Related papers: Lectures on Entropy. Part I
This is a written version of a series of lectures aimed at undergraduate students in astrophysics/particle theory/particle experiment. We summarize the important progress made in recent years towards understanding high energy astrophysical…
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological, and social processes. The…
These lecture notes in the De Rham-Hodge theory are designed for a 1-semester undergraduate course (in mathematics, physics, engineering, chemistry or biology). This landmark theory of the 20th Century mathematics gives a rigorous…
These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to…
The following three sections and appendices are taken from my thesis "The Foundations of Inference and its Application to Fundamental Physics" from 2021, in which I construct a theory of entropic inference from first principles. The…
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…
Informational entropy is often identified as physical entropy. This is surprising because the two quantities are differently defined and furthermore the former is a subjective quantity while the latter is an objective one. We describe the…
Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an introduction to neural networks for mathematics students at the…
These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as…
Introduction to the Lecture Note Volume "ITEP Lectures in Particle Physics", including 25 years of personal reminiscences.
This lecture note is intended to prepare early-year master's and PhD students in data science or a related discipline with foundational ideas in machine learning. It starts with basic ideas in modern machine learning with classification as…
Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…
These notes contain everything necessary to run a flipped course on "The Atmosphere" at an introductory undergraduate level. There are notes for the students to read before each course meeting and problems for them to work on in small…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
These lecture notes give an introduction to the theory of interacting particle systems. The main subjects are the construction using generators and graphical representations, the mean field limit, stochastic order, duality, and the relation…
A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on…
These are lecture notes compiled for a short lecture series at the 2023 Condensed Matter Summer School at the University of Minnesota. They are designed to be conversational and fun, and not to take the place of review articles that do a…