Self Driving Cars [S1E2: ALVINN] Welch Labs 2019-01-19 | PATREON: patreon.com/welchlabsTWITTER: @welchlabsMORE: http://www.welchlabs.comCODE: github.com/stephencwelch/self_driving_carsWelch Labs on backpropogationyoutube.com/watch?v=GlcnxUlrtekGreat 3B1B Video on backpropogationyoutube.com/watch?v=tIeHLnjs5U8FURTHER READINGBackpropagation: nature.com/articles/323533a0ALVINN: http://www.cs.cmu.edu/afs/cs/Web/People/bhamner/neuralNetworksProject/pomerleau_dean.pdfALVINN: pdfs.semanticscholar.org/df76/59b147d04186a4885cdbe10fcf60e2ffca4e.pdfALVINN: http://papers.nips.cc/paper/95-alvinn-an-autonomous-land-vehicle-in-a-neural-network.pdfVIDEO REFERENCESNvidia End-to-End: youtube.com/watch?v=qhUvQiKec2UAmnon Shashua: youtube.com/watch?v=GCMXXXmxG-IChris Urmso: youtube.com/watch?v=BtgBySRrN0QNavlab: youtube.com/watch?v=QFpBtOG87akMore Navlab: youtube.com/watch?v=ntIczNQKfjQMore more Navlab:youtube.com/watch?v=QFpBtOG87akMore more more navlab: youtube.com/watch?v=rV0H7u6tmIkYou guess it, more navlab: youtube.com/watch?v=5-acCtyKf7ENavlab on the news: youtube.com/watch?v=IaoIqVMd6tcMUSICpremiumbeat.com/royalty-free-tracks/vulturespremiumbeat.com/royalty-free-tracks/wandererpremiumbeat.com/royalty-free-tracks/girl-powerpremiumbeat.com/royalty-free-tracks/language-2SPECIAL THANKS TOTony FastKrish RavindranathKarthik NagaDean Pomerleau- And - Sid SarasvatiRoss HansonYana ChernobilskyVin Soma Antoine PintoutJaewon JungRaphael J VasquezAJ EnglehardtNate Fuller
Oppenheimers Gamble - The Plutonium Crisis Welch Labs 2023-07-22 | Oppenheimer reading listamazon.com/shop/welchlabsOpening scenes from Oppenheimer: oppenheimermovie.comReferencesThe Trinity High-Explosive Implosion System: The Foundation for Precision Explosive Applications: tandfonline.com/doi/full/10.1080/00295450.2021.1913954Critical Assembly: A Technical History of Los Alamos during the Oppenheimer Years, 1943–1945. Welch Labspatreon.com/welchlabstiktok.com/@welchlabswelchlabs.comErrataThank to Ferenci Tamás for catching an error - the image shown at 5:00 is not of the lensed implosion bomb but a later 72-block Y-1222 design.
Oppenheimer reading list book 10. Full list at www.amazon.com/shop/welchlabs Welch Labs 2023-07-19 | ...
Oppenheimer reading list book 9. Full list at www.amazon.com/shop/welchlabs Welch Labs 2023-07-17 | ...
Oppenheimers Apocalypse Math Welch Labs 2023-07-16 | ReferencesLos Alamos Report 602: sgp.fas.org/othergov/doe/lanl/docs1/00329010.pdfThe bomb - the end of the world? http://large.stanford.edu/courses/2015/ph241/chung1/docs/buck.pdfUltimate Catastrophe? tandfonline.com/doi/abs/10.1080/00963402.1976.11455623?journalCode=rbul20Welch Labspatreon.com/welchlabstiktok.com/@welchlabswelchlabs.com
Oppenheimer reading list book 8. Full list at www.amazon.com/shop/welchlabs Welch Labs 2023-07-15 | ...
Oppenheimer reading list book 7. Full list at www.amazon.com/shop/welchlabs Welch Labs 2023-07-15 | ...
Oppenheimer reading list book 7. Full list at www.amazon.com/shop/welchlabs. #oppenheimer Welch Labs 2023-07-15 | ...
Oppenheimer reading list book 6. Full list at www.amazon.com/shop/welchlabs Welch Labs 2023-07-13 | ...
#oppenheimer #readinglist #book number five. Full list at www.amazon.com/shop/welchlabs. Welch Labs 2023-07-12 | ...
A speck of matter god did not welcome into creation Welch Labs 2023-07-08 | TECHNICAL FOOTNOTEPlutonium has been discovered in trace amounts in nature under highly unusual geologic circumstances: epa.gov/radiation/radionuclide-basics-plutonium#plutoniumsourcesLINKSOppenheimer reading list: amazon.com/shop/welchlabsPatreon: patreon.com/welchlabsTikTok: tiktok.com/@welchlabsOther Stuff: welchlabs.com
Oppenheimer reading list part one: The Making of the Atomic Bomb by Richard Rhodes Welch Labs 2023-07-08 | ...
Bohr solves mystery; invents bomb Welch Labs 2023-07-01 | Niels Bohr’s hater-inspired flash of insight lead him to the perfect material to build the atomic bomb. LINKSpatreon.com/welchlabstiktok.com/@welchlabswelchlabs.com
The Most Dangerous Rock in the World Welch Labs 2023-06-24 | The most Dangerous Rock in the World. LINKSpatreon.com/welchlabstiktok.com/@welchlabswelchlabs.com
Its been a while... Welch Labs 2023-06-21 | New videos coming soon! TikTok: tiktok.com/@welchlabsPatreon: patreon.com/welchlabs
Self-Driving Cars [S1E4: RALPH] Welch Labs 2019-02-09 | PATREON: patreon.com/welchlabsTWITTER: @welchlabsMORE: http://www.welchlabs.comCODE: github.com/stephencwelch/self_driving_carsNO HANDS ACROSS AMERICAhttps://www.cs.cmu.edu/~tjochem/nhaa/nhaa_home_page.htmlRALPHieeexplore.ieee.org/document/528333https://www.ri.cmu.edu/pub_files/pub2/pomerleau_dean_1995_2/pomerleau_dean_1995_2.pdfpatents.google.com/patent/US5675489A/en?inventor=dean+pomerleau&oq=dean+pomerleauDRIVING VIDEOSKITTI Dataset: http://www.cvlibs.net/datasets/kitti/index.phpBerkeley Dataset: https://bair.berkeley.edu/blog/2018/05/30/bdd/VIDEO REFERENCESyoutube.com/watch?v=WZorfXa5pBcyoutube.com/watch?v=bdQ5rsVgPukyoutube.com/watch?v=QFpBtOG87akyoutube.com/watch?v=5-acCtyKf7Eyoutube.com/watch?v=ntIczNQKfjQyoutube.com/watch?v=B8R148hFxPwyoutube.com/watch?v=wTDG5gjwPGoyoutube.com/watch?v=C9G6JRUmg_Ayoutube.com/watch?v=rV0H7u6tmIkyoutube.com/watch?v=Dtj9J1A-PMkMUSICpremiumbeat.com/royalty-free-tracks/girl-powerpremiumbeat.com/royalty-free-tracks/jazz-manouche-foreverpremiumbeat.com/royalty-free-tracks/out-of-the-woodspremiumbeat.com/royalty-free-tracks/above-the-oceanSPECIAL THANKS TOTony FastKrish RavindranathKarthik NagaDean PomerleauChuck Thorpe- AND - Sid SarasvatiRoss HansonYana ChernobilskyVin SomaAntoine PintoutJaewon JungRaphael J VasquezAJ EnglehardtNate FullerHitoshi Yamauchi
Self-Driving Cars [S1E3: AI Failure?] Welch Labs 2019-02-02 | PATREON: patreon.com/welchlabsTWITTER: @welchlabsMORE: http://www.welchlabs.comCODE: github.com/stephencwelch/self_driving_carsFURTHER READING + REFEERENCESFor a bayesian approach to the same reliability testing math: stats.stackexchange.com/questions/73645/how-do-you-derive-the-success-run-theorem-from-the-traditional-form-of-bayes-theRand Report: rand.org/pubs/research_reports/RR1478.htmlZeiler and Fungus 2013: arxiv.org/abs/1311.2901WHO top 10 causes of death: https://www.who.int/news-room/fact-sheets/detail/the-top-10-causes-of-deathWHO injuries and violence facts: https://apps.who.int/iris/bitstream/handle/10665/44288/9789241599375_eng.pdf%3Bjsessionid=7558B4BDC59A52BB94AEC68A0AD79EE8?sequence=1Bojarski et al: arxiv.org/abs/1704.07911Dean Pomerleau: http://www.cs.cmu.edu/~bhamner/neuralNetworksProject/pomerleau_dean.pdfDean Pomerleau: https://www.ri.cmu.edu/pub_files/pub3/pomerleau_dean_1991_1/pomerleau_dean_1991_1.pdfDean Pomerleau: https://www.ri.cmu.edu/publications/life-in-the-fast-lane-the-evolution-of-an-adaptive-vehicle-control-system/Nvidia End to End: arxiv.org/abs/1604.07316Way ChauffeurNet: arxiv.org/abs/1812.03079VIDEO REFERENCESAmnon Shashua Talk: youtube.com/watch?v=GCMXXXmxG-INAVLAB: youtube.com/watch?v=rV0H7u6tmIkMUSICpremiumbeat.com/royalty-free-tracks/jazz-manouche-foreverpremiumbeat.com/royalty-free-tracks/out-of-the-woodspremiumbeat.com/royalty-free-tracks/wandererSPECIAL THANKS TOTony FastKrish RavindranathKarthik NagaAlex MonesMichael Grabchak- AND - Sid SarasvatiRoss HansonVin SomaAntoine PintoutJaewon JungRaphael J VasquezAJ EnglehardtNate FullerHitoshi Yamauchi
Self Driving Cars [S1E1: The ALV] Welch Labs 2019-01-11 | PATREON: patreon.com/welchlabsTWITTER: @welchlabsMORE: http://www.welchlabs.comCODE: github.com/stephencwelch/self_driving_carsFURTHER READINGOriginal ALV Paper: http://www.cs.ucsb.edu/~mturk/Papers/ALV.pdfGreat Book on SCI: amazon.com/Strategic-Computing-Machine-Intelligence-1983-1993/dp/0262529262/ref=sr_1_1?ie=UTF8&qid=1547071120&sr=8-1&keywords=strategic+computingGreat book on the history of AI: amazon.com/Ai-Daniel-Crevier/dp/0465001041/ref=sr_1_1?ie=UTF8&qid=1547071150&sr=8-1&keywords=ai+the+tumultuous+history+of+the+search+for+artificial+intelligenceVIDEO REFERENCESElon Musk at TED: youtube.com/watch?v=NcqI76Z4t1ACadillac Super Cruise: youtube.com/watch?v=_rxW68ADldITesla Perception: youtube.com/watch?v=VG68SKoG7vEWaymo Perception: youtube.com/watch?v=B8R148hFxPwChris Urmson TED talk: youtube.com/watch?v=tiwVMrTLUWgMUSICpremiumbeat.com/royalty-free-tracks/girl-powerpremiumbeat.com/royalty-free-tracks/out-of-the-woodspremiumbeat.com/royalty-free-tracks/language-2SPECIAL THANKS TOTony FastKrish RavindranathKarthik NagaCharles YoungChang LeeMathew Turk- And - Vin SomaRaphael J VasquezNate Fuller
How to Science [Part 6: Secret Math in Your Brain] Welch Labs 2018-03-22 | supporting pdf:http://www.welchlabs.com/guidessupport Welch Labs:patreon.com/welchlabsMIT Video:http://news.mit.edu/2016/music-tastes-cultural-not-hardwired-brain-0713
How to Science [Part 5: Mathematics] Welch Labs 2018-01-29 | pdf: http://www.welchlabs.com/guidessupport welch labs:patreon.com/welchlabsmusic:premiumbeat.com/royalty-free-tracks/jazz-manouche-foreverpremiumbeat.com/royalty-free-tracks/out-of-the-woodspremiumbeat.com/royalty-free-tracks/among-the-hills
How To Science [Part 4: Science] Welch Labs 2017-12-24 | PDF: http://www.welchlabs.com/guidesSupport Welch Labs: www.patreon.com/welchlabsMusic:premiumbeat.com/royalty-free-tracks/jazz-manouche-foreverpremiumbeat.com/royalty-free-tracks/out-of-the-woodspremiumbeat.com/royalty-free-tracks/truth-to-tell
How to Science [Part 3: Experiments] Welch Labs 2017-12-10 | PDF: http://www.welchlabs.com/guidesSupport Welch Labs: patreon.com/welchlabsMusic:premiumbeat.com/royalty_free_music/songs/jazz-manouche-foreverpremiumbeat.com/royalty_free_music/songs/razer-trap
How to Science [Part 2: Our Universe = Math?] Welch Labs 2017-09-25 | pdf for this video: http://www.welchlabs.com/guidessupport welch labs: patreon.com/welchlabsmusic:premiumbeat.com/royalty_free_music/songs/storytelling-pianopremiumbeat.com/royalty_free_music/songs/dark-eyes-gypsy-jazzpremiumbeat.com/royalty_free_music/songs/truth-to-tell
How to Science [Part 1: Music] Welch Labs 2017-09-09 | pdf: http://www.welchlabs.com/guidesmusic: premiumbeat.com/royalty_free_music/songs/storytelling-pianopatreon:patreon.com/welchlabscorrection:length table should be in cm, to mm!
Channel Update [April 2017] Welch Labs 2017-04-29 | Help me make more videos: patreon.com/welchlabsYouTube channels referenced: MinutePhysics, Veritaseum, VSauce, Physics Girl, CGP Grey, Mathologer, 3Blue1Brown, and Numberphile.A special thanks to Charles Young for all his fantastic help with the motion rig. Thanks to Joan and Alison Young for cutting out an absolutely amazing ransom note.Music: premiumbeat.com/royalty_free_music/songs/yours-faithfullypremiumbeat.com/royalty_free_music/songs/it-s-always-funny-in-philadelphia
Learning To See [Part 15: Information] Welch Labs 2017-04-15 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning To See [Part 14: Better Heuristics] Welch Labs 2017-04-01 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning To See [Part 13: Heuristics] Welch Labs 2017-03-18 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning To See [Part 12: Lets Get Greedy] Welch Labs 2017-03-04 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning to See [Part 11: Haystacks on Haystacks] Welch Labs 2017-02-18 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning to See [Part 10: World Domination] Welch Labs 2017-02-04 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning To See [Part 9: Bias Variance Throwdown] Welch Labs 2017-01-21 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning to See [Part 8: More Assumptions...Fewer Problems?] Welch Labs 2017-01-07 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning to See [Part 7: There is no f] Welch Labs 2016-12-24 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning To See [Part 6: Its Definitely Time to Play with Legos] Welch Labs 2016-12-10 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning to See [Part 5: To Learn is to Generalize] Welch Labs 2016-11-26 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning to See [Part 4: Machine Learning] Welch Labs 2016-11-12 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning To See [Part 3: Now I R1] Welch Labs 2016-10-28 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Learning To See [Part 2: Rules on Rules on Rules] Welch Labs 2016-10-15 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Code available soon.welchlabs.com@welchlabs
Imaginary Numbers Are Real [Part 13: Riemann Surfaces] Welch Labs 2016-09-03 | Want to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook: http://www.welchlabs.com/resources.Supporting Code: github.com/stephencwelch/Imaginary-Numbers-Are-RealImaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space. Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering. Part 1: IntroductionPart 2: A Little HistoryPart 3: Cardan's ProblemPart 4: Bombelli's SolutionPart 5: Numbers are Two DimensionalPart 6: The Complex PlanePart 7: Complex MultiplicationPart 8: Math WizardryPart 9: ClosurePart 10: Complex FunctionsPart 11: Wandering in Four DimensionsPart 12: Riemann's SolutionPart 13: Riemann SurfacesSpecial thanks to the fantastic Charles Jackson Young for helping me get the motion rig done in time for this video. You Rock!Want to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook: http://www.welchlabs.com/resources.
Imaginary Numbers Are Real [Part 12: Riemanns Solution] Welch Labs 2016-07-01 | Want to experiment with Riemann's idea yourself? You can download your very own copy of of the final w-planes to experiment with here: http://www.welchlabs.com/blog/2016/6/30/imaginary-numbers-are-real-part-12-riemanns-solutionSupporting Code: github.com/stephencwelch/Imaginary-Numbers-Are-RealImaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space. Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering. Part 1: IntroductionPart 2: A Little HistoryPart 3: Cardan's ProblemPart 4: Bombelli's SolutionPart 5: Numbers are Two DimensionalPart 6: The Complex PlanePart 7: Complex MultiplicationPart 8: Math WizardryPart 9: ClosurePart 10: Complex FunctionsPart 11: Wandering in Four DimensionsPart 12: Riemann's SolutionPart 13: Riemann SurfacesWant to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook: http://www.welchlabs.com/resources.
Imaginary Numbers Are Real [Part 11: Wandering in 4 Dimensions] Welch Labs 2016-06-17 | More information and resources: http://www.welchlabs.comSupporting Code: github.com/stephencwelch/Imaginary-Numbers-Are-RealImaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space. Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering. Part 1: IntroductionPart 2: A Little HistoryPart 3: Cardan's ProblemPart 4: Bombelli's SolutionPart 5: Numbers are Two DimensionalPart 6: The Complex PlanePart 7: Complex MultiplicationPart 8: Math WizardryPart 9: ClosurePart 10: Complex FunctionsPart 11: Wandering in Four DimensionsPart 12: Riemann's SolutionPart 13: Riemann SurfacesWant to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook: http://www.welchlabs.com/resources.
Imaginary Numbers Are Real [Part 10: Complex Functions] Welch Labs 2016-06-03 | Supporting Code: github.com/stephencwelch/Imaginary-Numbers-Are-RealMore information and resources: http://www.welchlabs.comImaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space. Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering. Part 1: IntroductionPart 2: A Little HistoryPart 3: Cardan's ProblemPart 4: Bombelli's SolutionPart 5: Numbers are Two DimensionalPart 6: The Complex PlanePart 7: Complex MultiplicationPart 8: Math WizardryPart 9: ClosurePart 10: Complex FunctionsPart 11: Wandering in Four DimensionsPart 12: Riemann's SolutionPart 13: Riemann SurfacesWant to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook: http://www.welchlabs.com/resources.
Learning To See [Part 1: Introduction] Welch Labs 2016-04-15 | In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Become a Patron for exclusive perks: patreon.com/welchlabsSupporting Code: github.com/stephencwelch/LearningToSeewelchlabs.com@welchlabs
Imaginary Numbers Are Real [Part 9: Closure] Welch Labs 2015-11-06 | More information and resources: http://www.welchlabs.comImaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space. Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering. Part 1: IntroductionPart 2: A Little HistoryPart 3: Cardan's ProblemPart 4: Bombelli's SolutionPart 5: Numbers are Two DimensionalPart 6: The Complex PlanePart 7: Complex MultiplicationPart 8: Math WizardryPart 9: ClosurePart 10: Complex FunctionsPart 11: Wandering in Four DimensionsPart 12: Riemann's SolutionPart 13: Riemann SurfacesWant to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook: http://www.welchlabs.com/resources.
Imaginary Numbers Are Real [Part 8: Math Wizardry] Welch Labs 2015-10-23 | More information and resources: http://www.welchlabs.comImaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space. Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering. Part 1: IntroductionPart 2: A Little HistoryPart 3: Cardan's ProblemPart 4: Bombelli's SolutionPart 5: Numbers are Two DimensionalPart 6: The Complex PlanePart 7: Complex MultiplicationPart 8: Math WizardryPart 9: ClosurePart 10: Complex FunctionsPart 11: Wandering in Four DimensionsPart 12: Riemann's SolutionPart 13: Riemann SurfacesWant to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook: http://www.welchlabs.com/resources.
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