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John Baez This is a course based on Fong and Spivak's book Seven Sketches in Compositionality: An Invitation to Applied Category Theory, taught by John Baez and turned into nice webpages by Simon Burton. For more details, dive right in and check out Lecture 1. Chapter 1: Ordered Sets Lecture 1 - Introduction Lecture 2 - What is Applied Category Theory? Lecture 3 - Preorders Lecture 4 - Galois Conn
John Baez July 26, 2021 Information geometry is the study of 'statistical manifolds', which are spaces where each point is a hypothesis about some state of affairs. This subject, usually considered a branch of statistics, has important applications to machine learning and somewhat unexpected connections to evolutionary biology. To learn this subject, I'm writing a series of articles on it. You can
Notes on Tetracategories Todd Trimble October 2006 1. History In 1995, at Ross Street's request, I gave a very explicit description of weak 4-categories, or tetracategories as I called them then, in terms of nuts-and-bolts pasting diagrams, taking advantage of methods I was trying to develop then into a working definition of weak n-category. Over the years various people have expressed interest in
How to Learn Math and Physics John Baez March 20, 2020 Introduction How to Learn Physics How to Learn Math More Advanced Math Introduction "How to learn math and physics" — the title is deliberately provocative. Everyone has to learn their own way. I don't know how you should learn math and physics. But presumably you came here looking for advice, so I'll give you some. My advice is aimed at peopl
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ZIP Attacks with Reduced Known Plaintext Michael Stay AccessData Corporation 2500 N. University Ave. Ste. 200 Provo, UT 84606 staym@accessdata.com Abstract. Biham and Kocher demonstrated that the PKZIP stream ci- pher was weak and presented an attack requiring thirteen bytes of plain- text. The deflate algorithm “zippers” now use to compress the plaintext before encryption makes it difficult to get k
The Beauty of Roots John Baez September 29, 2023 Around 2006, my friend Dan Christensen created a fascinating picture of all the roots of all polynomials of degree ≤ 5 with integer coefficients ranging from -4 to 4: Click on the picture for bigger view. Roots of quadratic polynomials are in grey; roots of cubics are in cyan; roots of quartics are in red and roots of quintics are in black. The hori
[Physics FAQ] - [Copyright] Original by Monwhea Jeng (Momo), Department of Physics, University of California, 1998. Yes—a general explanation History of the Mpemba Effect More-detailed explanations References Yes—a general explanation Hot water can in fact freeze faster than cold water for a wide range of experimental conditions. This phenomenon is extremely counterintuitive, and surprising even
John Baez Public Lecture at Categories in Algebra, Geometry and Mathematical Physics July 14, 2005 The Mysteries of Counting: Euler Characteristic versus Homotopy Cardinality We all know what it means for a set to have 6 elements, but what sort of thing has -1 elements, or 5/2? Believe it or not, these questions have nice answers. The Euler characteristic of a space is a generalization of cardinal
John Baez’s Stuff I'm a mathematical physicist. Among other things, I study networks and help researchers use them in scientific software, such as quickly adaptable models of infectious disease. I am a Professor of the Graduate Division but not accepting new students at this time. In the fall of 2023 I had a Leverhulme Visiting Professorship and gave a series of lectures on mathematics at the Univ
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