The relationships among the properties of flexible shapes have fascinated mathematicians for centuries.

This is the first part of a 3-part talk on p-adic numbers for advanced high school students. It is part of a series organized by the Berkeley mathematics circle. We define the 10-adic integers, which are similar to ordinary integers except their decimal expansion can be infinitely long. We show that one can do addition, multiplication, and subtraction with them. However they have some problems because it is possible for two nonzero 10adic integers to have zero product. We will see how to fix this in the next video. Links related to the video: Berkeley math circle: https://mathcircle.berkeley.edu/ Handout for talk: https://drive.google.com/file/d/1-UUjAqOIPK-PWUElAXWTdXJZVq7LFGAe Part 2 of talk: https://youtu.be/PeM5Hp0gWf4 Part 3 of talk: https://youtu.be/FWE3mA2otTU Further reading: Borevich and Shafarevich, Number theory, chapter 1.3 (advanced) J.-P. Serre, A course in arithmetic, chapter II (more advanced) N. Koblitz, p-adic numbers, p-adic functions, and zeta functions (very advanced, for anyone who is really ambitious)

When working with a monad, you work in its Kleisli category which is another example of a CCC. The above discussion relating function evaluation to function composition, would then relate Kleisli evaluation (=) to Kleisli composition (=). Woah, is `bind` just monadic function evaluation?

Hi, my name is Eitan. I’m a student of mathematics. Welcome to my personal blog. I intend to post mathematical exposition, but since this is a personal blog I will also post political thought…

Bartosz Milewski's 'Category Theory for Programmers' unofficial PDF and LaTeX source - GitHub - hmemcpy/milewski-ctfp-pdf: Bartosz Milewski's 'Category Theor...

Hi all, I wrote an Automatic Differentiation Manifesto, as the start to push for world's first general-purpose differentiable programming language.