The Mathematics of Trust // How Game Theory Explains Cooperation Dr. Trefor Bazett 2021-08-24 | Check out Brilliant ► brilliant.org/TreforBazett Join for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this playlist on Game Theory.My Game Theory Playlist ► youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXCooperation is crucial to so much of society, but it comes with something of a dilemma. If we cooperate, we can potentially get a higher payoff. But if the other player doesn't cooperate, we could be left with nothing and would have been better off just acting alone and getting something. This is the truth dilemma, and we can use Game Theory to study it. Specifically we will study the Stag Hunt game that considers hunters deciding to go for a Stag or a Hare. This is a Normal Form Game and we begin by noting that its payoff matrix doesn't have any dominating strategies, the main method we have seen previously in the game theory playlist. Instead we will define Nash Equilibriums and see how the Stag Hunt game actually has two equilibriums, one that maximizes payoff and one that minimizes risk. 0:00 The Trust Dilemma0:45 The Stag Hunt Game5:12 Nash Equilibria7:56 The Cooperation Problem10:57 Check out Brilliant.org/treforbazettCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
The Reciprocal Prime Series (this proof should be taught in calculus!) Dr. Trefor Bazett 2022-11-01 | ►Get my favorite calculator app for your phone or tablet: MAPLE CALCULATOR: maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857►Check out MAPLE LEARN for your browser to do compute and graph math: maplesoft.com/products/learn/?p=TC-9857►Check out MapleSoft's YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ. Thank you to MapleSoft for sponsoring today's video. What is the sum of 1/p, where p is prime? There are infinitely many prime numbers, but as they become larger they contribute smaller and smaller amounts to the sum. So, does that sum converge or diverge? In this video I want to share a really cool proof that they diverge that will play on the harmonic series and the geometric series - to famous series from calculus - as well as prime factorization to prove that indeed this must diverge. 0:00 The Reciprocal Prime Series0:30 The Harmonic and Geometries Series2:37 The proof of divergence10:27 Thanks to Maple CalculatorCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequations.net/pages/treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS I LOVE (affilliate link):► amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
The strangest function I know (linear but not continuous?? huh??) Dr. Trefor Bazett 2022-10-17 | Keep exploring at brilliant.org/TreforBazett. Get started for free, and hurry—the first 200 people get 20% off an annual premium subscription.When you think of linear functions from R to R, you are probably thinking about lines. However, I'm going to show you in this video a crazy example of a linear function that actually fails to be continuous. We are going to use a slightly more general notion of a linear function:f(x+y)=f(x)+f(y) & f(cx)=cf(x)To do this we will first think of the real numbers as a vector space over the rational numbers. Then a consequence of the Axiom of Choice is that every vector space has a basis, and thus there is a subset of the real numbers so every real number can be written as a linear combination of elements from this subset with rational coefficients. Ok, so what is our crazy function? Given any such expression for x, then f(x) is defined to be the sum of those rational coefficients. We can quickly check it satisfies the two properties of linearity, but it isn't continuous as its output is only rational numbers and so it misses all the reals. 0:00 A weird function0:35 Linearity more generally2:20 Defining the function4:15 It isn't continuous...5:18 ...but it is linear!7:25 Axiom of Choice9:16 R as a vector space over Q12:20 Check out brilliant.org/TreforBazettCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequations.net/pages/treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS I LOVE (affilliate link):► amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
The Problem of Traffic: A Mathematical Modeling Journey Dr. Trefor Bazett 2022-08-15 | How can we mathematically model traffic? Specifically we will study the problem of a single lane of cars and the perturbation from equilibrium that occurs when one car brakes, and that braking effect travels down the line of cars, amplifying as it goes along, due to the delayed reaction time of the drivers. The ultimate phenomena we would like to predict is that stop-and-go behaviour where cars don't just travel at a constant speed in rush hour, but alternate between braking and accelerating. However, when building this model our inputs are very microscopic considerations about how an individual car brakes or accelerates based on the following distance and relative velocity of the car ahead of it. This video also aims to be an introduction to broad themes in mathematical modelling of real world problems, where we define a problem, choose the inputs to the system we will consider, make assumptions, build the model, and finally assess the model. Finally, the real piece of mathematics we are going to get out of this are called differential-delay equations, and I'll show you a bit about how to solve such equations at the end. This video is part of the second iteration of the Summer of Math Exposition, hosted by @3Blue1Brown and @Leios Labs . There are so many great videos in this in this exposition so definitely check them out by using the hashtag #SoME2. 0:00 The Challenge of Traffic0:28 #SoME2 0:53 The Modelling Process1:27 Defining the Problem2:04 Choosing Which Variables to Consider4:03 Making Assumptions5:46 Building the Microscopic Model for Each Car9:56 Macroscopic Equilibrium 10:34 The Relationship between Density and Velocity16:23 Maximizing Flux and the Optimal Oensity20:33 Modelling a Sequence of Cars24:07 Modelling the First Car26:05 Full Model: A Differential Delay System27:06 Assessing the Model Graphically29:33 Assessing the Model Qualitatively31:45 Solving Differential Delay SystemsCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequations.net/pages/treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS I LOVE (affilliate link):► amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotographyg
How I Make Presentations Using LaTeX & Beamer Dr. Trefor Bazett 2022-08-03 | My favorite LaTeX editor is Overleaf ►https://www.overleaf.com?utm_source=yt&utm_medium=link&utm_campaign=im22tb My thanks to Overleaf for sponsoring today's video! Check out the previous videos in my LaTeX playlist:►youtube.com/playlist?list=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73If you are doing a presentation that involves lots of mathematics, we can leverage our LaTeX skills from earlier in the playlist to be able to quickly make a presentation that lets us display beautiful math equations and graphics, all with pretty themes and timing as you would expect in the larger non-mathy presentation software like Powerpoint. We will use a documentclass called beamer which provides the nuts and bolts for creating slides with timings. A convenient table of themes and color paletes can be found at the bottom of Overleaf's reference page on Beamer: overleaf.com/learn/latex/Beamer#Reference_guide0:00 My PhD Defense Presentation0:18 Why LaTeX and Overleaf1:29 Presentation Basics3:09 Making our first slides3:37 Itemized Lists with timings5:33 Displaying your presentation as a pdf5:55 Timing controls: onslide, only, and alerts8:28 Text size and aspect ratio in documentclass9:35 Themes and Colorthemes10:51 Preamble tweaks: navigation bar and transparency12:18 Theorems, Proofs, Examples, etc14:19 Multiple Columns16:32 Sections and Title Pages19:45 Creating a handout20:53 Versions and collaboration in OverleafCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequations.net/pages/treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS I LOVE (affiliate link):► amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
I almost failed calculus. Today Im a math prof. Dr. Trefor Bazett 2022-07-26 | ►Visit brilliant.org/TreforBazett to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscriptionToday I'm a mathematics professor, but when I was a student taking first year calculus for the first time, I really struggled! In this video I break down a few major factors that contributed. 1) Everyone has their own attitudes towards math, and Carol Dweck's notion of a Fixed Mindset affects our learning behaviours. For myself, I had this idea I was "good at math" which meant I wasn't doing effective learning behaviours to improve myself because I thought this was fixed. I also then quickly developed a lot of math anxiety where I worried my self-image as someone who was good at math would be proven untrue if I actually worked hard and then didn't succeed. Silly, but many of us have fixed mindsets that get in the way!2) I was really passive in my learning behaviours, doing things like copying down notes or reading notes, but not engaging in active learning behaviours I now think are more effective for your learning. 3) I just didn't love it! Now I love Calculus, but it took my falling in love with math later on to come back and see a lot of the beauty. When I first took it it was just lots of computations evaluated by procedural fluency as opposed to conceptual reasoning. I first feel in love with math in an absract algebra course full of theorems and proofs. 0:00 The state of Calculus1:08 Attitudes towards mathematics3:17 Passive learning behaviours4:18 Not in love with calculus4:49 My view on attitudes today7:15 Be an active learner!8:31 How I fell in love with math10:50 Learn math at brilliant.org/TreforBazettCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequations.net/pages/treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS I LOVE (affilliate link):► amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
This Infinitely Differentiable Function Breaks Taylor Series Dr. Trefor Bazett 2022-06-15 | ►Get my favorite calculator app for your phone or tablet: MAPLE CALCULATOR: maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857►Check out MAPLE LEARN for your browser to do compute and graph math: maplesoft.com/products/learn/?p=TC-9857►Check out MapleSoft's YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ. Thank you to MapleSoft for sponsoring today's video. Taylor Series are incredible. We can approximate a function with the Taylor Polynomial, and then hope that when we take the infinite series we get a series that is equal to the original function. However, this doesn't always work, for several reasons. The first is that we either can't compute the Taylor Series centered at some values (example ln(x) isn't defined at 0), or that the result series only converges on a limited interval of convergence as we see in our second example. The trickiest part however is that even when the Taylor Series converges, that doesn't immediately imply that it converges to the original function! We will see the very cool example of e^{-1/x^2} (with f(0) defined to be 0) that is infinitely differentiable (aka smooth) but whose taylor series is the zero series and thus clearly not the same as the original function. An analytic function is one whose taylor series convergences to the original function, so this example is an example of a smooth function that is non-analytic. Cool! 0:00 The big question about Taylor Series0:30 Review of Taylor Series2:20 Ln(x) and its Interval of Convergence7:08 An infinitely differentiable but non-analytic example9:55 Smooth vs AnalyticCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequations.net/pages/treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS I LOVE (affilliate link):► amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Your calculus prof lied to you (probably) Dr. Trefor Bazett 2022-06-06 | ►Visit brilliant.org/TreforBazett to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription.Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequations.net/pages/treforWhat is the indefinite integral of 1/x? The most common answer is ln|x|+C. This is a more satisfying answer than just ln(x)+C without absolute values because the domain of ln|x| and 1/x match (all real numbers except zero). However, this still isn't quite right as the indefinite integral is defined as ALL anti-derivatives. The slightly pedantic full answer is all piecewise defined functions that look like ln(x)+C for x bigger than 0 and ln(-x)+D for x smaller than 0, that is having different constants on both sides of the hole in the domain. This still satisfies a corollary of the Mean Value Theorem that asserts any two anti-derivatives differ by at most a constant provided we are on an open interval, which is what happens on each side of x=0. The animations in this video were made with Geogebra. 0:00 The indefinite integral of 1/x0:40 Why is ln|x| a better answer than ln(x)?3:14 Why do we always add +C ?3:58 What really is an indefinite integral?5:03The full answer7:17 The Mean Value Theorem and the +C8:30 Check out Brilliant.org/TreforBazettCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
How I make beautiful GRAPHS and PLOTS using LaTeX Dr. Trefor Bazett 2022-05-30 | My favorite LaTeX editor is Overleaf: ►https://www.overleaf.com?utm_source=yt&utm_medium=link&utm_campaign=im22tb My thanks to Overleaf for sponsoring today's video!Check out the previous videos in my LaTeX playlist:►youtube.com/playlist?list=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73I make most of my graph and plots inside of LaTeX using a package called pgfplots. LaTeX is a type setting language and I like using it for graphs specifically because I can control all aspects of my graphs very precisely, with formatting native and easily adjustable with the rest of my document, with syntax similar to the syntax of the rest of LaTeX that I use all the time, and best of all it is free and will remain readily available. In this video we will see how to do 2D graphs, scatter plots, bar charts, 3D surface plots and 3D line plots, as well as how to format all aspects of our plots and axes. 0:00 Why I use LaTeX and pgfplots for plots and graphs1:17 Why I use Overleaf as my LaTeX editor2:00 The simplest 2D plot3:57 Adjusting the preamble4:49 Customizing plot color, style, marks, samples6:25 Adjusting axis bounds, placement, labels and title9:04 Plot domain9:45 2nd example: ticks, tick labels, grid lines13:51 Adding text nodes15:18 3rd example: Scatter plot with imported data18:38 4th example: color coded scatter plot20:16 5th example: stacked bar chart21:23 Version history in overleaf22:00 6th example: 3D surface and mesh plots25:47 7th example: 3D curve plotThe full documention for pgfplots (it's long!) is here: iro.umontreal.ca/~simardr/pgfplots.pdfCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequations.net/pages/treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Diracs Belt Trick: Why a 2π rotation twists space but a 4π rotation fixes it Dr. Trefor Bazett 2022-05-23 | Visit ► brilliant.org/TreforBazett to help you learn STEM topics for free, and the first 200 people will get 20% off an annual premium subscription.Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforWhen you twist your arm or a belt by 360 degrees, the hand or endpoint is back to where it started but the rest of your arm or belt is still twisted. But if you do a 720 degree twist, you can manage to untwist your arm or belt! This is known as Dirac's Belt Trick or the Balinese Cup Trick. This crazy fact is even connected to physics with spin 1/2 particles, so let's try and figure out why! We will study rotations in 2 and 3 dimensions, and specifically study them topologically as opposed to algebraically as you might have seen before with rotation matrices. For a 2D rotation this is identified with points on a circle S^1. For a 3D rotation we need both an axis or rotation and an angle of rotation and we identify this with the solid ball of radius pi where a point in the ball gives a vector from the origin to the point that is our axis of rotation and the length of this vector is the angle. There is a catch: we have a double counting along the boundary so we have to identify antipodal points as the same. If you eliminate the origin (ie no rotation) this is sometimes called the Special Orthogonal Group SO(3) which is topologically the same as 3D Real Projective Space RP(3). A belt is then a path and I show an explicit way I can continuously deform the 4pi rotation path back to the identity. 0:00 Dirac's Belt Trick1:37 2D rotations and the Circle2:35 Axis and angle of 3D rotations3:24 Modelling rotations using a solid ball5:31 The double counting problem and identifying antipodes6:43 Paths of Rotations9:49 Deforming the 4π path12:49 Thanks to Brilliant.org/TreforBazettCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Untangling the beautiful math of KNOTS Dr. Trefor Bazett 2022-05-09 | Visit ► brilliant.org/TreforBazett to help you learn STEM topics for free, and the first 200 people will get 20% off an annual premium subscription.Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforSuppose you have two tangled knots. How can you tell whether they are the same knot or different knots? Welcome to Knot Topology. A knot is a nice embedding of a circle into three dimensional space, up to "ambient isotropy" where you can wiggle it around but not cut it. We can project this onto a plane to create a knot diagram. Then, two knot diagrams represent the same knot if and only if there is a sequence of Reidermeister moves between them. We next explore various knot invariants like the simpler tricolorability and then expand to the Alexander Polynomial and ultimately compute this polynomial for the trefoil knot. The software I used to make all the knots is called knotplot.com0:00 Mathematical Knots0:33 Knot Diagrams1:48 Reidermeister Moves 4:24 The equivalence problem6:05 The idea of Knot Invariants6:27 Tricolorability9:12 Alexander Polynomial14:37 Future direction in Knot Topology16:01 Brilliant.org/TreforBazettCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Beyond the Binomial Theorem: The Binomial Series Dr. Trefor Bazett 2022-05-03 | ►Get my favorite, free calculator app for your phone or tablet: MAPLE CALCULATOR: maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857►Check out MAPLE LEARN for your browser to do compute and graph math: maplesoft.com/products/learn/?p=TC-9857►Check out MapleSoft's YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ. Thank you to MapleSoft for sponsoring today's video. In this video we will be building up to the Binomial Series. We start with Pascal's Triangle, whose coefficients are found in the expansion for powers of binomials. We then take a combinatorial approach to come up with the Binomial Theorem which applies to positive integer powers of binomials. But what if the exponent is some other real number? Well we can use the power of Taylor Series to come up with the Binomial Series, and along the way we define a natural extension of the "n choose k" notation that work for arbitrary real numbers too. 0:00 Pascal's Triangle0:51 Expanding Binomials with Maple Calculator2:00 Connecting Coefficients to Pascal's Triangle4:03 Combinatorical Approach to Binormial Coefficients5:12 Binomial Theorem6:23 Extending "n choose k" formula8:22 Taylor Series Review10:00 The Binomial Series11:22 Binomial Series in Maple LearnCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
The Beautiful Story of Non-Euclidean Geometry Dr. Trefor Bazett 2022-04-25 | Visit brilliant.org/TreforBazett to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription.Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforIn this video we are going to explore the origins of non-Euclidean geometry. We look back to Euclid and his infamous book the Elements, where he outlined an axiomatic approach to Euclidean geometry using five postulates. The fifth, the parallel postulate, has always been controversial, a consistent system of geometry that accepted the first four postulates but rejected the parallel postulate wasn't discovered until the nineteen century by Janos Bolyai, Nikolai Lobachevsky, and Carl Gauss who independently worked towards something called hyperbolic geometry, one of multiple non-Euclidean geometries. We specifically will explore the Poincare disk, one model of hyperbolic geometry. Play around with the Geogebra page I used in the video ► geogebra.org/classic/sxakwtrr0:00 Euclidian Geometry and the Elements2:12 The Five Postulates3:21 Should the Parallel Postulate be a theorem?4:29 Spherical Geometry5:59 Janos Bolyai discovers Hyperbolic Geometry6:48 Hyperbolic Geometry and the Poincare Disk10:49 Resolving the Parallel Postulate Question11:19 Angles and Triangles13:44 Brilliant.org/TreforBazettCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
How to make beautiful math graphics using Tikz & LaTeX Dr. Trefor Bazett 2022-04-19 | Get started with LaTeX using Overleaf: ►https://www.overleaf.com?utm_source=yt&utm_medium=link&utm_campaign=im22tb My thanks to Overleaf for sponsoring today's video. Check out the previous videos in my LaTeX playlist:►youtube.com/playlist?list=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforIn this video we're going to talk about making diagrams and other graphics using the tikz package in LaTeX. This package makes it really easy to create all the normal geometric shapes like lines and circles, but more importantly to precisely control the look and placement of these graphics. The use of "nodes" makes it particularly easy to make complicated diagrams where one uses relative instead of absolute placements. You can also check out the actual document I use in this video here: ►overleaf.com/read/zzbhmgtkzyfb0:00 Intro to Tikz0:28 LaTeX Editors and Overleaf1:16 What to put in the preamble2:40 Drawing Lines, Circles, Ellipses6:02 Drawing Rectangles and Grids8:00 Centering and Scaling9:25 Color, Dashed, Fill, Shading11:52 Arrows and Thickness12:50 Text and Nodes15:35 Node Example Diagram21:38 More Complicated ExampleCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Weird notions of distance || Intro to Metric Spaces Dr. Trefor Bazett 2022-04-11 | Visit brilliant.org/TreforBazett to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription.Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequations.net/pages/dr-treforWeird, funky types of distance can still be thought of as "distance", but what actually is distance anyways? In this video we are going to introduce the big ideas of Metric Spaces. A Metric Space tries to generalize the notion of distance that we are all familiar with: straight line or Euclidean distance. We will see a couple other types of of distance such as the Manhattan distance aka the taxicab metric, as well as the Chebyshev distance which is basically how the king moves in chess. All of these are actually metrices! So what is a metric? Well it is a way of associating a distance that obeys three properties:1) d(A,B)=0 iff A=B2) d(A,B)=d(B,A) ie a symmetry property3) d(A,C) less than or equal to d(A,B)+d(B,C), called the triangle inequality. Metric spaces are a foundational idea in the field of mathematical analysis. 0:00 Euclidean or Straight Line Distance0:24 Taxicab Metric0:57 Chebyshev Metric1:49 Formulas for the distances4:34 Definition of Metric Spaces7:14 Open Balls9:31 Why care about Metric Spaces?10:45 Brilliant.org/TreforBazettCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Variation of Parameters || How to solve non-homogeneous ODEs Dr. Trefor Bazett 2022-03-28 | MY DIFFERENTIAL EQUATIONS COURSE PLAYLIST: ►youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBwMy Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqsCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforThe method of Variation of Parameters is a method to solve nonhomogeneous linear differential equations like y''+y=tan(x). We have seem previously in the ODE playlist that we can solve homogeneous constant coefficient equations like y''+y=0 easily. So the real goal here is how to adapt the homogeneous solutions to this nonhomogeneous case. The trick is instead of guessing a linear combination of the homogeneous solutions where the coefficients are constants, we guess a particular solution where the coefficients are actual functions (i.e. the parameters are being varied). Turns out that this method always works, up to our ability to find the homogeneous solution and solve the resulting integrals. This is in contrast to the previous method of undetermined coefficients, which was great in that it reduces the problem to algebra but bad in that it only sometimes works. 0:00 Homogeneous vs Nonhomogeneous1:35 Variation of Parameters Example7:07 Variation of Parameters General Formulas9:42 Undetermined CoefficientsCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Parsevals Identity, Fourier Series, and Solving this Classic Pi Formula Dr. Trefor Bazett 2022-03-14 | To celebrate #PiDay we solve the Basel Problem - that the sum of reciprocals of square naturals is pi^2/6 - using techniques from Fourier Analysis, in particular Parseval's Identity, which is a sort of infinite dimensional analog of Pythagoras. Check out my intro playlist on FOURIER SERIES► youtube.com/watch?v=wmCIrpLBFds&list=PLHXZ9OQGMqxdhXcPyNciLdpvfmAjS82hRCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequations.net/pages/dr-trefor0:00 The Basel Problem1:06 Fourier Series Refresher3:22 Parseval's Identity5:13 Inner Products & Generalized Pythagoras9:46 The proof that n^2/6=1/1+1/4+1/9...COURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
The Beautiful Barnsley Fractal #shorts Dr. Trefor Bazett 2022-03-07 | Check out my MATH MERCH at beautifulequation.com/pages/dr-trefor
This Infinite Integral Tower Actually Converges? Sorta... Dr. Trefor Bazett 2022-02-28 | Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforTake some function f(x) and compose it with itself over and over again, f(f(f(f(f.... What is the limit of that sequence? Certainly a converges for fixed points where f(x)=x, and indeed there is a whole theory about fixed point iteration that looks at the stability of fixed point. We've seen this in my previous video on cos(cos(cos(cos(... where the Banach Fixed Point Theorem guaranteed us a convergent sequence no matter where we started. In this video however, I've got a rather funky example, one where the f(x) is a particular integral and it has the golden ratio as a fixed point. However, it has all sorts of interesting dynamics beyond just the fixed points. My thanks to @Dr Barker who first introduced me to framing this problem in terms of integrals. The real goal of my video is to elaborate on Dr. Barker's video and explain what happens in the domain -phi up to phi. His video: youtube.com/watch?v=xnFCncV-288►My Previous video on cos(cos(cos(cos(cos(cos....: youtube.com/watch?v=qHnXE_h5c2M0:00 Intro0:25 Defining as a sequence2:41 Fixed Points4:16 Where it diverges to infinity6:10 -phi up to phi8:30 Eventually Fixed Points11:48 Summary12:47 Math Merch!!COURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
We need to talk about cheating in universities... Dr. Trefor Bazett 2022-02-03 | Cheating in university is a big money business and connects to a lot of larger issues in education. As a professor, I unpack what exactly the issue is, why it is happening, and what we can do about it. The type of cheating that I've faced most often since the twitch to online learning is called contract cheating where you spend money to have solutions provided to you. Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/trefor0:00 Intro0:32 What is Cheating2:18 The Business of Cheating5:55 Is Cheating Effective?11:57 Why Students Cheat14:08 What Can Teachers Do?17:35 My thoughtsCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
What is cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos(…?? // Banach Fixed Point Theorem Dr. Trefor Bazett 2022-01-10 | This weird expression of taking cos over and over again is just a sequence x_n=cos(x_{n-1}). There is a very cool theorem called the Banach Fixed Point Theorem that let' us figure out the limit of sequences like this and depends on cos(x) being a so called contractible mapping. Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequations.net/pages/dr-trefor0:00 The sequence1:17 Cos(x) Graphically3:25 Spiral Geometric View7:02 Banach Fixed Point TheoremCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
CALCULUS SPEEDRUN || Limits || Episode 1 Dr. Trefor Bazett 2021-12-09 | ►Try these exam-level limit problems yourself in this Maple Learn document: learn.maplesoft.com/#/?docId=4705771508203520&key=3A50C9AF56994D9F8EAE9CDA0E5A0FC057D97E1575E8439899BAD5BD2778AD0E►Study more efficiently with my favorite, free calculator app for your phone or tablet: MAPLE CALCULATOR: maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857Welcome to episode 1 of my calculus speedrun. In each video I'll go over a bunch of actual exam level problems I've previously given in my calculus courses as a math professor. In this first video we study limits. We're going to see 5 examples involving continuity of piecewise functions, exploiting the limit of sin(x)/x, using radical conjugates, limits at infinity, and finally dealing with compositions with continuous functions. If you are a bit more of a beginner at limits, then check out the full Calc 1 playlist below. 0:00 Intro to Calculus Speedrun0:47 Ex 1: Continuity for Piecewise Functions3:26 Ex 2: sin(x)/x style limits6:05 Ex 3: Square roots and radical conjugates8:49 Ex 4: Limits at infinity10:55 Ex 5: Limits of compositionsCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Power Sets and the Cardinality of the Continuum Dr. Trefor Bazett 2021-12-07 | Get better at math with Brilliant ► http://www.brilliant.org/treforbazett. Sign up for free, or the first 200 people who sign up using that link get 20% off an annual premium subscription. My thanks to Brilliant for sponsoring today's video!In this video we will learn about the power set, which is the set of all subsets of a given set. The cardinality of the power set of size n is given by 2^n. Finally, we will see a really interesting function that maps surjectively from the power set of the natural numbers using binary numbers to the interval [0,1] which is a continuum and we have previously seen by Cantor's diagonalization that [0,1] is uncountably infinite. In general, the power set of a set has a higher cardinality than the original set. 0:00 Definition of Power Sets2:18 Example with 3 elements3:10 Power Set of the Empty Set4:33 Cardinality of a (finite) power set5:52 Power Set of the Natural Numbers10:22 Cardinality and uncountably infiniteCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
My FINAL EXAM STUDY SYSTEM as a math prof Dr. Trefor Bazett 2021-12-02 | ►Study more efficiently with my favorite, free calculator app for your phone or tablet: MAPLE CALCULATOR: maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857►Check out MAPLE LEARN for your browser to make interactive math documents: maplesoft.com/products/learn/?p=TC-9857►Check out Maplesoft's YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQIt's cramming time, but how should you study? In this video I'm sharing my study system, all my top tips as a math professor to help you ace your exams. Ideally you would study slowly and carefully over months, but we all get there where the exam is in a couple days and now is the time to cram. We will talk about how to schedule your studying to leverage spaced retrieval and interleaving effects, how to emphasis active learning techniques like making predictions and practicing problems, where you should be putting most of your emphasis, how to analyze past mistakes, and what an effective study routine looks like. 0:00 How to Cram0:33 Be Kind To Yourself0:57 Schedule Smart2:17 Active vs Passive Learning3:06 Reviewing Notes5:03 Course Scaffold5:41 Practice, Practice, Practice 8:27 Correct Past Mistakes10:28 Self Regulated Learning11:40 Make Predictions12:42 Eat, Sleep, Food etcCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
IS CHESS A GAME OF CHANCE? Classical vs Frequentist vs Bayesian Probability Dr. Trefor Bazett 2021-11-24 | Learn more about probability - and so much more - at http://www.brilliant.org/treforbazett. My thanks to Brilliant for sponsoring today's video. Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforWhat, exactly, is probability? In this video we will see a few different perspectives on chance, the classical or a priori viewpoint, the frequentist or empirical viewpoint, and finally the Bayesian or subjective viewpoint. We're even going to consider the game of chess, what appears to be overwhelmingly a game of skill, but which the limits of our bounded rationality still results in probabilistic elements. 0:00 Intro to Probability0:50 Classical Probability2:09 Frequentist Probability5:18 Bayesian Probability7:14 Is Chess a game of chance?11:05 Underestimate the role of chance11:47 Brilliant.org/treforbazettClassical Probability: This is when we have a finite set of equally likely possibilities, and thus the probability of an event A is just the number of times A occurs out of all the possibilities. This is great when we know everything about a situation like a normal deck of cards. Frequentist Probability: This is when we do emperical studies and see how frequently event A occurs, particularly in the limit as we do a large number of studies. This is great when we don't know a priori exactly what is going on like some deck with an unknown number of cards removed, but the downside is we need to be able to do a large number of trials. Bayesian Probability: This is when we begin with a prior probability and when we gain new information we update our worldview (often using Bayes' Theorem) to get a posterior probability. This viewpoint is subjective because you and I may get different results given different information and different even if we had the same prior probability. COURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
My favorite LaTeX packages for writing beautiful math documents Dr. Trefor Bazett 2021-11-16 | Get started with LaTeX using Overleaf: ►https://www.overleaf.com?utm_source=yt&utm_medium=link&utm_campaign=im22tb Overleaf is an excellent cloud-based LaTeX editor that makes learning and using LaTeX just so much easier. My thanks to Overleaf for sponsoring this video!►Check out my LaTeX playlist from complete beginner to expert: youtube.com/playlist?list=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR730:00 Intro to LaTeX1:15 Sharing in Overleaf2:20 Links and urls with hyperref6:06 Code and quotes with fancyvrb8:40 Headers and Footers with fncyhdr10:19 The lastpage package11:35 Modifications with etoolbox13:12 Syncing with Github14:18 Fancy Chapters15:21 Colors with xcolor16:55 tcolorbox for fancy boxes and theorems21:45 SI units with SIunitx24:02 Spacing with setspace25:27 Acronyms and Glossaries with gloassaries-extra27:49 Tracking Changes in Review ModeIf you want to play with the exact Overleaf document I made in the video, check it out here: overleaf.com/read/rqcpcxshjtppFurther reading on some of the packages: Xcolor: overleaf.com/learn/latex/Using_colours_in_LaTeXHyperref: overleaf.com/learn/latex/HyperlinksFancyhdr: overleaf.com/learn/latex/Headers_and_footers#Reference_guideTcolorbox: overleaf.com/project/618021b7d7200cb739b0da5dSetspace: overleaf.com/learn/latex/Questions/How_can_I_double_space_a_document%3FAdditional LaTeX packages that I've talked about in previous videos: amsmath, amsfonts, amsthm, geometry, graphicx, lipsum. Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequations.net/pages/dr-treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Bayesian Truth Serum // Using MATH to catch liars Dr. Trefor Bazett 2021-11-09 | Get better at math with Brilliant ► brilliant.org/TreforBazett Learn math more effectively for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this video on the Bayesian Truth SerumCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforHow can we figure out how many people cheat on their homeworks or their taxes? We could just ask them, but they might lie! In this video we will explore a fascinating piece of mathematics called the Bayesian Truth Serum that leverages the power of Bayes' Theorem and Bayesian Analysis to create a special type of survey that incentivizes telling the truth. Telling the truth actually becomes something called a Bayesian Nash Equilibrium. Using this technique, researchers were able to find a much higher prevalence of contract-cheating on homework than previously reported. COURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Stirlings Incredible Approximation // Gamma Functions, Gaussians, and Laplaces Method Dr. Trefor Bazett 2021-11-02 | We prove Stirling's Formula that approximates n! using Laplace's Method.►Get my favorite, free calculator app for your phone or tablet: MAPLE CALCULATOR: maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857►Check out MAPLE LEARN for your browser to make beautiful graphs and much more: maplesoft.com/products/learn/?p=TC-9857►Check out Maplesoft's YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQIn his video we prove Stirling's Approximation Formula that n! is approximately sqrt(2 pi n)(n/e)^n in the limit as n goes to infinity. Our proof has three main ingredients. Firstly, we use the Gamma Function definition of n! being a specific improper integral. We will manipulate this integral and apply Taylor's Approximation to turn it into a quadratic, a trick called Laplace's Method. Finally this will become a Gaussian integral and with a change of variables we will get Stirling's Formula.Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforRelated Info:►My video comparing n! and n^n: youtube.com/watch?v=DZvqwuWuai0►Proof that the Gamma Function gives factorials: youtube.com/watch?v=KqokoYr_h1A&t=441s►The Gaussian Integral: youtube.com/watch?v=mrcRODAx-Vk►More reading on Laplace's Method: http://www.math.utah.edu/~davar/transparencies/Stirling.pdf0:00 Stirling's Formula0:55 Stirling's Formula graphically2:25 The Gamma Function3:09 Taylor Approximations5:01 The Gaussian Integral5:33 Laplace's MethodCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
How to write a thesis using LaTeX **full tutorial** Dr. Trefor Bazett 2021-10-26 | Get started with LaTeX using Overleaf: ►https://www.overleaf.com?utm_source=yt&utm_medium=link&utm_campaign=im22tb My thanks to Overleaf for sponsoring today's video. My LaTex Videos:►PART I: LaTeX for complete beginners : youtube.com/watch?v=Jp0lPj2-DQA►PART II: Full LaTeX tutorial: youtube.com/watch?v=-HvRvBjBAvg►PART IV: My Favorite Packages: youtube.com/watch?v=331YxgOJUGwCheck out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforIn this video I'll talk about all the major things needed to write a thesis using LaTeX, a markup language that is great for displaying any content with formulas. We'll start with the title page, abstract, dedication, acknowledgement. I'll show how to separate out chapter into different files, table of contents, manage appendices, figures, and bibliographies, cite reference, use footnotes, and adjust the margins of your document using the geometry package. 0:00 Intro0:43 Why LaTeX is great for writing a thesis1:25 My favorite LaTeX editors Overleaf.com2:16 Folders, Projects, and Templates3:26 Document Class and Title Page5:06 Abstract, Dedication, Acknowledgements6:59 Separate chapter files9:10 Managing Errors11:14 Table of Contents11:59 Appendices13:54 Collaboration and History using Overleaf.com15:20 Figures and List of Figures19:53 Bibliography and Citations23:55 Tracking Changes using Overleaf.com24:58 Footnotes27:15 Margins and FormattingMore reading:Bibliographies using Bibtex: overleaf.com/learn/latex/Bibliography_management_with_bibtexSyncing with Bibliography management tools like Zotera and Mendeley: overleaf.com/learn/how-to/How_to_link_your_Overleaf_account_to_Mendeley_and_ZoteroPage size and margins: overleaf.com/learn/latex/Page_size_and_marginsOverleaf's Premium features: overleaf.com/learn/how-to/Overleaf_premium_featuresPositioning of Figures: overleaf.com/learn/latex/Positioning_of_FiguresCheck out MY MATH MERCH (Collab with Beautiful Equations)►beautifulequations.net/pages/dr-treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
The Largest Numbers Ever Discovered // The Bizarre World of Googology Dr. Trefor Bazett 2021-10-21 | Check out Brilliant ► brilliant.org/TreforBazett Learn math more effectively for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this video on unfathomably large numbers. Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/treforWhat is the biggest number in the universe? What is the biggest number that any human has ever conceived of, or used in a proof, or been able to write down? In this video we are going to explore the fascinating world of googology, the study of unbelievably big numbers. We will begin near the bottom with "tiny" number like a googol (10^100) and a googolplex (10^googol) before realizing we will really need to do introduce better notation. We will then see Knuth's up-arrow notation that let's us form power towers of numbers, repeated exponentiation called tetration that is much like how exponentiation is repeated multiplication and multiplication repeated addition. And it goes up and up from there! We will see Graham's number which infamously got the googology ball rolling when it was used as an upper bound for a problem in graph theory and finally we will the unimaginable Tree(3) which comes out of a simple to state problem in graph theory and amazingly results in this incredible number. You can check our Ron Graham himself introduce how Graham's number comes about over on Numerphile here: youtube.com/watch?v=HX8bihEe3nA. You might also like to check out the googology wiki here: googology.wikia.org/wiki/Googology_Wiki 0:00 Intro to Googology1:13 Googol and Googolplex2:40 Towers of Exponents3:58 Knuth's up-arrow notation9:00 Graham's Number11:21 Tree(3)18:18 Brilliant.org/treforbazettCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
The most important limit in Calculus // Geometric Proof & Applications Dr. Trefor Bazett 2021-09-28 | ►Get my favorite, free calculator app for your phone or tablet: MAPLE CALCULATOR: maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857►Check out MAPLE LEARN for your browser to make beautiful graphs and much more: maplesoft.com/products/learn/?p=TC-9857►Check out Maplesoft's YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQThe limit of sin(x)/x as x goes to zero is perhaps the most important limit in Calculus and it is just one! This is equivalent to the small angle approximation that sin(x) is approximately just equal to x when x is sufficiently small. In this video we will begin with an application from astronomy using angular distance to estimate the size of objects in the universe. Then we will focus on the geometric proof of the limit of sin(x)/x which follows from some simple trigonometry. It is important to proof this geometrically because we can't just use L'Hopitals rule as that requires knowing that the derivative of sin(x) is just cos(x). As we will see, that proof however relies on this very limit!Check out my MATH MERCH line in collaboration with Beautiful Equations ►beautifulequation.com/pages/trefor0:00 Limit of sin(x)/x as x goes to 00:56 Astronomy Application2:49 Visual Intuition using Maple Learn3:47 Geometric Proof 8:16 Proof that the derivative of sin(x) is cos(x)COURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
The Evolution of Cooperation // Iterated Prisoners Dilemma Dr. Trefor Bazett 2021-09-21 | Check out Brilliant ► brilliant.org/TreforBazett Join for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this playlist on Game Theory.Check out the full Game Theory Playlist ► youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXHow does cooperation evolve over time? If you play the same game over and over again, how do you choose strategies where you reap the benefits of cooperation without being exploited. For example if someone always tries to cooperate, they loose poorly to someone who is always being selfish. We will contrast various types of repeated strategies but the one that tends to rise to the top is called Tit-For-Tat, where if someone is selfish back to you then you are selfish right back, and if they cooperate with you, you cooperate with them. Robert Axelrod introduced the idea of Iterated Prisoner's Dilemma tournaments where lots of people submit strategies and then the computer plays them all and this is where tit for tat rose up to the top. We will also think about repeated games like this from an evolutionary perspective and see how more cooperative strategies can become more popular over time, leading to the evolutionary origin of cooperation. 0:00 Intro0:42 The Prisoner's Dilemma3:21 Iterated Game Strategies5:20 Prober Strategy6:35 Grudge Strategy7:54 Tit for Tat Strategy10:44 Properties of Successful Strategies13:49 Evolution against Randoms15:25 Evolution of Cooperation18:23 www.brilliant.org/treforbazettCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
The Hierarchy of Big Functions || n^n greater than n! greater than e^n greater than n^100 Dr. Trefor Bazett 2021-09-14 | ►Get my favorite, free calculator app for your phone or tablet: MAPLE CALCULATOR: maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857►Check out MAPLE LEARN for your browser to make beautiful graphs and much more: maplesoft.com/products/learn/?p=TC-9857►Check out Maplesoft's YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQWhich function is bigger: n^n , n! , e^n , n^100 , ln(n) ? As n becomes large, all of these functions (or sequences, if you prefer) diverge to infinity. But some of them grow larger faster than others. We often think of exponentials as extremely fast growing, and they are, but they are actually slower than factorials and n to the exponent n. And all of those are faster than any polynomial like a quadratic and those are all faster then logarithms. We will state the big theorem for limits, see how to apply this theorem, and then prove the different limits involved. 0:00 The Hierarchy of Functions1:02 Graphing the Functions with Maple Learn2:57 The Big Theorem4:40 Applying the Big Theorem8:44 Proving that n^n beats n!10:20 Proving that polynomials beat logarithms11:49 Proving that factorials beat exponentialsCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1►GAME THEORY: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXOTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Intro to the Fundamental Group // Algebraic Topology with @Tom Rocks Maths Dr. Trefor Bazett 2021-09-09 | In this video I teach the amazing @Tom Rocks Maths a little bit of algebraic topology, specifically the fundamental group. Tom also taught me some really cool fluid dynamics and you can find our collab over at his channel here:►►► youtube.com/watch?v=bpeCfwY4qa0&ab_channel=TomRocksMaths0:00 What is Algebraic Topology?4:01 The alphabet to a topologist8:20 The algebra of loops about a ring14:50 Defining Homotopy Equivalence18:54 The Fundamental Group 23:58 Fundamental Group of R^225:50 Fundamental Group of a Sphere28:32 Fundamental Group of a Circle31:45 Fundamental Group of a Torus34:18 Proof of Brouwer's Fixed Point TheoremWe begin by talking about what connotations the words "algebraic" and "topology" have; "algebra" has a certain concreteness to it as we can add or multiply things, have explicit formulas, etc while "topology" is all about considering spaces that are thought of the same even if we continuously deformed like they were playdoh. Under this perspective, the alphabet only has three letters to a topologist, a single point, a single circle, and a double circle (the letter B). We then define more precisely the notion of a homotopy equivalence between two maps into a space X. There is an operation we call multiplication on such paths which captures the idea of doing one path followed by the next. It turns out that the homotopy equivalence classes of loops in a space X starting and finishing from a basepoint x_0 with this notion of multiplication form the fundamental group which we often write is Pi_1(X, x_0). Tom then computes the fundamental group of many spaces, the plane, the 2-sphere, the 1-sphere or circle, and finally - triumphantly - the torus! Finally we finish with a nice proof of Brouwer's Fixed Point theorem that uses the power of the fundamental group to arrive at a contradiction. COURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Nash Equilibriums // How to use Game Theory to render your opponents indifferent Dr. Trefor Bazett 2021-09-07 | Check out Brilliant ► brilliant.org/TreforBazett Join for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this playlist on Game Theory.Game Theory Playlist ► youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXNash Equilibria are one of the most powerful ideas in Game Theory, this was the subject of the movie Beautiful Mind. Given a normal form game, a mixed Nash Equilibrium is a choice of mixed strategy (i.e. probabilistic) for each player where no player can unilaterally improve their expected payoff. Incredibly, every such normal form game (with a finite number of players who can each choose from a finite number of pure strategies,) has a Nash Equilibrium! In this video I show you how to use pay-off matrices to computed the Expected Payoff aka Expectation Value for each action and use the Principle of Indifference to arrive at the Nash Equilibrium. We see two Nash Equilibrium examples, one from the football aka soccer world and one from economics with two firms in competition for a new market. 0:00 Intro to Nash Equilibriums0:56 Football Example Intuitively2:59 Mixed Strategies & the Indifference Principle4:00 Expected Payoff4:55 Definition of Nash Equilibrium5:32 Nash Existence Theorem6:06 Football Example Mathematically10:14 Economics Example14:45 Check out Brilliant.org/TreforBazettCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
My back to school routine as a PROFESSOR | One week until classes start! Dr. Trefor Bazett 2021-08-31 | ►Get my favorite, free calculator app for your phone or tablet: MAPLE CALCULATOR: maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857►Check out MAPLE LEARN in a browser to get step-by-step solutions to integrals and much more: maplesoft.com/products/learn/?p=TC-9857►Check out Maplesoft's YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQAh, back to school time. I know, I know, I'm a professor and my back to school routine is probably a bit different than your back to school routine, but actually I think there might be some overlap. 0:00 Sleep Routine1:17 Exercise Routine1:44 Find your classrooms2:20 Set concrete goals4:57 Maple Calculator and Maple Learn5:47 Note Taking6:27 Anki7:04 Read the Syllabus7:35 Read the textbookSome references:1) Why sleep is important for college students: nature.com/articles/s41539-019-0055-z2) Why an exercise routine is important for learning: sciencedaily.com/releases/2017/12/171221122543.htm#:~:text=Even%20a%20short%20burst%20of,power%2C%20says%20a%20new%20study.&text=A%2010%2Dminute%2C%20one%2D,London%2C%20Canada%2C%20have%20found.4) Maple Calculator: maplesoft.com/products/maplecalculator/download.aspx?p=TC-98575) Leverage Spaced-Retrieval practice with Anki: apps.ankiweb.net3) Why handwriting is better than typing for not taking: journals.sagepub.com/doi/abs/10.1177/0956797614524581COURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
MATH PROF vs TRICKY INTEGRALS Dr. Trefor Bazett 2021-08-17 | ►Get the MAPLE CACULATOR app for free that gives step-by-step solutions to integrals and much more:maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857►Check out MAPLE LEARN in a browser to get step-by-step solutions to integrals and much more: maplesoft.com/products/learn/?p=TC-9857►Check out Maplesoft's YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQIn this video we are going to try three tricky integrals using standard first year calculus integration techniques like integration by parts, partial fractions, trig substitution and conjugates, but each is a little bit disguised. Do I still remember how to do these???0:00 Double Integration by Parts5:02 Get Maple Calculator for step-by-step solutions7:12 u-subs and integration by parts12:13 conjugate, trig sub, integration by partsCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Intro to LaTeX **Full Tutorial** Part II (Equations, Tables, Figures, Theorems, Macros and more) Dr. Trefor Bazett 2021-08-10 | Get started with LaTeX using Overleaf: ►https://www.overleaf.com?utm_source=yt&utm_medium=link&utm_campaign=im22tb My thanks to Overleaf for sponsoring today's video. ►Part I of my tutorial on LaTeX is here: youtube.com/watch?v=Jp0lPj2-DQA►The rest of my LaTeX playlist is here: youtube.com/playlist?list=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR730:00 Intro to LaTeX and Overleaf 1:46 Formatting (bold, italics, underline)4:40 Equation References6:28 Align, Split & Multiline Equation12:32 Tables and Tabular17:39 Figures20:30 New Theorem Environments26:00 Custom Macros A partial list of the various commands used in this video (see the above documentation for more info):Boldface text: \textbf{blah}Italics: \textit{blah}Underline: \underline{blah}Equation Environment: \begin{equation}blah\end{equation}Label the equation: \label{blah}Reference the equation later \ref{blah}Align multiple equations \begin{align}blah & blah\\ blah & blah\end{align}Split equations \begin{split}blah & blah\\ blah & blah\end{split }Put an equation on multiple lines: \begin{multline}blah\\blah\end{multline}Make a table \begin{tabular} (hit enter in Overleaf will autocomplete the rest)Put the above into a table environment with \begin{table}blah\end{table}Make a figure with \begin{figure} (hit enter in Overleaf to autocomplete the rest)Make a newline with \newlineMake a theorem environment with \newtheorem{name}[numbering]{Name} (needs \usepackag{amsthm}Make a new command with \newcommand{}{}Check out MY MATH MERCH (Collab with Beautiful Equations)►beautifulequations.net/pages/dr-treforCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
How to find DOMINATING STRATEGIES with Game Theory Dr. Trefor Bazett 2021-08-03 | Check out Brilliant ► brilliant.org/TreforBazett Join for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this playlist on Game Theory.Check out Episodes 1 & 2 of the Game Theory Playlist ► youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXIn Game Theory, a strategy is a dominating strategy if it always gives us the best payoff regardless of how our opponent plays, and similarly a dominated strategy gives us the least payoff, regardless of how our opponent plays. For example, Rock-Paper-Scissors has no dominating strategies as all three options are equally good against someone playing randomly. If we have a normal form game, written down with a payoff matrix, then we can search for dominating or dominated strategies for each player to help decide how people will play. In more complicated games, iterated elimination of dominated strategies can collapse to a single choice for both players. We first saw this idea back in Episode 1 on the Prisoner's Dilemma, but we now focus more fully on exploring the idea. 0:00 Dominating Strategies2:23 Economics Example8:30 Iterated Elimination of Dominated Strategies12:15 Check out Brilliant.orgA note on the formal definition of a dominating strategy: a strategy a1 is a dominating strategy for player 1 if the payoff function u(a1,a2,...,an) is bigger than u(a1', a2,...,an) for all choices of a1' and al choices of a2,...,an. COURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Normal Form Games // Intro to Game Theory // Episode 2 Dr. Trefor Bazett 2021-07-14 | Check out Brilliant ► brilliant.org/TreforBazett Join for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this video!!The 1st episode in the Game Theory playlist on the Prisoners Dilemma: youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlXIn this video we introduce our first major category of game that we will study in Game Theory called Normal Form Games. These are games between a finite number of players, with each player having a finite number of options, and then a defined payoff for every possible set of chosen actions. The Prisoners Dilemma we saw previously is an example of a normal form game, as is good old Rock-Paper-Scissors. We will also see two more examples, one I call Hawk vs Dove, and one I call Sushi vs Thai. Each game can be represented by a payoff matrix. In the next episode we will discuss more about how to find optimal strategies to play Normal Form games, and if optimal strategies even exist!0:00 Normal Form Games1:45 Payoff Matrix3:14 Hawk vs Dove Game6:11 Sushi vs Thai Game8:26 Formal Definition of Normal Form Games11:22 Check out Brilliant.orgCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
How to succeed as a math student // A conversation with Kyle Broder // Part I Dr. Trefor Bazett 2021-07-11 | Check out Part II of my conversation with @Kyle Broder on his channel here: youtube.com/watch?v=YnTf0xGKWOU0:00 Welcome to Kyle Broder0:26 Attitudes about Math 4:48 Struggle in Math9:56 Procedural Fluency13:18 Collaboration in Math20:02 Mental Models23:32 Role of Self AssessmentCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
The Formulas behind Savings, Investing, and Annuities Dr. Trefor Bazett 2021-07-06 | ►Play around with the ANNUITY CALCULATOR I built using Maple Learn here: learn.maplesoft.com/index.html#/?d=PGALNIDQLNAMKQPJPUFSDSLOIOJPHNMIBUFMFFGKENLUOUGQASERIIJQPKEKJHEQGFOLNMBTDUFSBSOGHJJGNIIPPTBRBKMLFKEJ►Check out MAPLE CALCULATOR phone app : maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857►Check out Maplesoft's YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ►Episode #1 in the Money Math Series, covering simple interest, compounded interest, and continuously compounded interest: youtube.com/watch?v=_sNMVHKcp9s&ab_channel=Dr.TreforBazettIn Episode #2 of Money Math we investigate the formulas behind Annuities, which consist of a series of payments over time. For instance, if our goal is to save a million dollars be retirement, how much should we be saving each year from now until retirement? We will derive the formula for the future value of an annuity and play around with several scenarios for saving to get a million dollars. 0:00 Big Idea of Annuities2:26 Deriving the Annuity Formula6:00 Example with real numbers8:10 Building an Annuity CalculatorCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
THE PRISONERS DILEMMA // Intro to Game Theory // Episode 1 Dr. Trefor Bazett 2021-06-29 | Check out Brilliant ► brilliant.org/TreforBazett Join for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this video!!► Episode II: youtube.com/watch?v=TVlf43FmuPYWelcome to the first episode of my series on Game Theory. We begin with the classic Prisoner's Dilemma, a counterintuitive example where both prisoners have a dominating strategy to confess that actually works out to a worse scenario than if they had both denied. This gives a type of stable equilibrium called a Nash Equilibrium. We will see how we can use a payoff matrix to encode the information and reason about what will be the likely outcome. This video is part of a longer series on Game Theory. We will study competitive games and cooperative games, Normal Form games and Sequential Form games, pure Nash Equilibria and mixed Nash Equilibria, along with many other subjects and applications of Game Theory! New videos on Game Theory every two weeks. 0:00 Intro to Game Theory1:00 The Prisoner's Dilemma2:49 Payoff Matrix4:31 The best strategy9:23 Brilliant.org/treforbazettCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Unboxing the worlds most prestigious CHALK Dr. Trefor Bazett 2021-06-17 | Among the world's best mathematicians, there is one chalk more infamous and prestigious than all the rest: Hagoromo Fulltouch. This originally Japanese brand was loved so much by the math world that when the company shut down mathmaticians started hoarding the chalk until finally a South Korean company bought up the recipe, machines and brand. Today I find out whether Hagoromo Fulltouch chalk really is all it is....chalked up to be. I also unbox my Silver Play Button!!!Added a link to the chalk in my Amazon Affiliate store: amazon.com/shop/treforbazett. Thankfully it is MUCH less expensive now than it was during the crisis!!COURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
INTEREST: Simple Interest vs Compound Interest vs Continuous Interest Dr. Trefor Bazett 2021-06-01 | ►Play around with the INTEREST CALCULATOR I built using Maple Learn for simple interest, compounded interest, and continuously compounded interest here: learn.maplesoft.com/index.html#/?d=PGALNIDQLNAMKQPJPUFSDSLOIOJPHNMIBUFMFFGKENLUOUGQASERIIJQPKEKJHEQGFOLNMBTDUFSBSOGHJJGNIIPPTBRBKMLFKEJ►Check out MAPLE LEARN for browsers: maplesoft.com/products/learn/?p=TC-9857 ►Check out MAPLE CALCULATOR phone app : maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857►Check out Maplesoft's YouTube channel: youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQWelcome to the first episode of my financial math playlist! Each video we are going to cover one topic related to money, personal finance, investing, or economics. The goal is to break down the mathematical formulas involved in these topics so we can really understand and be smarter with our money. In this first episode we are going to be talking about interest rates. We will see the formulas for simple interest, compound interest, and continuously compounded interest. We will, for instance, if you have a loan starting with an initial principle, and a particular interests rate over the term of the loan, how much money is owed at the end? Well, it depends on the type of interest. With simple interest, the same interest payment of a fixed percentage is paid every single period. With compound interest however, the amount of interest in each period goes up as there is interest on the interest. We will see how to break down an annual interest rate that is compounded monthly, for instance. Finally, continuously compounded interest is a limit as you compound more and more and more frequently. 0:00 What is interest?1:20 Simple Interest5:19 Compound Interest9:27 Comparing different compounding periods13:40 Continuously Compounded InterestCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Learning CHESS vs Learning MATH Dr. Trefor Bazett 2021-05-26 | As a math professor, I've spent a lot of time thinking about how to learn math effectively. Recently I've been picking up the game of Chess, and those effective study habits from math are also great for learning chess, and vice versa. In this video I walk through and compare my study tips for the two disciplines. 0:00 Chess vs Math0:39 Master the small details2:04 Practice Yourself vs Learn from Experts3:56 Review4:54 Persistence 7:18 Memorization vs Understanding 11:04 Growth MindsetCOURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
7 Ways to Level Up Your MATH SUPERPOWERS Dr. Trefor Bazett 2021-05-19 | Here are seven projects you can do over a summer to become a better mathematician:1) Learn how to program and/or apply those skills to do something in math. I typically recommend Python for a first language for STEM students. R is useful for stats. But it doesn't have to be a general language it could also be Maple, Mathematica or MATLAB which are mathematical suites. The point is, be able to use your computer to help your math. (Disclosure: I'm sometimes sponsored by Maple, although not for this video). 2) Learn LaTeX, which lets you write beautiful math. Here is in my intro video on this: youtube.com/watch?v=Jp0lPj2-DQA&ab_channel=Dr.TreforBazett3) Do some Mathematical Modelling. The idea here is to find something in your life or that interests you, and build out a mathematical model of that idea. Lot's to choose form, but one idea could be to take the basic idea of the SIR model for modelling pandemics, and adjust it to include new factors (my intro video on it: youtube.com/watch?v=Qrp40ck3WpI)4) Learn a new topic. Some ideas: Intro to Proofs and Discrete Math (youtube.com/watch?v=rdXw7Ps9vxc&list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS), my soon to be coming Game Theory series which is great for a general audience, or for those with more mathematical experience in Algebra, Analysis, and Linear Algebra, Category Theory is a really cool topic. 5) Read a math book! I have a few I enjoy at my Amazon Affiliate Store (I get a tiny percentage): amazon.com/shop/treforbazett6) Read some Math Papers. A great repository of preprints and published papers is arxiv.org. 7) Make a Math Education Video. @3Blue1Brown and @LeiosOS started a discord server here to bring people together interested in Math Exposition. discord.com/invite/Q3cC2GXN2fHave fun and feel free to share in the comments any other ideas!0:00 Programming1:55 Learn LaTeX2:40 Mathematical Model Something3:58 Learn a New Math Topic 5:34 Read a Math Book6:19 Read some Math Papers7:55 Make a Math VideoMY DIFFERENTIAL EQUATIONS PLAYLIST: ►youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBwOpen Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqsOTHER COURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
The beautiful geometric view of FOURIER SERIES // The Linear Algebra Perspective Dr. Trefor Bazett 2021-05-12 | Fourier Series can sometimes seem very computational and full of integrals, but there is actually a very deep and important geometric picture that is analogous to Linear Algebra. So many core ideas from linear algebra like bases, linear independence, orthogonality, inner products, and projections all have their analogs in Fourier Series. Effectively the idea of computing a Fourier Series is just decomposing a vector in an orthonormal basis. Cool! The rest of my Fourier Series Playlist: youtube.com/watch?v=wmCIrpLBFds&list=PLHXZ9OQGMqxdhXcPyNciLdpvfmAjS82hR&ab_channel=Dr.TreforBazett0:00 Vector Space of Periodic Functions2:55 Bases5:57 Inner Product Space10:47 Projections13:27 The Big PictureMY DIFFERENTIAL EQUATIONS PLAYLIST: ►youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBwOpen Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqsOTHER COURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
Computing the Fourier Series of EVEN or ODD Functions **full example** Dr. Trefor Bazett 2021-05-09 | In this video we do a full example of computing out a Fourier Series for the case of a sawtooth wave. We get to exploit the fact that this is an odd function where f(-x)=-f(x)) as we can simplify considerably our computations of the Fourier Coefficients if the function is either even or odd. Previous videos in the Fourier Series playlist: youtube.com/playlist?list=PLHXZ9OQGMqxdhXcPyNciLdpvfmAjS82hROpen Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqsOTHER COURSE PLAYLISTS:►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m► CALCULUS II: youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n►MULTIVARIABLE CALCULUS (Calc III): youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd►VECTOR CALCULUS (Calc IV) youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa►DIFFERENTIAL EQUATIONS: youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw►LAPLACE TRANSFORM: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1OTHER PLAYLISTS:► Learning Math Seriesyoutube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw►Cool Math Series:youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpihoBECOME A MEMBER:►Join: youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/joinMATH BOOKS & MERCH I LOVE:► My Amazon Affiliate Shop: amazon.com/shop/treforbazettSOCIALS:►Twitter (math based): http://twitter.com/treforbazett►Instagram (photography based): http://instagram.com/treforphotography
