-19 pandemic and how data models affect decision-making.https://www.imagwiki.nibib.nih.gov/ https://www.imagwiki.nibib.nih.gov/content/committee-credible-practice-modeling-simulation-healthcare-description https://www.biorxiv.org/content/10.1101/2020.08.07.239855v1 https://www.imagwiki.nibib.nih.gov/content/10-simple-rules-conformance-rubric2021-04-1534 minBuilding Better SystemsBuilding Better Systems#7: Aditya Thakur – “If it goes too slow, they'll turn it off”: Analysis Tools That WorkDr. Aditya Thakur, a computer science professor at U.C. Davis, walks us through his work on developing analysis tools that he wished he had while working in industry at places like Google. Aside from program analysis, we talk about making a research group successful by exposing them to industry. Towards the end, he shares his work on techniques and tools for repairing a trained deep neural network once a mistake has been discovered. Along the way, we learn about things like abstract interpretation, non-determinism, the trickiness of parallelism, and other concepts pertinent to analysis in an approachable way.2021-04-021h 13The Shitcoin.com ShowThe Shitcoin.com ShowCrypto alpha and whale games with Kevin Zhou from Galois Capital"Bulls and bears make money but pigs get slaughtered."   That's just one of the A++ takeaways in this week's episode as Andreas and Blake welcome Kevin Zhou, Co-Founder of Galois Capital! In this alpha-filled episode with Andreas' former roommate we covered:   - If crypto firms have the edge over traditional finance. - Why yield farming has turned into a whale's game. - Risk versus rewards when trading crypto. - Why Kevin doesn't talk about religion, politics or blockchains at dinner parties.   The links:  Check out Galois Capital - https://galois.capi...2021-03-2527 minThe FrayThe FrayThe Man Out Of Time - Evariste Galois Ep.8We change it up in this episode as we start to focus on the genesis of Galois' beloved France. Its a deep dive into prehistoric ultra marathon runners, porn as history, one of the darkest days in Roman history and how it call came down to a flock of geese. Also Happy one year anniversary to The Fray! Thanks as always for listening 2021-03-231h 32Pazzi CuriosiPazzi CuriosiGalois, matematico indomabileLa tragica vita del più irriverente tra i matematici: Évariste Galois.Più che una singola lettura, questa settimana vorrei segnalarvi una squisita raccolta di 5 "gettoni di scienza" dedicati a Galois, composti per Radio 3 da Roberta Fulci. Qui sotto trovate il link:https://www.raiplayradio.it/playlist/2018/07/Radio3-Scienza-Evariste-Galois-ab8ccf46-f142-401a-8c11-d8d71425c727.html2021-03-0613 minLa Quarta Llei de NewtonLa Quarta Llei de NewtonÉvariste Galois: Perseverance, TRa TRaCrits d'eufòria i el Perseverance ja ha "amartat", mentre alguns encara esteu decidint si val la pena documentar bé la vostra feina o no. Aquesta setmana comencem plens d'emoció creuant els dits perquè aquest petit robot que hem enviat no trobi res, pel bé de tots. Meravellats per aquesta fita, repassem les fites dels nanos de segon de batxillerat, comentant alguns dels treballs de recerca més brillants de la història (el TR de la Rosalía el comentarem al proper episodi). I seguint el fil de joves promeses, topem amb la història d'un xaval que més que u...2021-02-2450 minBuilding Better SystemsBuilding Better Systems#6: Dan Guido – What the hell are the blockchain people doing, and why isn't it a dumpster fire?Dan Guido, CEO of Trail of Bits, walks us through how they work with customers to make long-term improvements in security and software quality. He also describes what blockchain has done right, and how the rest of the software world should learn from them.You can watch this episode on our Youtube Channel. https://youtube.com/c/BuildingBetterSystemsPodcastJoey Dodds: https://galois.com/team/joey-dodds/ Shpat Morina: https://galois.com/team/shpat-morina/  Dan Guido: https://www.linkedin.com/in/danguido/Trail of Bits blog: https://blog.trailofbits.com...2021-02-041h 01Building Better SystemsBuilding Better Systems#5: Talia Ringer – Proof Engineering for the PeopleTalia Ringer, a Ph.D. candidate at University of Washington, explains how they do deep people-centric PL research. We discuss proof repair, UX for software correctness, and how to ask users of tools for feedback to react to.You can watch this episode on our Youtube Channel. Joey Dodds: https://galois.com/team/joey-dodds/ Talia Ringer: https://dependenttyp.es/ Contact us: podcast@galois.com Galois, Inc.: https://galois.com/   2021-01-1130 minBuilding Better SystemsBuilding Better Systems#4: Alex Malozemoff – New attack on homomorphic encryption libraries: what does it mean?Principal Researcher, Alex Malozemoff, walks us through what homomorphic encryption is, what CKKS is, and how a recent new attack on CKKS will impact progress on homomorphic encryption.You can watch this episode on our Youtube channel.Galois, Inc.Joey DoddsShpat MorinaAlex MalozemoffOn the Security of Homomorphic Encryption on Approximate Numbers by Baiyu Li and Daniele MicciancioContact us: podcast@galois.com  2020-12-1517 minBuilding Better SystemsBuilding Better Systems#3: Stephen Magill & Tom DuBuisson – Musing on continuous code analysisThe founders of MuseDev discuss making modern static analysis usable and leveraging the latest promising research for automatic bug finding. MuseDev is a spin-off of Galois. Video of this podcast can be found on our Youtube channel: Galois, Inc.: https://galois.com/ Joey Dodds: https://galois.com/team/joey-dodds/ Shpat Morina: https://galois.com/team/shpat-morina/ Muse.dev Tom Dubuisson: https://www.linkedin.com/in/thomas-dubuisson-62910453/ Stephen Magill, https://www.linkedin.com/in/stephen-magill-2070a096/Continuous Reasoning: Scaling the impact of formal methods by Pete...2020-12-031h 00Momentos de Historia de las MatemáticasMomentos de Historia de las MatemáticasGalois el RebeldeEvariste Galois fue un joven genio matemático de la Francia de principios del siglo XIX que murió de forma trágica en un duelo. La leyenda nos dice que la noche antes estuvo recopilando todos sus descubrimientos matemáticos para que se pudieran publicar. Aunque no fue exactamente de este modo, Galois en su corta existencia logró desarrollar una parte importante del álgebra superior. En este audio contamos cómo fueron sus poco más de veinte años de vida.2020-11-291h 00Pillole di MatematicaPillole di MatematicaGaloisTutti i giovani matematici vorrebbero essere Galois, grazie al suo incredibile genio ad appena vent’anni è riuscito a stravolgere il mondo dell’Algebra. Tuttavia il suo carattere sopra le righe e tante ferite aperte lo hanno portato ad essere forse uno dei più grandi rimpianti della storia della matematica.2020-11-2812 minInterdire d\'Interdire – CultureInterdire d'Interdire – Culture#164 – Colonialisme vert, Déclin vert, Érotisme féminin, Piano contemporain – Guillaume Blanc, Yaron Herman, Aurélie Galois, et Silas BassaEnregistré le 12 Novembre 2020  Frédéric Taddeï reçoit Guillaume Blanc, historien de l’environnement, Yaron Herman, pianiste de jazz, Aurélie Galois, peintre, et Silas Bassa, pianiste.  Avec :  Guillaume Blanc, historien de l’environnement, pour son livre « L’invention du colonialisme vert », aux éditions Flammarion  Yaron Herman, pianiste de jazz, pour son livre « Le déclic créatif », chez Fayard  Aurélie Galois, peintre, pour son ouvrage « Bijoux indiscrets »  Silas Bassa, pianiste, pour son troisième album « Silas ».  Source :  https://bit.ly/3EZn3VG2020-11-1255 minInterdire d\'Interdire – CultureInterdire d'Interdire – Culture#164 – Colonialisme vert, Déclin vert, Érotisme féminin, Piano contemporain – Guillaume Blanc, Yaron Herman, Aurélie Galois, et Silas BassaEnregistré le 12 Novembre 2020  Frédéric Taddeï reçoit Guillaume Blanc, historien de l’environnement, Yaron Herman, pianiste de jazz, Aurélie Galois, peintre, et Silas Bassa, pianiste.  Avec :  Guillaume Blanc, historien de l’environnement, pour son livre « L’invention du colonialisme vert », aux éditions Flammarion  Yaron Herman, pianiste de jazz, pour son livre « Le déclic créatif », chez Fayard  Aurélie Galois, peintre, pour son ouvrage « Bijoux indiscrets »  Silas Bassa, pianiste, pour son troisième album « Silas ».  Source :  https://bit.ly/3EZn3VG2020-11-1255 minInterdire d\'Interdire – CultureInterdire d'Interdire – Culture#164 – Colonialisme vert, Déclin vert, Érotisme féminin, Piano contemporain – Guillaume Blanc, Yaron Herman, Aurélie Galois, et Silas BassaEnregistré le 12 Novembre 2020  Frédéric Taddeï reçoit Guillaume Blanc, historien de l’environnement, Yaron Herman, pianiste de jazz, Aurélie Galois, peintre, et Silas Bassa, pianiste.  Avec :  Guillaume Blanc, historien de l’environnement, pour son livre « L’invention du colonialisme vert », aux éditions Flammarion  Yaron Herman, pianiste de jazz, pour son livre « Le déclic créatif », chez Fayard  Aurélie Galois, peintre, pour son ouvrage « Bijoux indiscrets »  Silas Bassa, pianiste, pour son troisième album « Silas ».  Source :  https://bit.ly/3EZn3VG2020-11-1255 minBuilding Better SystemsBuilding Better Systems#2: Jean Yang – "Formal" Methods? How about "Business Casual" Methods? Part 2Video of this podcast can be found on our Youtube channelJean Yang: https://www.linkedin.com/in/jean-yang-96575030/Akita Software: https://www.akitasoftware.com/Galois, Inc.: https://galois.com/Joey Dodds: https://galois.com/team/joey-dodds/Shpat Morina:  https://galois.com/team/shpat-morina/Contact us: marketing@galois.com 2020-10-2835 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第24回(p45-47)　3.1.3 Structureレポート https://akasakas.cool/wp-content/uploads/2021/04/History24_3.1.3-Structure2019082128.pdf 第24回(p45-47) 3 History of Ring Theory 3.1 Noncommutative ring theory 3.1.3 Structure --- Send in a voice message: https://anchor.fm/tecum/message2020-10-2623 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第23回(p43-45)　3.1.2 Classificationレポート https://akasakas.cool/wp-content/uploads/2020/10/History23_3.1.2-Classification20190821.pdf 第23回（p43-45） 3 History of Ring Theory 3.1 Noncommutative ring theory 3.1.2 Classification --- Send in a voice message: https://anchor.fm/tecum/message2020-10-2632 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第22回(p42-43)　3.1.1 Examples of Hypercomplex Number Systemsレポート https://akasakas.cool/wp-content/uploads/2020/10/History22_3.1.1-Examples-of-Hypercomplex-Number-Systems20190814.pdf 第22回（p42-43） 3 History of Ring Theory 3.1 Noncommutative ring theory 3.1.1 Examples of Hypercomplex Number Systems --- Send in a voice message: https://anchor.fm/tecum/message2020-10-2625 minBuilding Better SystemsBuilding Better Systems#1: Jean Yang – "Formal" Methods? How about "Business Casual" Methods? Part 1Video of this podcast can be found on our Youtube channel. Jean Yang: https://www.linkedin.com/in/jean-yang-96575030/Akita Software: https://www.akitasoftware.com/Galois, Inc.: https://galois.com/Joey Dodds: https://galois.com/team/joey-dodds/Shpat Morina:  https://galois.com/team/shpat-morina/Contact us: marketing@galois.com 2020-10-2329 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第21回(p41-42)　3 History of Ring Theory　3.1 Noncommutative ring theoryレポート　https://akasakas.cool/wp-content/uploads/2020/10/History21_3History-of-Ring-Theory20190731.pdf 第21回　 3 History of Ring Theory 3.1 Noncommutative ring theory --- Send in a voice message: https://anchor.fm/tecum/message2020-10-1023 minThe FrayThe FrayThe Man Out Of Time - Evariste Galois Ep. 1We begin new series with a new topic, the short but fascinating life of 19th Century French mathematician Evariste Galois. This is the first episode in a multi part series that will journey to very wellspring of mathematical equations as well as the depths of depravity and terror that was the menacing French Revolution. All to get to the bottom of one of history's most remarkable and mysterious thinkers. So please join me as we enter to the fray-iest of frays with The Man Out of Time. 2020-09-291h 08ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第20回(p35-36)2.5-Divergence-of-developments-in-group-theory第20回(p35-36) レポート　https://akasakas.cool/wp-content/uploads/2020/09/第20回2.5-Divergence-of-developments-in-group-theory20190724勉強会.pdf 第20回(p35-36) カテゴリーA History of Abstract Algebra 2 History of Group Theory 2.5-Divergence-of-developments-in-group-theory --- Send in a voice message: https://anchor.fm/tecum/message2020-09-1416 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第19回(p33-35)2.4-Consolidation-of-the-abstract-group-conceptレポート　https://akasakas.cool/wp-content/uploads/2020/09/第19回2.4-Consolidation-of-the-abstract-group-concept20190717勉強会.pdf カテゴリーA History of Abstract Algebra 第19回(p33-35) 2 History of Group Theory 2.4-Consolidation-of-the-abstract-group-concept --- Send in a voice message: https://anchor.fm/tecum/message2020-09-1044 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第18回(p30-33) 2.3 Emergence of abstraction in group theoryレポートhttps://akasakas.cool/wp-content/uploads/2020/09/第18回2.3-Emergence-of-abstraction-in-group-theory20190703勉強会-1.pdf カテゴリーA History of Abstract Algebra 第18回(p30-33) 2 History of Group Theory 2.3 Emergence of abstraction in group theory ＊p32Another mathematician who advanced the abstract pointから録音はありません。 --- Send in a voice message: https://anchor.fm/tecum/message2020-09-0753 minPodcast Bebas LinearPodcast Bebas Linear#24: Mati Muda Seperti GaloisPada episode ini kami membahas Évariste Galois (baca: Evarist Galwa), matematikawan yang mati muda secara mengenaskan namun menjadi legenda melalui Teori Galois dalam cabang aljabar. Ada juga update review hasil IMC 2020.2020-08-071h 32EmbeddedEmbeddedIntegrity of the Curling ClubDan Zimmerman (@dmz) spoke with us about voting, voting machines, building trust in software, and transparency. Dan works for Galois (https://galois.com/ , @galois) and Free and Fair (https://freeandfair.us/, @free_and_fair). He worked on the US Vote Foundation’s E2E-VIV Project on the Future of Voting. The artifacts from that project are on github: github.com/GaloisInc/e2eviv. Dan (and Galois) worked with Microsoft on ElectionGaurd, a suite of tools to help make elections end-to-end verifiable,  The tools are open source: github.com/microsoft/electionguard The Helios verifiable onl...2020-07-311h 03ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第17回(p28-30) 2.2.3 Transformation Groupsレポート https://akasakas.cool/wp-content/uploads/2020/07/第17回2.2.3-Transformation-Groups20190626勉強会.pdf カテゴリーA History of Abstract Algebra 第17回(p28-30)  2 History of Group Theory 2.2 Development of “specialized” theories of groups 2.2.3 Transformation Groups --- Send in a voice message: https://anchor.fm/tecum/message2020-07-2426 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第16回（p26-27） 2.2 Development of “specialized” theories of groups 2.2.2 Abelian Groups（その2）レポート　https://akasakas.cool/wp-content/uploads/2020/05/第16回2.2.2-Abelian-Groups（その２）20190612勉強会.pdf https://akasakas.cool/　カテゴリーA History of Abstract Algebra 第16回　（p26-27） 2 History of Group Theory 2.2 Development of “specialized” theories of groups  2.2.2 Abelian Groups　アベル群（その2） クロネッカーは、有限の可換群の暗黙の定義を与える過程の中で、「マグニチュード（量）」の結びつきの法則をひねり出すことをめざしていた。 クロネッカー路線は、1879年にフロベニウスとシュティッケルベルガーによって、「交換可能な要素の群について」という重要論文の中で持ち上げられた。 --- Send in a voice message: https://anchor.fm/tecum/message2020-05-141h 04ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第15回（p26-27） 2.2 Development of “specialized” theories of groups 2.2.2 Abelian Groups　（その１）レポート　https://akasakas.cool/wp-content/uploads/2020/05/第15回2.2.2-Abelian-Groups（その１）20190607勉強会.pdf https://akasakas.cool/　カテゴリーA History of Abstract Algebra 第15回　（p26-27） 2 History of Group Theory 2.2 Development of “specialized” theories of groups  2.2.2 Abelian Groups　アベル群（その１） 代数的数論はフェルマー(Pierre de Fermat、1607年 - 1665年)の最終定理(1630年ごろ)；【n を3以上の整数とするとき，xn+yn=zn を満たす正の整数 x,y,z の組は存在しない。】との関係で登場してきた。 1846年にディリクレが代数的数体の単位元units(１位の数)を研究し、ほとんど同じ頃クンマーが“イディアル数（理念的な数）“を導入した。 シェリングは、２項2次形式の同値類の作る可換群に対する一つの基底を見つけた。 クロネッカーは、1870年の論文で、従来よりはるかに抽象的な視点を取ることによって始めた。 --- Send in a voice message: https://anchor.fm/tecum/message2020-05-141h 03ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第14回（p24-26）2.2 Development of “specialized” theories of groups 2.2.1 Permutation Groups（その2）レポート　https://akasakas.cool/wp-content/uploads/2020/05/第14回2.2.1-Permutation-Groups（その2）20190605勉強会.pdf 　https://akasakas.cool/ カテゴリーA History of Abstract Algebra 第14回　（p24-26） 2 History of Group Theory 2.2 Development of “specialized” theories of groups  2.2.1 Permutation Groups（その2）  　19世紀前半における置換理論に対する他の主たる貢献者はコーシーだった。 コーシーが証明した諸定義のうち、(ⅲ)　S3 、S4 、S5 、S6のすべての部分群の決定（S6には間違いがあったけど）がある。ここで、S3の部分群を全てあげよと言う宿題が出た。３！＝６個の要素｛1,2,3,4,5,6｝をどう考える？ コーシーやガロアがいかに偉大であっても、ジョルダンがいなければ今日のコーシーやガロアはいない。 数学に概念的な統合をもたらすということが、ジョルダンの深い希望の表現だった。彼がそのような概念的な統合を達成しようとしたことは、栄光であるとともに限界だった。彼の置換論的な見方は、すぐに変換群としての群の概念に取って代わられることになった。 --- Send in a voice message: https://anchor.fm/tecum/message2020-05-1453 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第13回（p22-23） 2.2 Development of “specialized” theories of groups 2.2.1 Permutation Groups（その1）レポート　https://akasakas.cool/wp-content/uploads/2020/05/第13回2.2.1-Permutation-Groups（その1）20190515勉強会.pdf https://akasakas.cool/ 　カテゴリーA History of Abstract Algebra 第13回　（p22-23） 2 History of Group Theory 2.2 Development of “specialized” theories of groups  2.2.1 Permutation Groups（その1）  　群論の発展における４大起源とは、第１起源 -古典代数  -、第２起源  -数論- 、第３第４起源 -幾何と解析- である。それぞれの期が、置換群論、可換群論、変換群論へと発展してきた。 2.2.1 Permutation Groups 置換群 　ラグランジュ（Joseph-Louis Lagrange, 1736 - 1813）は、5次以上の方程式がベキ根によっては解けないことについても研究し、根の置換など群論の先駆けとなるような研究も行っている。数学史における群論的な思考を暗示する初めての事例だった。  基礎的な概念的な進歩を達成し、多くの人から（置換）群論の創始者とみなされているのはガロア（Évariste Galois, 1811 - 1832）だった。彼は正規部分群の基本的な概念を創り、それを用いて大きな成果をあげた。 　ガロアは二十歳で死んだ。復古王政（1814年ナポレオン没落後、1830年の７月革命まで）の時代にあって、若き数学者の死は革命への参加とも決闘とも言われたが、その名をガロア群として数学の世界に名を残す。 --- Send in a voice message: https://anchor.fm/tecum/message2020-05-1246 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第12回（p21-22）2.1.4 Analysisレポート　https://akasakas.cool/wp-content/uploads/2020/05/第12回2.1.4-Analysis20190510勉強会-.pdf https://akasakas.cool/ カテゴリーA History of Abstract Algebra 第12回　（p21-22） 2 History of Group Theory 2.1.4 Analysis解析 解析関数というのは、多変数関数で微分可能なもの、実関数は微分可能というのだが、一般に複素変数の関数では微分可能と言わないで解析的という。解析的とは、微分可能よりもう少し条件が厳しくて複素平面というかこの場合はn次元上の全てのところでべき級数に展開される、そういうような条件を満たすもの。 リー（Marius Sophus Lie, 1842ー1899）は、自らをアーベル（Niels Henriｋ Abel：１８０２−１８２９享年27歳）、ガロア（Evariste Galois：１８１１−１８３２享年20歳）の後継者と考えていて、連続変換群を定義する。 リーの研究は、ピカール（Charles Émile Picard、1856ー1941）とビジョー（Ernest Vessiot 1865 ー1952)によるリー論のその後の公式化を基礎付けるものだった。 ポアンカレ（Jules-Henri Poincaré 1854ー1912）とクライン（Felix Christian Klein, 1849ー1925）は、1876年頃に「保型関数」とそれらに結びついた群で研究を始めた。 １９世紀初めに若くしてなくなった二人の数学者アーベルとガロアの研究は、１９世紀後半には多くの後継者たちによって、群論として体系化された。 --- Send in a voice message: https://anchor.fm/tecum/message2020-05-1216 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第1 1回 （p20-21）2.1.3 Geometryレポート　https://akasakas.cool/wp-content/uploads/2020/05/第11回2.1.3-Geometry20190503勉強会-.pdf https://akasakas.cool/ カテゴリーA History of Abstract Algebra 第11回　（p20-21） 2 History of Group Theory 2.1.3 Geometry １９世紀の数学の大発見と言えるのが、collineation共線性の発見である。３点が同一直線上にあるという条件で、点A,B,Cがある時、ベクトルAB、ベクトルACに対して、片方はもう片方の実数倍で表される。３本の直線が１点を共有するとき共点という。３点が同一直線上にあることとき共線という。共点と共線は双対（そうつい）といって、射影幾何では同じこと。 クラインは明確に群という考えを出した。クラインのエルランゲンプログラムへ導いたいくつかの背景について、ここで述べている。 --- Send in a voice message: https://anchor.fm/tecum/message2020-05-0544 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第10回 （p19-20）2.1.2 Number Theoryレポート　https://akasakas.cool/wp-content/uploads/2020/05/第10回2.1.2-Number-Theory20190501勉強会.pdf https://akasakas.cool/　カテゴリーA History of Abstract Algebra 第10回　（p19-20） 2 History of Group Theory 2.1.2 Number Theory　数論 ガウスのDisquisitiones Arithmeticae（数論講義）は、数学者たちを19世紀の丸々１００年を支配した。 ガウス記号を知っているよね、と言われても学習した記憶がない。プログラムのintみたいだが、負の数になると違ってくる。集合の概念がつかめなければ、18世紀以前の数学から脱皮できない。 素数５の因数分解は、(2+i)(2-i)となるなんて、なるほど・・・i(アイ)は変身（変心）するものだ。 いよいよ群の登場。４つのパターン。 　mを法とする(mod.m)整数加法群 ５mod.7=5、５＾２mod.7=4、５＾３mod.7=6、５＾４mod.7=2、５＾５mod.7=3、５＾６mod.7=1、５＾７mod.7=5、〜ー＞７乗で戻る！ Φ関数とはどういう関数か？互いに素な自然数の個数のこと。12  と互いに素な 12 以下の自然数の個数は，12=2^2⋅3 より，12(1−1/2)(1−1/3)=4 個。素因数分解がカギ、この公式を覚えるだけじゃダメ、証明できなくちゃ・・・ Z＊p（ゼットピースター）の任意の要素が与えられた時、要素のorder(次数/位数)がp − 1の約数であることを示した。ここがキモ！　例えばpを素数7として整数4の場合を考える。4mod.7=4、4^２mod.7=2、4^３mod.7=1、4^４mod.7=4、4^５mod.7=2、4^６mod.7=1。だから p -1=6の約数3を位数とする要素も単位元となる！　 １のn乗根が巡回群をなしているということが、複素数を勉強して一番嬉しい話である。フェルマーの定理：x2 + y2は４で割ると必ず１余る。これは、ガウスの２次形式論と言って、とてもエレガントな理論である。証明も簡単であると。（私はやっていないが） --- Send in a voice message: https://anchor.fm/tecum/message2020-05-0458 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第９回 （p17-19）2 History of Group Theory　2.1.1 Classical Algebraレポート　https://akasakas.cool/wp-content/uploads/2020/05/第9回2.1.1-Classical-Algebra20190424勉強会.pdf https://akasakas.cool/　カテゴリーA History of Abstract Algebra 2 History of Group Theory 群論の入門編で議論された主な概念の起源、定理、および一般的な理論について概説する。群論の進化に関する「物語ストーリー」は1770年に始まり、20世紀に拡大したが、主要な発展は19世紀に起こった。その世紀の一般的な数学的特徴の一つに、人間の活動としての数学の見方、つまり物理的状況を参照せず、または物理的状況からの動機なしで可能になったこと。これは革命と呼んでもいい。 2.1 Sources of group theory　群論の4つの源 (a) 古典代数（ラグランジュ、1770） (b) 数論Number theory (Gauss, 1801) (c) 幾何Geometry (クラインKlein, 1874) (d) 解析Analysis (Lie, 1874; ポワンカレPoincaré and Klein, 1876) 2.1.1 Classical Algebra古典代数 ラグランジュが1770年「代数方程式の解に関する省察」を書いた当時の代数学の主な問題は、多項式に関するものだった。 そこには根の存在と本質を扱う“理論的な”問題がありました。 方程式の根たちの置換の研究は。代数方程式におけるラグランジュ一般理論の礎となった。この置換の研究は、彼が頭の中で考え、“方程式の解の真の原理”を形成した。たとえば、f（x）が根x1、x2、x3、x4を持つ4次方程式であるならば、R（x1、x2、x3、x4）はx1x2 + x3x4と取ることができ、この関数はx1、x2、x3、x4の24個の置換のもとで異なる値は３個しかとらない。 --- Send in a voice message: https://anchor.fm/tecum/message2020-05-0348 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第８回 （p13-14）1.8 Symbolical algebraレポート　https://akasakas.cool/wp-content/uploads/2020/05/第8回1.8-Symbolical-algebra20190417勉強会.pdf https://akasakas.cool/　カテゴリーA History of Abstract Algebra 第8回　（p13-14） 1.8 Symbolical algebra　記号代数学 負の数と複素数、18世紀（FTAはそれらを不可避にした）において頻繁に使われるけれども、ほとんど理解されなかった。例えば、ニュートンは負の数を、「無より小さい」量と説明し、ライプニッツは、複素数を“存在と不存在の間の両生類”であると言った。オイラーは“ +の記号がついていたら正の量、−の記号がついていたら負の量、と呼ぶ”と主張した。 （−1）（−1）= 1のような負の数の取り扱い規則は、古代から知られていた。けれども過去にはいかなる証明も与えらなかった。18世紀の後半と19世紀始めの間に、数学者たちは、なぜそのような規則が成り立つのかということに疑問を持ち始めた。 この話題についての最も包括的な仕事は、1830年のピーコック（解析協会のリーダー）のTreatise of Algebra（代数学論）であった。ピーコックのthe Principle of Permanence of Equivalent Forms(等値形式の恒久普遍原理)は、本質的に記号代数学の法則が算術的代数学の法則になると言っている。 次の数十年に、イギリス数学者たちが、ピーコックが予言したことを、通常の算術の法則とは何通りもの仕方で異なっている性質を持った代数（多元環）を導入することによって、実際に具体化した。 --- Send in a voice message: https://anchor.fm/tecum/message2020-05-0246 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第７回 （p10-12）1.7 The theory of equations and the Fundamental Theorem of Algebraレポート　https://akasakas.cool/wp-content/uploads/2020/05/第7回1.7-The-theory-of-equations-and-the-Fundamental-Theorem-of-Algebra20190402勉強会.pdf https://akasakas.cool/ カテゴリーA History of Abstract Algebra 第7回（p10-12） 1.7 The theory of equations and the Fundamental Theorem of Algebra方程式の理論と代数学の基本定理FTA FTAとは、「次数が 1 以上の任意の複素係数一変数多項式には複素根が存在する」 という定理である。17世紀前半にジラールらによって主張された。 ビエタとデカルトの研究は、16世紀の終わりから17世紀の始めころ、数値方程式の可解性から文字係数を持つ方程式の理論的な研究へと関心の的が移った。多項式の理論が出現し始めた。その主たる関心は、そのような文字係数を持つ方程式の根の存在、本質、そして個数決定することだった。 　FTAの最初の証明は、1746年にダランベールから与えられたが、すぐオイラーによる証明が続いた。ダランベールの証明は解析学からアイデアを用いていたが、オイラーはほとんど代数学的であった。二つの証明は両方とも、特に、すべてのn次方程式が、実数の法則に従って計算することができるn個の根を持つということを仮定している点で、不完全であり厳密さに欠けていた。 ガウスは、1797年（彼がほんの20歳であった時）に完成し、1799年に出版した博士論文の中で、当時の標準では十分厳密なFTAの証明を与えた。 　19世紀の始め、FTAは相対的に新しいタイプの定理、existence theorem(存在定理) になった。すなわち、ある数学的な対象－多項式の根－は、単に理論上だけで、存在することが示された。２０世紀になると計算できるかどうかは別、存在することが証明されればいいと変わった。これは数学の歴史において大革命と言える。 --- Send in a voice message: https://anchor.fm/tecum/message2020-05-021h 19ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第６回 （p8-10）1.6 Algebraic notation: Viète and Descartesレポート　https://akasakas.cool/wp-content/uploads/2020/05/第6回1.6-Algebraic-notation-Viète-and-Descartes20190328勉強会.pdf 　https://akasakas.cool/ カテゴリーA History of Abstract Algebra 第6回　（p8-10） 1.6 Algebraic notation: Viète and Descartes 代数的記号法　ビエタとデカルト ３千年もの間、記号なしに代数学が発展してきた。代数学に対しての記号表記の導入と完成は、16世紀と17世紀初めに主にビエタとデカルトによってなされた。 ビエタの基本的なアイデアは、任意の係数（定数）を方程式に導入し、そしてこれらを方程式の未知数（変数）と区別することであった。彼は子音(B, C, D, . . .) を定数とし、母音(A, E, I, . . .)を変数とした。これは有名な話です。 シナゴゲとアナリキケって知ってる？ギリシャ語で、（さすが数学の祖だ）、 「method of synthesis」は、シナゴゲに相当するもので、総合の方法というもので、「method of analysis」は、分析の方法。シナゴゲというのは、答えがあるとすれば、こうでなくてはならない、という理論をいう。それに対して答えがまさにそうであるということを分析的に論ずることを、解析と言う。 解析は総合に比べて、一段低い位置にあった訳ですが、近世に実はその解析にこそ命があると、解析と総合の地位の逆転が起こるわけです。これが数学史の歴史の中で最も重要な事です。 ビエタの欠点 (ⅰ) 彼の表記法は、「短縮」だった。 (ⅱ) ビエタは、代数表記において、全ての項は同一次数を持たなければならないと“同次性”を要求した。 (ⅲ) 代数的解は幾何学的証明であった。ビエタといえども例外ではなかった。 (ⅳ)　ビエタは方程式の根を正の実数に限定した。 ２千年の間、幾何学は、数学の言語となるべく大きい位置を持っっていたけれど、今や代数学が数学の言語としての役割を果たし始めた。 --- Send in a voice message: https://anchor.fm/tecum/message2020-04-2731 minー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第２回（p2-8） 1.2 The Greeks 第3,4,5回 レポートのみレポート　https://akasakas.cool/wp-content/uploads/2020/05/第2回1.2-The-Greeks20190313勉強会.pdf https://akasakas.cool/wp-content/uploads/2020/05/第3・4・5回1.3-Al-Khwarizmi1.4-Cubic-and-quartic-equations1.5The-cubic-and-complex-numbers.pdf https://akasakas.cool/  カテゴリーA History of Abstract Algebra 1   History of Classical Algebra 1.2 The Greeks 古代ギリシャ Euclid（ユークリッド/エウクレイデス）は、古代ギリシャBC３００年頃の数学者で、「Elements（原論）」の著者であり、「幾何学の父」と称される。このユークリッド幾何学は１９世紀末から２０世紀初頭まで使われてきた。 ギリシャ代数学の業績はDiophantus’ Arithmetica　（ディオファントスの数論）である。２００年頃の人だからユークリッドの時代から500年以上経っている。ディオファントスは、代数で記号を導入した。３とか５とか数で表現してきたものが、xを使って方程式を扱うことになる。これが代数学の最初の大きな出会いになる。 Diophantusの代数学 (a) 二つの基本的ルール。一方の辺から他方の辺へ移行する際のルール、式の両辺から同一の項を消去するルール。移行するときはプラスマイナスが変わる、同一のものは消していいということ。 (b) 未知数の負ベキの定義をした。そして、指数法則を明確にした。 (c) 負係数の演算についていくつかの諸規則を述べている。例えば、マイナスにマイナスをかけた時はプラスになる。 (d) 古代ギリシャの伝統の鎖から離れていた。 x^3 −2x^2 +10x −1 = 5 をギリシャ文字で表すことはクイズのようで、手間がかかるが楽しい。 ςシグマは未知数（ζゼータではない）、Φファイは引き算、Īōイオシグマは等しいという相当性、Δσ （デルタの上付きシグマ）は未知数の平方、Κσ（カッパの右肩シグマ）は立方、などなど。 --- Send in a voice message: https://anchor.fm/tecum/message2020-04-271h 06ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会ー A History of Abstract Algebra by I.Kleiner ー 長岡亮介数学勉強会第１回（p1-2）1 History of Classical Algebra 1.1 Early rootsレポート　https://akasakas.cool/wp-content/uploads/2020/05/第1回1.1-Early-roots20190306勉強会.pdf https://akasakas.cool/　カテゴリーA History of Abstract Algebra 1   History of Classical Algebra   1.1 Early roots  およそ紀元前1700年頃のバビロニア人は２次方程式を解いている。係数も変数も無く、しかも60進法を用いて。 ＜問＞ I have added the area and two-thirds of the side of my square and it is 0;35[35/60 in sexagesimal notation]. What is the side of my square? ＜解＞ You take 1, the coefficient. Two-thirds of 1 is 0;40. Half of this, 0;20, you multiply by 0;20 and it [the result] 0;6,40 you add to 0;35 and [the result] 0;41,40 has 0;50 as its square root. The 0;20, which you have multiplied by itself, you subtract from 0;50, and 0;30 is [the side of] the square この文章が理解できた時、とても嬉しかった。およそ４千年前のバビロニア人と...2020-04-0235 minFlippening - For Crypto InvestorsFlippening - For Crypto InvestorsPart 2: "Behind The Scenes" At A High-Volume Crypto OTC Desk w/ Kevin Zhou of Galois Capital (Ep. 0031)Today’s episode is the second part of an in-depth conversation is with Kevin Zhou, head trader at Galois Capital. Galois Capital is a high-volume US-based OTC desk. Some of Kevin’s previous positions include Head of Trading at Kraken, and prior to that, Head of Trading at Buttercoin, one of the very first crypto asset companies backed by Y Combinator. Kevin has been trading crypto since 2011. Continuing from the first part of the conversation, in this episode, you’ll learn more about how OTC desks grow their businesses and add customers, how OTC desks differentiate themselves from o...2018-11-241h 10Flippening - For Crypto InvestorsFlippening - For Crypto Investors"Behind The Scenes" At A High-Volume Crypto OTC Desk w/ Kevin Zhou of Galois Capital - Part 1 (Ep. 0030)Today’s conversation is with Kevin Zhou, head trader at Galois Capital. Galois Capital is a high-volume US-based OTC desk. Some of Kevin’s previous positions include Head of Trading at Kraken, and prior to that, Head of Trading at Buttercoin, one of the very first crypto asset companies backed by Y Combinator. Kevin has been trading crypto since 2011.In this conversation, you’ll get a behind the scenes look into how OTC desks operate and make money. The world of OTC trading can be opaque. Although the term OTC desk is often used, there’s much less tal...2018-11-1858 minBlockChannelBlockChannelEpisode 49: Building a Sustainable Crypto Business, with Galois CapitalOn this episode of BlockChannel, Mckie and Dee sit down with Amentum advisor, and mentor to Steven McKie, Kevin Zhou of Galois Capital. Kevin has been in the crypto space for many years, having worked as the Head of Trading at Kraken, and early employee of the exchange Buttercoin back in the day, Kevin has a new firm called Galois Capital. We sit back as he schools us on what it takes to get a crypto business up and running, and some lessons he's learned along the way. Show Link(s): Galois Capital: http://galois.capital Galois Twitter: http://twitter...2018-09-3039 minEpilagóricosEpilagóricos¿Qué hubiera pasado si Galois hubiera vivido 100 años?Hablamos de la vida de Galois y su aportación matemática en el álgebra, a pesar de su corta vida. Comentamos la influencia de la teoría de grupos en la actualidad.2018-09-1823 minExperienciasExperienciasAnálisis de la experiencia: GaloisAnálisis de la experiencia que realizan los alumnos del IES Bajo Guadalquivir de Lebrija (Sevilla) que entrevistan a Évariste Galois, dentro del proyecto la Radio Ficción en el Aula de Matemáticas, desarrollado durante el curso escolar 2017/2018 en el área de Matemáticas Orientadas a las Enseñanzas Académicas en 3º ESO.2018-07-1504 minExperienciasExperienciasEntrevistamos a Évariste GaloisEntrevista ficticia realizada a Évariste Galois por alumnos del IES Bajo Guadalquivir de Lebrija (Sevilla), dentro del proyecto la Radio Ficción en el Aula de Matemáticas, comenzado durante el curso escolar 2015/2016, y retomado en el 2017/2018 con alumnos y alumnas en el área de Matemáticas Orientadas a las Enseñanzas Académicas en 3º ESO (14-15 años).2018-07-1503 minLinou SAISON 3Linou SAISON 3Secret défense VS commissaire Galois - Episode 3 - 17052018 fmSecret défense VS commissaire Galois - Episode 3 - 17052018 fm2018-05-1717 minLinou SAISON 3Linou SAISON 3Lis nous, LINOU - Secret Défense VS Commissaire Galois, épisode 2 - 03052018 fmLis nous, LINOU - Secret Défense VS Commissaire Galois, épisode 2 - 03052018 fm2018-05-0320 minLinou SAISON 3Linou SAISON 3Lis nous, LINOU -Secret Défense VS Commissaire Galois - épisode 1 - 26 avril 2018 fmLis nous, LINOU -Secret Défense VS Commissaire Galois - épisode 1 - 26 avril 2018 fm2018-04-2612 minIn Our Spare TimesIn Our Spare TimesÉvariste GaloisOxford graduate students discuss the life and work of 19th century French mathematical prodigy Évariste Galois To appear on a commemorative stamp is surely the greatest stamp of fame. Évariste Galois -- 'Révolutionnaire et Géomètre', as the French stamp says -- was one of the most unusual and enigmatic mathematicians in history. He died when he was just 20 years old, in dramatic circumstances, but during his brief span he created mathematics which, in the decades after his death, would go on to revolutionise all aspects of the discipline.2017-01-1842 minIn Our Spare TimesIn Our Spare TimesÉvariste GaloisOxford graduate students discuss the life and work of 19th century French mathematical prodigy Évariste Galois To appear on a commemorative stamp is surely the greatest stamp of fame. Évariste Galois -- 'Révolutionnaire et Géomètre', as the French stamp says -- was one of the most unusual and enigmatic mathematicians in history. He died when he was just 20 years old, in dramatic circumstances, but during his brief span he created mathematics which, in the decades after his death, would go on to revolutionise all aspects of the discipline.2017-01-1842 minTalk Tech to MeTalk Tech to MeCyber Security: Charlie Kawasaki of GaloisTalk Tech to Me | Cyber Security: Charlie Kawasaki of Galois | Trends in cyber security, how companies and individuals can defend themselves, and the urgent need for strong talent in cyber security.2016-11-0119 minMagic Read AlongMagic Read AlongPut an Iframe on it, Done!DreamforceElmlang PSADenotational Design From Meanings to Programs - Conal ElliottAdd a type parameter! One 'simple' design change, a panoply of outcomes - Stephen CompallBoston Haskell Lightning talks - Dec. 2014Modularity and Abstraction in Functional Programming - Chris MartensÉvariste GaloisFunctional Geekery Episode 67 - Hardy JonesGalois ConnectionGalois Connections - Array out Bounds CheckingMaking Impossible States Impossible - Richard FeldmanPractically functional programming - Connect.Techh3h3productions2016-10-0624 minre:ID Podcastre:ID PodcastEpisode 150: Galois using biometrics to secure private dataGalois, a Portland-based company that focuses on cyber security primarily for the U.S. government, is the final winner of the fourth round of NSTIC pilots. Galois and its partners will build a tool that relies on biometric authentication to enable the storing and sharing of private information online. They also intend to develop transit ticketing on smart phones, integrating the secure system into an Internet of Things (IoT) enabled smart home. Galois Identity Research Lead Isaac Potoczny-Jones spoke with Regarding ID's Gina Jordan about the project, which involves two separate production pilots.2015-10-0906 min