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Indem Ernst Zermelo eine neue Ordnungsregel in der Mathematik einführt, löst er ein riesiges Problem der Mengenlehre – und entfacht gleichzeitig die größte Debatte, die es in der Mathe-Community je gegeben hat. Die Idee für diesen Podcast hat Demian Nahuel Goos am MIP.labor entwickelt, der Ideenwerkstatt für Wissenschaftsjournalismus zu Mathematik, Informatik und Physik an der Freien Universität Berlin, ermöglicht durch die Klaus Tschira Stiftung. (00:00:00) Einleitung (00:02:04) Lehrerkind in der Hochindustrialisierung (00:03:22) Göttingen als Hochburg für Mathematik (00:04:44) Die zukünftigen Probleme der Mathematik (00:05:45) Upgrade der Mengenlehre (00:08:09) Kritik an Zermelos Werkzeug (00:09:36) Zermelos Revanche (00:13:10) Grundregeln der Mathematik (00:14:38) Axiome in der Mengenlehre (00:15:58) Das „magische“ Auswahlaxiom (00:18:16) Mathematische Folgen des Auswahlaxioms (00:24:03) Manon und Demian zum Auswahlaxiom (00:26:39) Schlusswort zu Zermelo (00:27:28) Verabschiedung >> Artikel zum Nachlesen: https://detektor.fm/wissen/geschichten-aus-der-mathematik-ernst-zermelo
Indem Ernst Zermelo eine neue Ordnungsregel in der Mathematik einführt, löst er ein riesiges Problem der Mengenlehre – und entfacht gleichzeitig die größte Debatte, die es in der Mathe-Community je gegeben hat. Die Idee für diesen Podcast hat Demian Nahuel Goos am MIP.labor entwickelt, der Ideenwerkstatt für Wissenschaftsjournalismus zu Mathematik, Informatik und Physik an der Freien Universität Berlin, ermöglicht durch die Klaus Tschira Stiftung. (00:00:00) Einleitung (00:02:04) Lehrerkind in der Hochindustrialisierung (00:03:22) Göttingen als Hochburg für Mathematik (00:04:44) Die zukünftigen Probleme der Mathematik (00:05:45) Upgrade der Mengenlehre (00:08:09) Kritik an Zermelos Werkzeug (00:09:36) Zermelos Revanche (00:13:10) Grundregeln der Mathematik (00:14:38) Axiome in der Mengenlehre (00:15:58) Das „magische“ Auswahlaxiom (00:18:16) Mathematische Folgen des Auswahlaxioms (00:24:03) Manon und Demian zum Auswahlaxiom (00:26:39) Schlusswort zu Zermelo (00:27:28) Verabschiedung >> Artikel zum Nachlesen: https://detektor.fm/wissen/geschichten-aus-der-mathematik-ernst-zermelo
Indem Ernst Zermelo eine neue Ordnungsregel in der Mathematik einführt, löst er ein riesiges Problem der Mengenlehre – und entfacht gleichzeitig die größte Debatte, die es in der Mathe-Community je gegeben hat. Die Idee für diesen Podcast hat Demian Nahuel Goos am MIP.labor entwickelt, der Ideenwerkstatt für Wissenschaftsjournalismus zu Mathematik, Informatik und Physik an der Freien Universität Berlin, ermöglicht durch die Klaus Tschira Stiftung. (00:00:00) Einleitung (00:02:04) Lehrerkind in der Hochindustrialisierung (00:03:22) Göttingen als Hochburg für Mathematik (00:04:44) Die zukünftigen Probleme der Mathematik (00:05:45) Upgrade der Mengenlehre (00:08:09) Kritik an Zermelos Werkzeug (00:09:36) Zermelos Revanche (00:13:10) Grundregeln der Mathematik (00:14:38) Axiome in der Mengenlehre (00:15:58) Das „magische“ Auswahlaxiom (00:18:16) Mathematische Folgen des Auswahlaxioms (00:24:03) Manon und Demian zum Auswahlaxiom (00:26:39) Schlusswort zu Zermelo (00:27:28) Verabschiedung >> Artikel zum Nachlesen: https://detektor.fm/wissen/geschichten-aus-der-mathematik-ernst-zermelo
Stephen Wolfram answers questions from his viewers about the history science and technology as part of an unscripted livestream series, also available on YouTube here: https://wolfr.am/youtube-sw-qa Questions include: You recently talked about relearning the history of thermodynamics. Can I ask for resources for learning the history of thermodynamics? - Can you talk about the history of mathematical/computational linguistics (the one that studies the principles and regularities of natural languages)? There are famous Soviet mathematicians (Andreev, Sobolev, Kantorovich, Markov - son of his great father) of Kolmogorov's school who advanced this field in the 1950s through the 1970s. - What do you think about the science of statistics? Is AI just computational Statistics? - What's the most exciting thing about the AI art revolution taking place now? Was there ever a time like it? - What did Henri Poincaré think about the infinities considered by Cantor, Hilbert and Zermelo? Do engineers need the concept of a complete infinity?
SPEKTER presents SPEKTRUM RADIO, bringing you the hottest new sounds in tech house, minimal tech, and deep house. From the rising stars to the underground's newest emerging artists, SPEKTER has dug deep to bring you not just their favorite tracks, but tunes that are sure to get your body moving and your soul vibing. This week features tracks from ZERMELO, JakeShoreDrive, Vanstone, LNDN, Nadia, JOHNJOSE, Erosian, Attenboro, and more. TRACKLIST: FRED AGAIN – JUNGLE (FORBES REMIX) VANSTONE, LNDN – FIJI ZERMELO – IT'S GOIN DOWN LUCLOVER – L$D (JAKESHOREDRIVE REMIX) SPEKTER, REVEREND HAUS – CLOSER (BENI HANA REMIX) LEX & WOOD, KARSTEN SOLLORS – NIGHTSHADE (NADIA REWORK) BLIMEY O'REILLY – GROOVINATOR BECKY G, EL ALFA – FULANITO (EROSIAN EDIT) JOHNJOSE – LA REPUBLICA KID FROST – LA RAZA (M.O.G EDIT) BILL WITHERS – LOVELY DAY (ATTENBORO EDIT) KSI – HOLIDAY (SPEKTER REMIX)
Love Techy Like? mix 226 1. Phases. H O W L I N G 2. Roll Call. Lane 8 and Anderholm 3. Everything Is Roses. Synthemesc (Mass Digital remix) 4. Raining. Kaskade & Adam K (feat.Sunsun)(Rich DietZ remix) 5. Vibe Check. Rich DietZ 6. Space Girl. Gene Farris 7. Free Your Mind. Kyle Kinch (KC Gilmore remix) 8. Goosebumps. Marco Anzalone (Extended Club Mix) 9. Heard This. Ratman & Bobbin 10. Ninguém Manda Em Mim. Ká Hernandes, Dramaki (Extended Mix) 11. Straight Outta Fire. D'Arabia (Boogie Cafe) 12. Disco Nap 2020. Oxymoron & Allen Oh (Toastercookie remix) 13. For Ya. Mancodex 14. Elevate. Jace Mek ft. Clarity Country Club Disco 15. Rhythm Poetry. Jargen 16. Street Lights. Mihalis Safras (Moon Harbour) 17. Better Now x Hilo (WUKONG Divine Edit) 18. Bonkers. Dizzee Rascal & Armand Van Helden (Cloverdale Rework) 19. Diggin in the Crates. Zermelo feat Vanilla ACE 20. Take On Me. A-Ha (Sad Panda remix) 21. Bucci Bang (Radio Edit) 22. Ain't Sick. Gabe The Babe 23. Bob Ross. Rich DietZ 24. Sleepin' in. The Kount 26 may 2020 mixed genre. house. dance. tech house.
We first discuss Zermelo’s theorem: that games like tic-tac-toe or chess have a solution. That is, either there is a way for player 1 to force a win, or there is a way for player 1 to force a tie, or there is a way for player 2 to force a win. The proof is by induction. Then we formally define and informally discuss both perfect information and strategies in such games. This allows us to find Nash equilibria in sequential games. But we find that some Nash equilibria are inconsistent with backward induction. In particular, we discuss an example that involves a threat that is believed in an equilibrium but does not seem credible.
1. Chromeo - Juice (Chris Lake Remix)2. Kelly Clarkson - Love So Soft (Mark Knight & Ben Remember Remix)3. Gorgon City - Grooves On The Vinyl4. Liam Payne - Bedroom Floor (Cash Cash Remix)5. G-Wizard ft Samrai - LA Story (Where It's ATT Remix)6. EDX - Runnin' (Clean) (Extended) 7. Dua Lipa - New Rules (KREAM Remix)8. MK - 17 (Solardo Remix)9. CamelPhat & Elderbrook vs Robert Miles - Children Cola (Rudeejay & Da Brozz x Luis Rodriguez Mash-Boot)10. Jennifer Lopez - Let's Get Loud (Kevin D Remix)11. Camila Cabello ft Young Thug - Havana (Pat C's Better On Me Mashup)12. Zermelo & Force Legato - Get Down13. Tom & Jame - In The Air14. Oliver Heldens - What The Funk (Steve Aoki Remix)15. Timmy Trumpet & Savage - Deja Vu16. Jaggs - On My Bass17. Will Sparks & Luciana - Bad Connection18. R3HAB & KSHMR - Islands19. Ed Sheeran vs Oasis vs Dimitri Vegas & Like Mike vs Martin Garrix - Shape Of Wonderwall Tremor (Grenno Mashup)20. Porter Robinson - Language (Domastic Remix)21. Galantis & Throttle - Tell Me You Love Me22. Bingo Players vs TJR - Time To Cry (Chumpion Mashup)23. Blasterjaxx & Timmy Trumpet - Narco (Clean)24. Alice Deejay - Better Off Alone (Josh Le Tissier Bootleg)
1. Chromeo - Juice (Chris Lake Remix)2. Kelly Clarkson - Love So Soft (Mark Knight & Ben Remember Remix)3. Gorgon City - Grooves On The Vinyl4. Liam Payne - Bedroom Floor (Cash Cash Remix)5. G-Wizard ft Samrai - LA Story (Where It's ATT Remix)6. EDX - Runnin' (Clean) (Extended) 7. Dua Lipa - New Rules (KREAM Remix)8. MK - 17 (Solardo Remix)9. CamelPhat & Elderbrook vs Robert Miles - Children Cola (Rudeejay & Da Brozz x Luis Rodriguez Mash-Boot)10. Jennifer Lopez - Let's Get Loud (Kevin D Remix)11. Camila Cabello ft Young Thug - Havana (Pat C's Better On Me Mashup)12. Zermelo & Force Legato - Get Down13. Tom & Jame - In The Air14. Oliver Heldens - What The Funk (Steve Aoki Remix)15. Timmy Trumpet & Savage - Deja Vu16. Jaggs - On My Bass17. Will Sparks & Luciana - Bad Connection18. R3HAB & KSHMR - Islands19. Ed Sheeran vs Oasis vs Dimitri Vegas & Like Mike vs Martin Garrix - Shape Of Wonderwall Tremor (Grenno Mashup)20. Porter Robinson - Language (Domastic Remix)21. Galantis & Throttle - Tell Me You Love Me22. Bingo Players vs TJR - Time To Cry (Chumpion Mashup)23. Blasterjaxx & Timmy Trumpet - Narco (Clean)24. Alice Deejay - Better Off Alone (Josh Le Tissier Bootleg)
Neste episódio falarei um pouco sobre algumas teorias de conjuntos e como essas teorias possuem diferentes conceitos e permitem concluir resultados muitas vezes conflitantes entre si (embora corretos dentro de seus próprios escopos).
Neste episódio falarei um pouco sobre algumas teorias de conjuntos e como essas teorias possuem diferentes conceitos e permitem concluir resultados muitas vezes conflitantes entre si (embora corretos dentro de seus próprios escopos).
In the first part of the lecture we wrap up the previous discussion of implied default probabilities, showing how to calculate them quickly by using the same duality trick we used to compute forward interest rates, and showing how to interpret them as spreads in the forward rates. The main part of the lecture focuses on the powerful tool of backward induction, once used in the early 1900s by the mathematician Zermelo to prove the existence of an optimal strategy in chess. We explore its application in a series of optimal stopping problems, starting with examples quite distant from economics such as how to decide when it is time to stop dating and get married. In each case we find that the option to continue is surprisingly valuable.
In the first part of the lecture we wrap up the previous discussion of implied default probabilities, showing how to calculate them quickly by using the same duality trick we used to compute forward interest rates, and showing how to interpret them as spreads in the forward rates. The main part of the lecture focuses on the powerful tool of backward induction, once used in the early 1900s by the mathematician Zermelo to prove the existence of an optimal strategy in chess. We explore its application in a series of optimal stopping problems, starting with examples quite distant from economics such as how to decide when it is time to stop dating and get married. In each case we find that the option to continue is surprisingly valuable.
We first discuss Zermelo's theorem: that games like tic-tac-toe or chess have a solution. That is, either there is a way for player 1 to force a win, or there is a way for player 1 to force a tie, or there is a way for player 2 to force a win. The proof is by induction. Then we formally define and informally discuss both perfect information and strategies in such games. This allows us to find Nash equilibria in sequential games. But we find that some Nash equilibria are inconsistent with backward induction. In particular, we discuss an example that involves a threat that is believed in an equilibrium but does not seem credible.
We first discuss Zermelo's theorem: that games like tic-tac-toe or chess have a solution. That is, either there is a way for player 1 to force a win, or there is a way for player 1 to force a tie, or there is a way for player 2 to force a win. The proof is by induction. Then we formally define and informally discuss both perfect information and strategies in such games. This allows us to find Nash equilibria in sequential games. But we find that some Nash equilibria are inconsistent with backward induction. In particular, we discuss an example that involves a threat that is believed in an equilibrium but does not seem credible.