Trigonometry without Geometry // Introduction to Real Analysis ThatMathThing 2026-09-19 | Trigonometry without Geometry // Introduction to Real Analysis
The Structure of a new AI architecture (KAN) ThatMathThing 2024-09-23 | Here I disentangle what a layer is in this new framework.//LinkThe story of Arnold and Ponryagin over the Fields Medalmathoverflow.net/questions/27144/why-didnt-vladimir-arnold-get-the-fields-medal-in-1974//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//PapersKAN Manuscript Ziming Liu et al - arxiv.org/abs/2404.19756Kolmogorov's Paper - cs.uwaterloo.ca/~y328yu/classics/Kolmogorov57.pdf//BooksV. I. Arnold - Mathematical Methods of Classical Mechanics - amzn.to/3wMuQWeSteve Brunton and J. Nathan Kutz - Data Driven Science and Engineering amzn.to/4daHtemHolger Wendland - Scattered Data Approximation amzn.to/4daHtemGregory Fasshauer - Meshfree Approximation Methods with MATLAB amzn.to/3U1KMeMGregory Fasshauer - Kernel Based Approximation Methods using MATLAB amzn.to/4d1CwExIngo Steinwart and Andreas Christmann - Support Vector Machines amzn.to/4d5C7km// CodeBitBucketbitbucket.org/joelrosenfeld/figures-from-kan-videos/src/main//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuThis content is partially supported by National Science Foundation - Award ID 2027976, Air Force Office Of Scientific Research - Award FA9550-20-1-0127 and FA9550-21-1-0134. I am responsible for all opinions and content, and what I say does not necessarily reflect the sponsoring organizations.DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
Book Writing - Fourier Transforms! ThatMathThing 2024-09-21 | Fourier Transforms from the ground up! Appending in my Book
applying to grad school. who do you ask? #gradschool #collegeadmissions ThatMathThing 2024-09-15 | ...
good and HORRIBLE letters or recommendation #collegeadmissions ThatMathThing 2024-09-14 | What does a letter of recommendation look like anyway?
why are letters of recommendation are important #gradschool #collegeadmissions ThatMathThing 2024-09-13 | Why exactly are letters or recommendation still important today?
Christopher Nolan made a mistake in Oppenheimer #oppenheimer #oppenheimermoviereview ThatMathThing 2024-08-31 | ...
The Old Los Alamos is open to Tourists #oppenheimer #losalamos ThatMathThing 2024-08-20 | Los Alamos Historical Society: losalamoshistory.org
Oppenheimers mistake that EVERYONE missed ThatMathThing 2024-08-18 | Even Christopher Nolan's science consultants missed this mistake in Oppenheimer, and the more physics you know, the more likely you are going to miss it!// Links //Donate to the Los Alamos Historical Society: losalamoshistory.orgDirac's Quantum Mechanics Boo (with modern notation): amzn.to/4fMF8YdAll of Oppenheimer's Papers: academictree.org/physics/publications.php?pid=52640Dirac's First Edition: archive.org/details/principlesquantummechanics1stdirac1930//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuThis content is partially supported by National Science Foundation - Award ID 2027976, Air Force Office Of Scientific Research - Award FA9550-20-1-0127 and FA9550-21-1-0134. I am responsible for all opinions and content, and what I say does not necessarily reflect the sponsoring organizations.DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
Why the world NEEDS Kolmogorov Arnold Networks ThatMathThing 2024-05-22 | We discuss the importance and contribution that the KAN method accomplishes.//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//PapersKAN Manuscript Ziming Liu et al - arxiv.org/abs/2404.19756Kolmogorov's Paper - cs.uwaterloo.ca/~y328yu/classics/Kolmogorov57.pdf//BooksV. I. Arnold - Mathematical Methods of Classical Mechanics - amzn.to/3wMuQWeSteve Brunton and J. Nathan Kutz - Data Driven Science and Engineering amzn.to/4daHtemHolger Wendland - Scattered Data Approximation amzn.to/4daHtemGregory Fasshauer - Meshfree Approximation Methods with MATLAB amzn.to/3U1KMeMGregory Fasshauer - Kernel Based Approximation Methods using MATLAB amzn.to/4d1CwExIngo Steinwart and Andreas Christmann - Support Vector Machines amzn.to/4d5C7km// CodeBitBucketbitbucket.org/joelrosenfeld/figures-from-kan-videos/src/main//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuThis content is partially supported by National Science Foundation - Award ID 2027976, Air Force Office Of Scientific Research - Award FA9550-20-1-0127 and FA9550-21-1-0134. I am responsible for all opinions and content, and what I say does not necessarily reflect the sponsoring organizations.DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 KAN do attitude1:15 Curse of Dimensionality2:38 The Kolmogorov Arnold Representation4:27 Conquering the Curse of Dimensionality6:37 Wrap Up
Fourier Series and their Convergence (Proof!) (Theory of Machine Learning) ThatMathThing 2024-05-06 | We give a proof of the convergence of Fourier Series and talk about orthogonal bases.//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//BooksSteve Brunton and J. Nathan Kutz - Data Driven Science and Engineering amzn.to/4daHtemHolger Wendland - Scattered Data Approximation amzn.to/4daHtemGregory Fasshauer - Meshfree Approximation Methods with MATLAB amzn.to/3U1KMeMGregory Fasshauer - Kernel Based Approximation Methods using MATLAB amzn.to/4d1CwExIngo Steinwart and Andreas Christmann - Support Vector Machines amzn.to/4d5C7km// CodeBitBucketbitbucket.org/joelrosenfeld/convergence-of-fourier-series/src/mainTry Through MATLAB Online for free (20 hours free use per month)matlab.mathworks.com/open/github/v1?host=bitbucket.org&repo=joelrosenfeld/convergence-of-fourier-series//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuThis content is partially supported by National Science Foundation - Award ID 2027976, Air Force Office Of Scientific Research - Award FA9550-20-1-0127 and FA9550-21-1-0134. I am responsible for all opinions and content, and what I say does not necessarily reflect the sponsoring organizations.DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 Introduction1:16 Othonormal Bases5:19 Fourier Series9:00 Hilbert Spaces have Orthonormal Bases11:17 Fourier Series and Completeness15:18 Approximate Identities and Trigonometric Polynomials20:45 Where can you learn more?
Reproducing Kernels and Functionals (Theory of Machine Learning) ThatMathThing 2024-04-22 | In this video we give the functional analysis definition of a Reproducing Kernel Hilbert space, and then we investigate approximations within this space using moments as data. We draw a comparison with polynomial best approximations over L^2, and get comparable results with a new basis function made from kernels.//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//BooksSteve Brunton and J. Nathan Kutz - Data Driven Science and Engineering amzn.to/4daHtemHolger Wendland - Scattered Data Approximation amzn.to/4daHtemGregory Fasshauer - Meshfree Approximation Methods with MATLAB amzn.to/3U1KMeMGregory Fasshauer - Kernel Based Approximation Methods using MATLAB amzn.to/4d1CwExIngo Steinwart and Andreas Christmann - Support Vector Machines amzn.to/4d5C7km// CodeBitBucketbitbucket.org/joelrosenfeld/rkhs-moments-approximation/src/mainTry Through MATLAB Online for free (20 hours free use per month)matlab.mathworks.com/open/github/v1?host=bitbucket.org&repo=joelrosenfeld/rkhs-moments-approximation//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuThis content is partially supported by National Science Foundation - Award ID 2027976, Air Force Office Of Scientific Research - Award FA9550-20-1-0127 and FA9550-21-1-0134. I am responsible for all opinions and content, and what I say does not necessarily reflect the sponsoring organizations.DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 Start1:11 Reproducing Kernel Hilbert Spaces5:01 Two Examples12:01 Customizing Bases for Approximation14:22 Comparing Best Approximations21:03 Wrap up and Watch Next
Putting DATA in Hilbert Spaces: Proving the Riesz Theorem (Theory of Machine Learning) ThatMathThing 2024-04-14 | In this video we introduce and prove the Riesz representation theorem for Hilbert spaces. This is the fundamental theorem that enables much of machine learning and data science, since it allows us to embed information and measurements from the real world into a Hilbert function space.//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuThis content is partially supported by National Science Foundation - Award ID 2027976, Air Force Office Of Scientific Research - Award FA9550-20-1-0127 and FA9550-21-1-0134. I am responsible for all opinions and content, and what I say does not necessarily reflect the sponsoring organizations.DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 What are functionals?2:54 Functionals over R^n3:55 Who proved this theorem?5:00 Recapping the Projection Theorem6:09 How do you prove this anyway?16:25 Wrapping up
How does a BEST approximation do with extrapolation? #mathformachinelearning ThatMathThing 2024-04-10 | We take a best approximation in L2 and look at how far we can trust the approximation.
What is a BEST approximation? (Theory of Machine Learning) ThatMathThing 2024-04-08 | Here we start our foray into Machine Learning, where we learn how to use the Hilbert Projection Theorem to give a best approximation of a function. This way we learn a function using an optimization procedure. To do this, we use the moments of a function.//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Codebitbucket.org/joelrosenfeld/best-approximation-in-l2/src/mainOr open it directly in MATLAB Online:matlab.mathworks.com/open/github/v1?host=bitbucket.org&repo=joelrosenfeld/best-approximation-in-l2&project=bestapproximation.m//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuThis content is partially supported by National Science Foundation - Award ID 2027976, Air Force Office Of Scientific Research - Award FA9550-20-1-0127 and FA9550-21-1-0134. I am responsible for all opinions and content, and what I say does not necessarily reflect the sponsoring organizations.DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
The Hilbert Projection Theorem - Full Proof! (Theory behind Machine Learning) ThatMathThing 2024-04-01 | In this video we embark on the study of spaces of (potentially) infinite dimension, Hilbert spaces. Here we give the full proof the Hilbert Projection theorem, which is the most critical piece of their study.//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuThis content is partially supported by National Science Foundation - Award ID 2027976, Air Force Office Of Scientific Research - Award FA9550-20-1-0127 and FA9550-21-1-0134. I am responsible for all opinions and content, and what I say does not necessarily reflect the sponsoring organizations.DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
when are you too old to learn math? ThatMathThing 2024-01-17 | When is it too late to start learning math? And how can you start?To try everything Brilliant has to offer—free—for a full 30 days, visit brilliant.org/ThatMathThing .//BooksRudin - amzn.to/3KeL0ICDummit and Foote Abstract Algebra amzn.to/3QxGvwNFolland Real Analysis amzn.to/3dCuCaoHungerford Algebra amzn.to/3pIJyGVPedersen Analysis NOW amzn.to/3c27MZo//Watch NextReal Analysis Survival Guide youtu.be/v5rD0B-zfXwThis is why you have imposter syndrome youtu.be/5CN_KovhHbYSoME2 Entry youtu.be/3ARBkAM2hRgReal Analysis:How to think of Real Numbers youtu.be/fD9VggL7RYUThe Banach Fixed Point Theorem youtu.be/_I790SqNDjsThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Control Theory:The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//MusicMusic is provided by Epidemic Sound.Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
How to get ahead in your math classes ThatMathThing 2024-01-10 | So you have the time and you want to get ahead in your math courses. Here I talk about the best resources for doing so, whether you are a beginning learner or a graduate student in mathematics.To try everything Brilliant has to offer—free—for a full 30 days, visit brilliant.org/ThatMathThing .//BooksRudin - amzn.to/3KeL0ICDummit and Foote Abstract Algebra amzn.to/3QxGvwNFolland Real Analysis amzn.to/3dCuCaoHungerford Algebra amzn.to/3pIJyGVPedersen Analysis NOW amzn.to/3c27MZo//Watch NextReal Analysis Survival Guide youtu.be/v5rD0B-zfXwThis is why you have imposter syndrome youtu.be/5CN_KovhHbYSoME2 Entry youtu.be/3ARBkAM2hRgReal Analysis:How to think of Real Numbers youtu.be/fD9VggL7RYUThe Banach Fixed Point Theorem youtu.be/_I790SqNDjsThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Control Theory:The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//MusicMusic is provided by Epidemic Sound.Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
Can an AI Learn Physics from Data? (Parameter Identification) ThatMathThing 2024-01-01 | It took millennia for us to arrive at the right ideas behind physics. Starting with the Babylonians to the Greeks to Kepler then Newton, and they all made their models from the data that they had available to them. Today, I'll tell you how we can use data to automatically produce physical models through AI concepts, and this approach is called "parameter identification."//BooksBrunton and Kutz - Data Driven Methods in Science and Engineering - amzn.to/4aCRkIrBillings - Nonlinear System Identification - amzn.to/3RJGNSZ//Watch NextReal Analysis Survival Guide youtu.be/v5rD0B-zfXwThis is why you have imposter syndrome youtu.be/5CN_KovhHbYSoME2 Entry youtu.be/3ARBkAM2hRgReal Analysis:How to think of Real Numbers youtu.be/fD9VggL7RYUThe Banach Fixed Point Theorem youtu.be/_I790SqNDjsThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Control Theory:The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//MusicMost music provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
Uniform Continuity over Compact Sets ThatMathThing 2023-10-30 | Here we talk about continuity and its connections with compactness. Compactness was first defined around the same time as metric spaces, by Maurice Frechet, and they are more or less a generalization of finite sets. Their interactions with continuous functions have opened up the entire field of functional analysis over the past century, so let's look at the interactions between these important objects.To try everything Brilliant has to offer—free—for a full 30 days, visit brilliant.org/ThatMathThing . The first 200 of you will get 20% off Brilliant’s annual premium subscription.(This video was sponsored by Brilliant)//BooksRudin - amzn.to/3KeL0ICDummit and Foote Abstract Algebra amzn.to/3QxGvwNFolland Real Analysis amzn.to/3dCuCaoHungerford Algebra amzn.to/3pIJyGVPedersen Analysis NOW amzn.to/3c27MZo//Watch NextReal Analysis Survival Guide youtu.be/v5rD0B-zfXwThis is why you have imposter syndrome youtu.be/5CN_KovhHbYSoME2 Entry youtu.be/3ARBkAM2hRgReal Analysis:How to think of Real Numbers youtu.be/fD9VggL7RYUThe Banach Fixed Point Theorem youtu.be/_I790SqNDjsThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Control Theory:The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//MusicMost music provided by Epidemic Sound with the exception of one song by Tom Fox at Johnny Harris' PatreonUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 Start1:14 Maurice Frechet1:58 Motivation through Finite Sets3:36 Brilliant.org Sponsorship5:37 Continuity via Open Sets11:01 Continuous Images of Compact Sets12:51 Uniform Continuity and Heine's Theorem18:37 Frechet Not Appreciated19:38 Maximum value on Compact Sets24:03 Wrap Up
Applying for TENURE in Floridas Political Scene ThatMathThing 2023-10-23 | I am applying for tenure at a Florida university while Ron Desantis is working to eliminate it. Let's talk about what tenure is, where it came from, and why it is (or isn't) important.To be clear, the statements in this video are made as a private citizen and not in an official capacity as an employee of the University of South Florida.//BooksRudin - amzn.to/3KeL0ICDummit and Foote Abstract Algebra amzn.to/3QxGvwNFolland Real Analysis amzn.to/3dCuCaoHungerford Algebra amzn.to/3pIJyGVPedersen Analysis NOW amzn.to/3c27MZo//Watch NextReal Analysis Survival Guide youtu.be/v5rD0B-zfXwThis is why you have imposter syndrome youtu.be/5CN_KovhHbYSoME2 Entry youtu.be/3ARBkAM2hRgReal Analysis:How to think of Real Numbers youtu.be/fD9VggL7RYUThe Banach Fixed Point Theorem youtu.be/_I790SqNDjsThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Control Theory:The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//MusicHenry's Abode is from Tom Fox, provided through the Johnny Harris Patreon.Sunrise in Paris is by Dan Henig (provided through YouTube Music)The rest of the music is provided by Epidemic Sound.Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 Start0:59 I don't like politics2:18 How hard is it?4:03 What is Tenure?7:17 Applying for Tenure8:56 Where did tenure come from?10:54 Attack on Tenure13:46 Whelp...
Proof and Intuition for the Weierstrass Approximation Theorem ThatMathThing 2023-10-16 | This is an in depth look at the Weierstrass Approximation Theorem and the proof that can be found in Rudin's Principles of Mathematical Analysis. This proof resolves the polynomial approximation problem, a moment problem, and can even be seen as previewing Dynamic Mode Decompositions.//ArticlesAnton Schep - Weierstrass' Proof of the Weiestrass Approximation Theoremhttps://people.math.sc.edu/schep/weierstrass.pdfWeierstrass' 1885 Manuscript - math.auckland.ac.nz/hat/people/weierstrass.html//CodeBit Bucket - bitbucket.org/joelrosenfeld/weierstrass-approximation//BooksRudin - amzn.to/3KeL0ICDummit and Foote Abstract Algebra amzn.to/3QxGvwNFolland Real Analysis amzn.to/3dCuCaoHungerford Algebra amzn.to/3pIJyGVPedersen Analysis NOW amzn.to/3c27MZo//Watch NextReal Analysis Survival Guide youtu.be/v5rD0B-zfXwThis is why you have imposter syndrome youtu.be/5CN_KovhHbYSoME2 Entry youtu.be/3ARBkAM2hRgReal Analysis:How to think of Real Numbers youtu.be/fD9VggL7RYUThe Banach Fixed Point Theorem youtu.be/_I790SqNDjsThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Control Theory:The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//MusicMost music provided by Epidemic Sound with the exception of one song by Tom Fox at Johnny Harris' PatreonUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 The Weierstrass Approximation Theorem2:14 First Simplification4:42 Uniform Convergence7:30 Can never be too old to do math!8:18 The Main Characters of the Proof10:43 Walter Rudin's Approach14:11 Qn - A Delta Sequence18:30 Uniform Continuity19:27 The Proof of the Weierstrass Approximation Theorem25:17 MATLAB Code for the Weierstrass Approximation Theorem26:11 Is it a Polynomial?28:27 Closing Remarks
Recommendation Letters: The Good, the Bad, and the Career-Killing ThatMathThing 2023-10-06 | Your letters of recommendation are pivotal in any application, but why do they matter in 2023 and how can a single letter ruin your entire career?//BooksRudin - amzn.to/3KeL0ICDummit and Foote Abstract Algebra amzn.to/3QxGvwNFolland Real Analysis amzn.to/3dCuCaoHungerford Algebra amzn.to/3pIJyGVPedersen Analysis NOW amzn.to/3c27MZo//Watch NextReal Analysis Survival Guide youtu.be/v5rD0B-zfXwThis is why you have imposter syndrome youtu.be/5CN_KovhHbYSoME2 Entry youtu.be/3ARBkAM2hRgReal Analysis:How to think of Real Numbers youtu.be/fD9VggL7RYUThe Banach Fixed Point Theorem youtu.be/_I790SqNDjsThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Control Theory:The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//MusicThis Heist is by Tom Fox, provided through the Johnny Harris Patreon.The rest of the music is provided by Epidemic Sound.Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 Start0:53 Why do letters of recommendation matter?2:01 What does a good letter of recommendation look like?3:42 This is a bad letter.5:27 Who do you ask for a letter?7:32 How can it all go wrong?
What is Continuity? According to a Mathematician. ThatMathThing 2023-09-28 | What is continuity and what is the popcorn function? From primitive notions to the modern day, there have been a variety of attempts at understanding continuity and functions. We talk about them here, in this video.To try everything Brilliant has to offer—free—for a full 30 days, visit brilliant.org/ThatMathThing . The first 200 of you will get 20% off Brilliant’s annual premium subscription.(This video was sponsored by Brilliant)//ArticlesA Study of Maurice Fréchet: I. His Early Work on Point Set Theory and the Theory of FunctionalsAngus E. Taylorjstor.org/stable/41133673//BooksRudin - amzn.to/3KeL0ICDummit and Foote Abstract Algebra amzn.to/3QxGvwNFolland Real Analysis amzn.to/3dCuCaoHungerford Algebra amzn.to/3pIJyGVPedersen Analysis NOW amzn.to/3c27MZo//Watch NextReal Analysis Survival Guide youtu.be/v5rD0B-zfXwThis is why you have imposter syndrome youtu.be/5CN_KovhHbYSoME2 Entry youtu.be/3ARBkAM2hRgReal Analysis:How to think of Real Numbers youtu.be/fD9VggL7RYUThe Banach Fixed Point Theorem youtu.be/_I790SqNDjsThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Control Theory:The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 Start0:55 Intuitive Continuity2:39 Something is wrong with Power Series3:41 Making Popcorn in MATLAB5:33 Frechet and his Metric Spaces7:10 Making popcorn... no really10:15 Continuity in Metric Spaces11:10 Discontinuity of the Popcorn Function12:23 Topology was STOLEN!14:26 Continuity of the Popcorn Function15:27 The last words on Continuity
Surviving your PhD ThatMathThing 2023-08-21 | This video is a breakdown on how you need to prioritize your time over the 5 years of a PhD program. The first year is different from the last, and I break each year down according to responsibilities.To try everything Brilliant has to offer—free—for a full 30 days, visit brilliant.org/ThatMathThing . The first 200 of you will get 20% off Brilliant’s annual premium subscription.(This video was sponsored by Brilliant)//BooksRudin - amzn.to/3KeL0ICDummit and Foote Abstract Algebra amzn.to/3QxGvwNFolland Real Analysis amzn.to/3dCuCaoHungerford Algebra amzn.to/3pIJyGVPedersen Analysis NOW amzn.to/3c27MZo//Watch NextReal Analysis Survival Guide youtu.be/v5rD0B-zfXwThis is why you have imposter syndrome youtu.be/5CN_KovhHbYSoME2 Entry youtu.be/3ARBkAM2hRgReal Analysis:How to think of Real Numbers youtu.be/fD9VggL7RYUThe Banach Fixed Point Theorem youtu.be/_I790SqNDjsThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Control Theory:The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XMIntroduction to Control Theory youtu.be/0v4WFmOm764//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
The Riemann Rearrangement Theorem // I can make this sum anything I want ThatMathThing 2023-08-18 | Here we investigate the Riemann Rearrangement Theorem from the 19th century. Analysis was changed forever after this discovery.//BooksA great companion text to Rudin is Maxwell Rosenlicht's Introduction to Analysis. The explanations are a lot clearer and the book is under $20.amzn.to/3NFYiACWalter Rudin - Principles of Mathematical Analysis 3rd Edition - amzn.to/3MDHUisGerald Folland - Real Analysis: Modern Techniques and Their Applications - amzn.to/3JmK6NpR. Shankar - Principles of Quantum Mechanics - amzn.to/40825xjTom Apostol - Mathematical Analysis 2nd Edition - amzn.to/3mwxFlC//Reference for Cantor’s Workhttps://www.ias.ac.in/article/fulltext/reso/019/11/0977-0999//Exercises- Show that the elements of the Cantor set can be written in base-3 as 0.a_1 a_2 a_3 … where each a_i is either 0 or 2.//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Mastering the Art of Reading a Proof: By Example youtu.be/WPWf_s6Q1QQIntroduction to Control Theory youtu.be/0v4WFmOm764//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 Introduction0:40 Anticipating Topology1:48 Proof of Part A3:53 Can a sequence converge to more than one point?5:17 Proof of Part B8:21 Using a Theorem Backwards8:47 Functional Analysis Example10:28 What about a PROOF?
INSIDE Oppenheimer’s Secret Home ThatMathThing 2023-08-10 | A behind the scenes look at Oppenheimer's home in Los Alamos. Donate to the Los Alamos Historical Society at: losalamoshistory.org// BooksThe American Prometheus- Audible - amzn.to/3E71OAZ- Paperback - amzn.to/44RfFqF// Linkslosalamoshistory.org/history-blog/the-oppenheimer-house-through-time//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
Using MATH to make fractals in Photoshop ThatMathThing 2023-05-21 | We work to make some fractals using only Photoshop while discussing the underlying mathematics.//BooksIf you want to learn more about fractals, then I'd recommend picking up FRACTALS EVERYWHERE amzn.to/3Wq6rOK//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Mastering the Art of Reading a Proof: By Example youtu.be/WPWf_s6Q1QQIntroduction to Control Theory youtu.be/0v4WFmOm764//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
An Introduction to Sequences in Real Analysis ThatMathThing 2023-04-10 | Here we dissect a theorem statement about convergent sequences from Rudin's Principles of Mathematical Analysis (a.k.a. Baby Rudin). There is a lot to unpack here, including some allusions to Topology.//BooksA great companion text to Rudin is Maxwell Rosenlicht's Introduction to Analysis. The explanations are a lot clearer and the book is under $20.amzn.to/3NFYiACWalter Rudin - Principles of Mathematical Analysis 3rd Edition - amzn.to/3MDHUisGerald Folland - Real Analysis: Modern Techniques and Their Applications - amzn.to/3JmK6NpR. Shankar - Principles of Quantum Mechanics - amzn.to/40825xjTom Apostol - Mathematical Analysis 2nd Edition - amzn.to/3mwxFlC//Reference for Cantor’s Workhttps://www.ias.ac.in/article/fulltext/reso/019/11/0977-0999//Exercises- Show that the elements of the Cantor set can be written in base-3 as 0.a_1 a_2 a_3 … where each a_i is either 0 or 2.//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Mastering the Art of Reading a Proof: By Example youtu.be/WPWf_s6Q1QQIntroduction to Control Theory youtu.be/0v4WFmOm764//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 Introduction0:40 Anticipating Topology1:48 Proof of Part A3:53 Can a sequence converge to more than one point?5:17 Proof of Part B8:21 Using a Theorem Backwards8:47 Functional Analysis Example10:28 What about a PROOF?
What did we all miss in this 2000 year old problem? ThatMathThing 2023-04-03 | Two high school girls, Ne'Kita Jackson and Calcea Johnson discovered something we all missed for this 2000 year old problem. And it's really cool!//BooksWant to learn more geometry? Oliver Byrne's Elements of Euclid is a great text that examines Euclid's first six books in geometry with very nicely illustrated figures.Check it out here: amzn.to/3K6Geip//Watch NextTrigonometry without Geometry - youtu.be/9XFBw8Hfk5kIntroduction to Control Theory youtu.be/0v4WFmOm764Fixed Point Iteration - Loki gets slapped 16 times for SCIENCE youtu.be/_I790SqNDjs//LinksThe Pythagorean Proposition in Microfilm - files.eric.ed.gov/fulltext/ED037335.pdfMathTrain Video - youtube.com/watch?v=nQD6lDwFmCc//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//BooksWalter Rudin - Principles of Mathematical Analysis 3rd Edition - amzn.to/3MDHUisFundamentals of Differential Equations - Nagle, Saff, and Snider amzn.to/3qeGD9C//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!//Watch NextIntroduction to Control Theory youtu.be/0v4WFmOm764Fixed Point Iteration - Loki gets slapped 16 times for SCIENCE youtu.be/_I790SqNDjs//Music Provided by Epidemic SoundBetween The Lines - Elijah NDetective - DexterUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//BooksModern Control Systems - Dorf and Bishop amzn.to/331JQAmFundamentals of Differential Equations - Nagle, Saff, and Snider amzn.to/3qeGD9CFeedback Control Theory - Doyle, Francis, Tannenbaum amzn.to/3HFvuov//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 Introduction1:25 What is the Pythagorean Theorem?3:49 A First Proof4:44 Reverse Engineering a Proof5:32 Johnson Jackson Proof Case 16:12 Johnson Jackson Proof Case 29:29 Consequence of Calculus?
The Art of Impromptu Presentations: How to Deliver a Memorable Talk ThatMathThing 2023-03-27 | You don't want to blow your one shot to show people your life's work. Let's talk about how you can do that effectively.If you want to learn how to make a career in academics, make a research PROGRAM, and give good talks, then you should read "A PhD is not Enough" - amzn.to/3lLoNvD//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Stock Footage Provided Byhttp://www.pexels.co//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
An Introduction to Cantor and Infinity ThatMathThing 2023-03-06 | Infinity is hard to understand, and Cantor, who introduced it, was ridiculed for it.//BooksDavid Burton - History of Mathematics - amzn.to/3mrp8DUMaxwell Rosenlicht - Introduction to Analysis - amzn.to/3NFYiACWalter Rudin - Principles of Mathematical Analysis 3rd Edition - amzn.to/3MDHUisGerald Folland - Real Analysis: Modern Techniques and Their Applications - amzn.to/3JmK6NpR. Shankar - Principles of Quantum Mechanics - amzn.to/40825xjTom Apostol - Mathematical Analysis 2nd Edition - amzn.to/3mwxFlC//Reference for Cantor’s Workhttps://www.ias.ac.in/article/fulltext/reso/019/11/0977-0999//Exercises- Show that the elements of the Cantor set can be written in base-3 as 0.a_1 a_2 a_3 … where each a_i is either 0 or 2.//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Mastering the Art of Reading a Proof: By Example youtu.be/WPWf_s6Q1QQIntroduction to Control Theory youtu.be/0v4WFmOm764//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 Introduction1:16 Kronecker on Cantor2:03 How did Cantor get here?6:08 Uncountability of Perfect Sets10:14 What are Perfect Sets anyway?11:37 Cantor's set14:14 Wrap Up!
An Introduction to Compact Sets ThatMathThing 2023-02-27 | Compact sets are the foundation that modern mathematics is built on, and here we explore their definition and properties. Optimization problems are justified because continuous functions take maximum values on compact sets, our first spaces of functions get magnitudes and distance because of compact sets. And all of this is because Maurice Frechet wanted to generalize the work of Weierstrass.//BooksWalter Rudin - Principles of Mathematical Analysis 3rd Edition - amzn.to/3MDHUisGerald Folland - Real Analysis: Modern Techniques and Their Applications - amzn.to/3JmK6NpR. Shankar - Principles of Quantum Mechanics - amzn.to/40825xjMaxwell Rosenlicht - Introduction to Analysis - amzn.to/3NFYiACTom Apostol - Mathematical Analysis 2nd Edition - amzn.to/3mwxFlC//Exercises- Prove the product to sum identities for exponentials first for rational numbers then for real numbers.//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Mastering the Art of Reading a Proof: By Example youtu.be/WPWf_s6Q1QQIntroduction to Control Theory youtu.be/0v4WFmOm764//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 Introduction1:52 ChatGPT still can't math...4:36 What is a compact set?6:20 Compact sets are closed8:32 Prisms are closed9:20 The Heine Borel Theorem10:17 Frechet's Definition10:58 Wrap up
What are Metric Spaces and Limit Points? ThatMathThing 2023-02-20 | This video introduces metric spaces, open sets, limit points and closed sets.//BooksWalter Rudin - Principles of Mathematical Analysis 3rd Edition - amzn.to/3MDHUisGerald Folland - Real Analysis: Modern Techniques and Their Applications - amzn.to/3JmK6NpR. Shankar - Principles of Quantum Mechanics - amzn.to/40825xjMaxwell Rosenlicht - Introduction to Analysis - amzn.to/3NFYiACTom Apostol - Mathematical Analysis 2nd Edition - amzn.to/3mwxFlC//Exercises- Prove the product to sum identities for exponentials first for rational numbers then for real numbers.//Watch NextThe Real Analysis Survival Guide youtu.be/v5rD0B-zfXw Mastering the Art of Reading a Proof: By Example youtu.be/WPWf_s6Q1QQIntroduction to Control Theory youtu.be/0v4WFmOm764//Music Provided by Epidemic SoundUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!0:00 Start1:35 Neighborhoods and Open Sets2:39 Limit Points and Closed Sets4:17 Metric Spaces and Topologies4:43 A Mistake in Baby Rudin9:16 Wrap Up
Nailing the Job Talk ThatMathThing 2023-02-17 | Crafting a Job Talk is completely different from a regular talk. Let's talk about it, because you don't want to get this wrong (and lose the job).//Music Provided by Epidemic SoundSee you again next year by Mr Kent and Ruby RedUse this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:epidemicsound.com/referral/644nao//Stock Footage Provided Byhttp://www.pexels.co//Recording EquipmentCanon SL3: amzn.to/3nZ11KUCanon T6i: amzn.to/3FUpkQhRode VideoMic: amzn.to/3lhldGaBlue Yeti Microphone: amzn.to/3I1y88NYeti Nano Microphone: amzn.to/3I1mriASanDisc 256GB SD Card: amzn.to/3E3LOOrNeewer 5600K USB LED Lights: amzn.to/3xvB9cNNeewer 18 inch Ring Light: amzn.to/2ZvgCscCamera Power Adapter: amzn.to/3D3upUuDISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
