Community Discussion list Contact Andrius Kulikauskas m a t h 4 w i s d o m @ g m a i l . c o m +370 607 27 665 Eičiūnų km, Alytaus raj, Lithuania Thank you for your support! Patreon Paypal to ms@ms.lt Bookshelf Thank you! Upload Upcoming Videos Here is a list of upcoming videos that I'm working on. I have ordered them starting with those which I expect to complete soonest. The geometry behind Dynkin diagrams Or how 120 + 120 = 90. Yoneda Lemma I want to make a video about the Yoneda Lemma and how it functions as a knowledge switch relating the four levels of knowledge: Whether, What, How, Why. I will probably do several short ones. 24 Ways of Figuring Things Out in Math I want to make a video about the 24 ways of figuring things out in mathematics. Hermite polynomials In my analysis of the combinatorics of orthogonal polynomials related to Sheffer polynomials, I want to focus on the special case of the Hermite polynomials. Minkowski space and Moebius transformations I want to understand the connection and present it with a video. Calculating representations of Clifford algebras as relevant for Bott periodicity Q-analogue of Binomial Coefficients I want to make a video about the q analogue of the binomial coefficients and how we get the mythical "field with one element" when we take the limit q goes to 1. That is important for modeling choice when we have only one choice to choose from. I think this is relevant for modeling God. Mathematical Beauty Awakens the Imagination I made a picture in a talk I gave in Lithuanian http://www.ms.lt/sodas/Mintys/MatematikosGrožisŽadinaVaizduotę I gave this as an example of mathematical beauty where our mind can break out of the limits of what we can see. I compare that with the visual beauty of the Mandelbrot set, which exemplifies Christopher Alexander's 15 properties of life, including three related to one (good shape), all (local symmetry of background), many (positive, concave space). Animating the 4-simplex. Visualizing 4 dimensions with 5 points. I wonder how best to animate the 4-simplex. I know some Python. I should learn the basics of Manim. I draw a tetrahedron (four points - four dimensions) and introduce a fifth point at the center (which becomes a fifth dimension when I wiggle it around). Using Pascal's triangle we see how the row for an edge 1 2 1 becomes the row for a triangle 1 3 3 1 (one center, three vertices, three edges, one face) becomes the row for a tetrahedron 1 4 6 4 1 (one center, four vertices, six edges, four faces, one volume) becomes the row for a 4-simplex 1 5 10 10 5 1 (one center, five vertices, ten edges, ten faces, five volumes, 1 4-dimensional-cell) 24 Ways of Figuring Things Out in Biology I have a talk on biology that I could translate from Lithuanian into English. Buckminster Fuller's 24 Ways of Figuring Things Out I will want to make a video on Buckminster Fuller's ways of figuring things out. This is part of my study of adjunctions with the goal of classifying adjunctions. This particular adjunction is an equivalence. I have been studying algebraic topology at the New York Category Theory Meetups and you are welcome to join us. I want to present what I know of the language of wondrous wisdom with a series of videos based on slides which I talk about. The first will be an overview and then I will drill down to focus on various structures. This is a talk that I gave. This is a talk that I gave. Structure of Finite Fields Understand the structure of finite fields of cardinality {$q^n$} and then consider what happens when we take the limit {$q\rightarrow 1$}. This should give insight into modeling {$F_1$}. Yates Index Set Theorem Explain what this says about the foursome of levels of knowledge: Whether, What, How, Why. Raudys Hierarchy of Statistical Methods Understand the Raudys hierarchy and how it may express the divisions of everything. (1) the Euclidean distance classifier; (2) the standard Fisher linear discriminant function (DF); (3) the Fisher linear DF with pseudo-inversion of the covariance matrix; (4) regularized linear discriminant analysis; (5) the generalized Fisher DF; (6) the minimum empirical error classifier; (7) the maximum margin classifier. Norman Anderson's Information Integration Theory Investigate how averaging (by the unconscious) is teased apart as addition and multiplication (by the conscious). Shu-Hong Zhu's Thesis Present as an example of the sevensome. And relate to linear fractional transformations. Symmetric functions of the eigenvalues of a matrix Seeking a relation to the six representations, for example, a connection with Hopf algebras. {$K^{-1}K=I$} and nonexistence of an involution Set this up as a problem where the nonexistence of an adjunction indicates the nonexistence of a combinatorial interpretation for an involution. Eight dualities Investigate the kinds of dualities.
Šis puslapis paskutinį kartą keistas November 23, 2022, at 03:19 PM