The n-Category Café - University of Texas at Austin
网页6 天之前 · Earlier on the *n*-Café, I once outlined a simple proof of Stirling’s formula using Laplace’s method. When I started thinking about statistical mechanics, I got interested in an alternative proof using the Central Limit Theorem, mentioned in a comment by Mark Meckes. Now I want to dramatize that proof using energy particles.
Axiomatic Set Theory 1: Introduction | The n-Category Café
网页6 天之前 · Re: Axiomatic Set Theory 1: Introduction. In page 12 of your notes you write, “Every calculus book defines a sequence as a function with domain N \mathbb {N}. Now, we don’t usually think of sequences as functions, and that’s reflected in the notation. No one says ‘let f f be a sequence’; we say ‘let (xn)∞ n=0 (x_n)_ {n=0}^\infty ...
Galois Theory | The n-Category Café - University of Texas at Austin
网页2024年8月15日 · About 40 short explanatory videos. A large collection of problems. Nearly 500 multiple choice questions. I’m a little bemused by the popularity of the Galois theory notes. I’ve made quite a few sets of course notes public before, e.g.: Fourier analysis. General topology. Linear algebra. Category theory.
Introduction to Categorical Probability | The n-Category Café
网页2024年8月13日 · A probability distribution on a finite set X is a function p: 2X → [0, 1] assigning to each subset A ⊂ X a number p(A) such that. p(∅) = 0, p(X) = 1, and for disjoint subsets A1, …, Ak ⊂ X, ∑ip(Ai) = p(⋃iAi). For our purposes, a simpler characterization exists from the fact that we can consider a finite set to disjointly consist ...
The n-Category Café
网页2024年8月31日 · Earlier on the n -Café, I once outlined a simple proof of Stirling’s formula using Laplace’s method. When I started thinking about statistical mechanics, I got interested in an alternative proof using the Central Limit Theorem, mentioned in a comment by Mark Meckes. Now I want to dramatize that proof using energy particles.
How to Apply Category Theory to Thermodynamics
网页2022年7月25日 · The functor Ent: ConvRel → Set is defined as follows: For convex space A, Ent(A) takes A to the set of entropy functions on A, which is a an object in Set. For morphism R: A → B, Ent[R] is a morphism Ent[R]: Ent(A) → Ent(B). For entropy function S: A → ˉℝ, we define. Ent[R](S)(p) = sup {a | (a, p) ∈ R} S(a).
The Uniform Measure | The n-Category Café - University of Texas …
网页2020年11月24日 · Re: The Uniform Measure. By Proposition 6.3 in your paper with Emily, each μ t \mu_t is balanced (for the similarity kernel K t K^t). Theorem 2 in Simon’s paper implies that if supp (μ t) supp (\mu_t) is the entire ball and μ t \mu_t is balanced, then μ t \mu_t must be a weight measure for the ball at scale t t.
Topos Theory and Measurability | The n-Category Café
网页2021年7月28日 · There was an interesting talk that took place at the Topos Institute recently – Topos theory and measurability – by Asgar Jamneshan, bringing category theory to bear on measure theory. Jamneshan has been working with Terry Tao on this: Asgar Jamneshan, Terence Tao, Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical ...
Category Theory in Context | The n-Category Café - University of …
网页2016年11月16日 · In my final year at Harvard and again in my first year at Johns Hopkins, I had an opportunity to teach an advanced undergraduate/beginning graduate-level topics course entitled “Category Theory in Context.”Its aim was to provide a first introduction to the basic concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions ...
The n-Category Café Archives - University of Texas at Austin
网页2013年7月28日 · Tom Leinster: Axiomatic Set Theory 1: Introduction (September 22, 2024) Set theory course based on everyday principles for sets and functions. John Baez: The Space of Physical Frameworks (Part 4) (September 15, 2024) I’ll explain exactly what I mean by ‘classical statistical mechanics’, and how free entropy is defined in this subject.
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