Galois Theory | The n-Category Café - University of Texas at Austin
Aug 15, 2024 · Galois Theory Posted by Tom Leinster. I’ve just arXived my notes for Edinburgh’s undergraduate Galois theory course, which I taught from 2021 to 2023.. I first shared the notes on my website some time ago. But it took me a while to arXiv them, because I wanted to simultaneously make public most of the other course materials.
ACT 2025 | The n-Category Café
Dec 4, 2024 · Submission Important dates . All deadlines are AoE (Anywhere on Earth). February 26: title and brief abstract submission; March 3: paper submission
The n-Category Café - University of Texas at Austin
Jan 22, 2025 · I’ve been blogging a bit about medieval math, physics and astronomy over on Azimuth. I’ve been writing about medieval attempts to improve Aristotle’s theory that velocity is proportional to force, understand objects moving at constant acceleration, and predict the conjunctions of Jupiter and Saturn.A lot of interesting stuff was happening back then!
Axiomatic Set Theory 10: Cardinal Arithmetic | The n-Category Café
Nov 22, 2024 · Previously: Part 9. The course is over! The grand finale was the theorem that. X × Y ≅ X + Y ≅ max (X, Y) X \times Y \cong X + Y \cong max(X, Y) . for all infinite sets X X and Y Y.Proving this required most of the concepts and results from the second half of the course: well ordered sets, the Cantor–Bernstein theorem, the Hartogs theorem, Zorn’s lemma, and so on.
Random Permutations (Part 14) | The n-Category Café
I see; very interesting! So in this kind of situation, it can be easier to work with a Poisson random variable with mean n n than it is to work with the plain old number n n itself. I like it. To implement a similar idea here — that is, to relate the statistics of random permutations and random endomorphisms — we’d surely need to know something about the number of elements in the ...
Triangulations of the Sphere (Part 1) | The n-Category Café
Oct 26, 2024 · I’m writing a short column about this paper: W. P. Thurston, Shapes of polyhedra and triangulations of the sphere. Let me describe one of the key ideas as simply as I can.
Axiomatic Set Theory 5: Relations | The n-Category Café
Oct 18, 2024 · Previously: Part 4.Next: Part 6 I called this chapter of my course “Relations”, but I should have called it “Specifying subsets and functions”, because that’s what it’s all about. This week, we saw that it’s possible to define subsets of a set X X by expressions like {x ∈ X: some property of x holds}, \{ x \in X : \text{some property of }\ x\ \text{ holds} \},
Adjoint School 2025 | The n-Category Café
Oct 31, 2024 · The quantum computation topic, and mentor, have changed to this: Structuring Quantum Effects with Monads and Arrows. Mentor: Juliana Kaizer Vizzotto Category theory provides a mathematical framework for understanding structures and their relationships abstractly.
Mathematical Expressions - University of Texas at Austin
The WebTeX Examples include more examples of superscripts and subscripts, as well as an example of tensor notation. Prescripts. Superscripts and subscripts may also be placed before an expression. These can be created with the \multiscripts{}{}{} command, a generalization of \tensor.Here, the second argument is the base, while the first argument contains the prescripts and the third argument ...
Axiomatic Set Theory 4: Subsets | The n-Category Café
Oct 11, 2024 · Thanks, Jonathan. I’ve been thinking periodically about your paper Up with categories, down with sets; out with categories, in with sets! as I grapple with presenting this material to the students.. is there a reasonable way in your setup to get the right analogue of the separation axiom, that given a set X X and a “reasonable” formula ϕ …