| This is an old list of subjects for a compilation image. | |
| At the bottom of the file I've dumped the Mathematica code to render it in an image. | |
| More visually pleasing ways to do it have been suggested to me here: | |
| https://mathematica.stackexchange.com/questions/2768/how-to-partition-a-disk-into-individually-spaced-bricks | |
| I will recompile it eventually and make some nice pic. | |
| Please comment if you feel I should add something or re-order. | |
| Intuitionistic Logic |
| % The document discussed in this video: | |
| % | |
| % https://youtu.be/avc3Iv7Yojs | |
| \subsection{Binomial theorem} | |
| $\left(x+y\right)^n =\sum_{k=0}^n \{\frac{n!}{k!\,(n-k)!}\}\, x^k y^{n-k} = x^n + x\,y\,\sum_{k=1}^{n-1}\{ \frac{n!}{k!\,(n-k)!} \}x^{k-1} y^{n-(k+1)} + y^n$ | |
| e.g. |
| % This is the tex file used in the video explaining the Weierstrass factorization theorem: | |
| % https://youtu.be/SEHPs8nrqLY | |
| % | |
| % In this video we're going to explain the Weierstrass factorization theorem, giving rise to infinite product representations of functions. Classical examples are that of the Gamma function or the sine function. | |
| % | |
| % https://en.wikipedia.org/wiki/Weierstrass_factorization_theorem | |
| % https://en.wikipedia.org/wiki/Infinite_product | |
| \begin{abstract} | |
| We give a quick and dirty motivation for the Weierstrass factorization theorem. |
| This is the text used in the video | |
| https://youtu.be/eeLa9tIhFMs | |
| Minimal logic, or minimal calculus, is an intuitionistic and paraconsistent logic, | |
| that rejects both the Law of Excluded Middle (LEM) as well as | |
| the Principle Of Explosion (Ex Falso Quodlibet, EFQ). | |
| # Classically via true and false proposition |
In this video we come across about 50 online resources for category theory:
I quickly comment on about 20 major ones. I link to the university sites, arXiv sites or Amazon page - most of the mentioned books are online available.
Here's another category theory list on github
| % This is the LaTeX file to the video explanation of quaternion algebras here | |
| % | |
| % https://youtu.be/tkS_6xY132g | |
| Let $a,b,c$ be non-zero elements in a field $\mathbb F$ with characteristic not $2$. \\ | |
| In this video we're discussing an unital algebras in $\mathrm{Mat}_{2\times 2}$ for some field.\\ | |
| More concretely, they are representations of (abstract) quaternion algebras are denoted by $(a,b\, |\, F)$. | |
| \subsection{Generators} | |
| $$ |
| Below you find the links discussed in this video on field of characteristic 2: | |
| https://youtu.be/xxkJru5uPUQ | |
| --- | |
| https://en.wikipedia.org/wiki/Field_(mathematics) | |
| https://en.wikipedia.org/wiki/Characteristic_(algebra) |
| Those are the notes and TeX file for the video: | |
| https://youtu.be/cCbn5x0z7pA | |
| # References | |
| https://en.wikipedia.org/wiki/Lie_algebra#Definition_of_a_Lie_algebra | |
| https://en.wikipedia.org/wiki/Jacobi_identity |
| % This is the LaTeX file to the video explanation of quaternion algebras here | |
| % | |
| % (see youtube video of the same name) | |
| Let $a,b,c$ be non-zero elements in a field $\mathbb F$ with characteristic not $2$. \\ | |
| In this video we're discussing an unital algebras in $\mathrm{Mat}_{2\times 2}$ for some field.\\ | |
| More concretely, they are representations of (abstract) quaternion algebras are denoted by $(a,b\, |\, F)$. | |
| \subsection{Generators} | |
| Let |
| % This is the text used in the youtube video | |
| % | |
| % https://youtu.be/ccsldiiJH7k | |
| \section{Kinetic energy and moment of inertia tensor of a rigid body} | |
| Fix an (inertial) coordinate system, $O$. | |
| ``Clearly'', the configuration space of a rigid body in this system is ${\mathbb R}^3\times {\rm SO}(3).$ | |
| \subsection{Preparation: Complex numbers} |
