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Dr. Will Wood
Приєднався 28 сер 2020
Simple animations to explain complicated mathematical concepts.
The Revolutionary Genius Of Joseph Fourier
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In this video, we explore the life and work of Fourier, culminating in the famous Fourier Series.
FAQ : How do you make these animations?
Animations are mostly made in Apple Keynote which has lots of functionality for animating shapes, lines, curves and text (as well as really good LaTeX). For some of the more complex animations, I use the Manim library. Editing and voiceover work in DaVinci Resolve.
Supporting the Channel.
If you would like to support me in making free mathematics tutorials then you can make a small donation over at
www.buymeacoffee.com/DrWillWood
Thank you so much, I hope you find the content useful.
This video was sponsored by Brilliant
In this video, we explore the life and work of Fourier, culminating in the famous Fourier Series.
FAQ : How do you make these animations?
Animations are mostly made in Apple Keynote which has lots of functionality for animating shapes, lines, curves and text (as well as really good LaTeX). For some of the more complex animations, I use the Manim library. Editing and voiceover work in DaVinci Resolve.
Supporting the Channel.
If you would like to support me in making free mathematics tutorials then you can make a small donation over at
www.buymeacoffee.com/DrWillWood
Thank you so much, I hope you find the content useful.
This video was sponsored by Brilliant
Переглядів: 156 794
Відео
Dirichlet Invented this Function to Prove a Point
Переглядів 219 тис.10 місяців тому
In 1829, Dirichlet invented the first nowhere continuous function. FAQ : How do you make these animations? Animations are mostly made in Apple Keynote which has lots of functionality for animating shapes, lines, curves and text (as well as really good LaTeX). For some of the more complex animations, I use the Manim library. Editing and voiceover work in DaVinci Resolve. Supporting the Channel. ...
This Function Maps Any Interval to the Real Line (Conway's Base-13 Function)
Переглядів 70 тис.Рік тому
In this video we'll explore Conway's "Base-13 function" which maps any real interval to the real line. It is a function which is discontinuous everywhere, yet still has the intermediate value property: making it a counter example to the converse of the intermediate value theorem. #some3 FAQ : How do you make these animations? Animations are mostly made in Apple Keynote which has lots of functio...
Minimax Approximation and the Exchange Algorithm
Переглядів 14 тис.Рік тому
In this video we'll discuss minimax approximation. This is a method of approximating functions by minimisation of the infinity (uniform) norm. The exchange algorithm is an iterative method of finding the approximation which minimises the infinity norm. FAQ : How do you make these animations? Animations are mostly made in Apple Keynote which has lots of functionality for animating shapes, lines,...
Pick's Theorem (From Euler's Planar Graph Formula)
Переглядів 6 тис.2 роки тому
In this video we'll discuss Pick's Theorem: probably the most famous theorem in lattice geometry. We'll use Euler's results from graph theory (namely, his planar graph formula) to prove this theorem. References and Notes: Ref. 1. This proof is given in full in Garbett (2010) - documents.kenyon.edu/math/GarbettJSenEx2011.pdf Also see Ref. 1 for proof that any primitive lattice polygon can be div...
A really Satisfying Proof about Triangles on a Lattice.
Переглядів 4,3 тис.2 роки тому
In this video we'll discuss an important result in lattice geometry: All primitive lattice triangles have and area of 1/2. Incidentally, the method of proof shows that all primitive lattice parallelograms have an area of 1. #SOME2 References and Notes: Ref. 1 This proof is entirely based on Garbett (2010) - documents.kenyon.edu/math/GarbettJSenEx2011.pdf Ref 2. This video shows how the determin...
The Riemann Zeta Function in the Integer Lattice
Переглядів 11 тис.2 роки тому
In this video we discuss visible points on the integer lattice and it's connection to the Riemann zeta function. Sources: 1. The main derivation was based on the blog post shreevatsa.wordpress.com/2008/11/07/lattice-points-visible-from-the-origin/ 2. A slightly more formal version of the argument given above for the probability of two integers being coprime is given in the introduction in: hal....
How Newton discovered Taylor series (but didn't tell anyone)
Переглядів 32 тис.2 роки тому
In this video we explore the independent discovery of Taylor series by Isaac Newton and the manuscript which "never left Newtons hands". Chapters 0:00 - Introduction 01:55 - James Gregory's discovery 04:22 - Isaac Newton's discovery 06:23 - Outro In-video References: 1. Meijering, E., 2002. A chronology of interpolation: from ancient astronomy to modern signal and image processing. Proceedings ...
Newton Interpolation and Divided Differences
Переглядів 44 тис.2 роки тому
In this video, we introduce the Newton Interpolation method and Divided Differences. We start with the general concept, then the recurrence relation and the divided difference table. Finally, we run through a quick example in order to understand how the method is used in practice. Chapters 0:00 - Introduction 05:40 - The Recurrence Relation 10:56 - The Divide Difference Table 12:48 - Example Er...
MSc Mathematics at The Open University
Переглядів 12 тис.2 роки тому
This video is intended to give you an overview of the postgraduate course MSc Mathematics at The Open University. The way I see it, this video will give you a flavour of the course and how it works without being too overwhelming with the details. Please note that module costs shown in the video are for UK students. Links: The Course - www.open.ac.uk/postgraduate/qualifications/f04 Diagnostic Qu...
Bijective Functions and the Continuum Hypothesis
Переглядів 16 тис.3 роки тому
This video is largely about bijective functions. Specifically why bijective functions have inverses, why bijective functions can be used to show two sets are the same size and how the continuum hypothesis can be written as a statement about bijections. Chapters: 0:00 - Introduction 01:02 - Definitions 03:32 - Inverses 05:28 - Cardinality 08:29 - Continuum Hypothesis The product links below are ...
Relations and Functions: The Modern Definition of a Mathematical Function.
Переглядів 13 тис.3 роки тому
In this video, we discuss how the definition of a function has changed over time, largely due to the development of set theory. Chapters 0:00 - Introduction and Motivation 01:50 - Products of Sets 02:53 - Relations 03:59 - Functions The product links below are Amazon affiliate links. If you buy certain products on Amazon soon after clicking them, I may receive a commission. The price is the sam...
The Vandermonde Matrix and Polynomial Interpolation
Переглядів 57 тис.3 роки тому
The Vandermonde matrix is a used in the calculation of interpolating polynomials but is more often encountered in the proof that such polynomial interpolates exist. It is also often encountered in the study of determinants since it has a really nice determinant formula. Chapters 0:00 - Introduction 01:01 - Uniqueness 02:30 The Vandermonde Matrix The product links below are Amazon affiliate link...
An existence proof for arbitrarily large prime gaps.
Переглядів 63 тис.3 роки тому
In this video we'll discuss prime gaps. In particular, we'll prove that there are arbitrarily large gaps between two consecutive prime numbers. The product links below are Amazon affiliate links. If you buy certain products on Amazon soon after clicking them, I may receive a commission. The price is the same for you, but it does help to support the channel :-) This video was based on an exercis...
The Fundamental Theorem of Arithmetic
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The Fundamental Theorem of Arithmetic
Convex Norms and Unique Best Approximations
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Convex Norms and Unique Best Approximations
Convex Sets | Introduction, Definition and Examples
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Convex Sets | Introduction, Definition and Examples
Approximating Functions in a Metric Space
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Approximating Functions in a Metric Space
The Lp Norm for Vectors and Functions
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The Lp Norm for Vectors and Functions
Normed Linear Spaces | Introduction, L1 and L2 Norms
Переглядів 28 тис.4 роки тому
Normed Linear Spaces | Introduction, L1 and L2 Norms
Others explain set theory much better than you Mr Wood!
Wait... if C(U) = ø Then C(C(A)) = C(U) = ø
👽
Amazing video! I'd love to see more videos like this! Is this undecidability related to the undecidability in Turing machines?
Sir, so good, thank you heartfully, very grateful, the concepts around it all beame so clear......
Lovely video. Please keep posting 🙏. I will watch your work with great interest !
Im dead
Amazing!
Thank you bro! You helped me study for my 8th grade math olympiad!! I could not understand this topic and I was scrolling through yt for videos like these. Video like these are truly a blessing. Thank you once again!!
Ngl, nothing make sense in his explanation. It is like he is just reading it out of the book, and doing it just for the sake of doing. Trash
❤
God will Bless you guys
background music name?
Thank you for this❤
caralho
Fantastic
16:47
Why watching math videos in “British” accent is so satisfying!! 😊
thankssss for this in 2025
I think I’m all set. In theory. A set theory…
20:33
тролль гнёт ель
amazing calm music, idk very calming. feels like it helps
This video is really helpful
Read about this one in Counterexamples in Analysis in my second year - so happy you made this as I don't have the book, regrettably.
can’t believe I had to listen through all my teacher’s yapping for a whole hour and not understand any shit while I could have just listened to this video and understand the whole theory in just fucking 30 minutes
But sir, the set of all sets that do not contain themselves, this set, does it contain itself?
Watched this few days to exam and let me tell you I have grasped all that was taught in class and understood it even more than the first time
8:15 Man I took the uniqueness of the empty set for granted, but it's so obvious and senseful now that I see it proved.
God knows I hate math that involves "guessing"
How can we read the sentence of Fourier, when you passe it so quick? Thats because is totally unrelated to the theme of the video? I suspect...
I am not sure if you will receive this message: You are an extraordinary teacher: A Master in your field! May the universe favor you in your endeavors!👍🏿🇮🇱👍🏻
❤❤
I loved how easily you described the concept compared with many confusing material that I studied
now THIS is revolutionary
You saved me 🥹
if an empty set is a subset of every set, then the empty set is not empty?
OMG thank you so much
Thank you
Is {÷,+,a,b} set?
Huge thanks for the amazing work !!!!!!!!♥♥♥♥
i cried
Thanks ❤
thank you so muchh!!!
A class is a set. And an inherited class is a subset of that class.
this has nothing to do with set theory. you did not even explain what a strongly inaccessible cardinal is…
Omg thank u sooo much u made it so much easier to understand ❤
It starts out on the wrong foot. In Set Theory, which the video title pretends to have as its subject matter, every object of the theory is a single set. That does not encapsulate any real world physical things, as it is claimed. It is only around 26:14 that the video enters into the actual reality of sets, where every element of a set is itself a set, although it seems to view it as something unusual.
Teaching meathod is very nice
1:05 { } these are BRACES, not "curly brackets" 🙄
Braces are also known as curly brackets or curly braces