math and physics
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Home Page Introduction The equations at the top of this page are the two most important principles of the theory of abstract objects.
The Theory of Abstract Objects
ScienceDaily (Oct. 12, 2011) — Researchers from Cornell University in Ithaca, N.Y., have demonstrated for the first time that it's possible to cloak a singular event in time, creating what has been described as a "history editor."
Erasing history? Temporal cloaks adjust light's throttle to hide an event in time
Video Lectures | Public lectures given at the Institute for Advanced Study
Suppose that G is a connected, quasisplit, orthogonal or symplectic group over a field F of characteristic 0. We shall describe a classification of the irreducible representations of G(F) if F is local, and the automorphic representations of G in the discrete spectrum if F is global. The classification is by harmonic analysis and endoscopic transfer, which ultimately ties the representations of G to those of general linear groups.
This book is a continuing work in progress. When I have time, I edit, expand and add to the chapters. For the convenience of readers who need a stable version that will not change, there are archived versions, which are snapshots of the state of the book at the date indicated:
Einstein for Everyone - StumbleUpon
In academic year '90-'91 advanced physics students, 2 from HC and 1 from BMC, wrote this set of 'Math Appendices' with a bit of assistance and direction from me. They undertook this project because they felt that something of the sort would have been helpful to them in their physics courses.
MathAppendices
In this introduction, we will briefly discuss those elementary statistical concepts that provide the necessary foundations for more specialized expertise in any area of statistical data analysis.
Elementary Concepts in Statistics
Sets: curly brace notation, cardinality, containment, empty set {, power set P(S), N-tuples and Cartesian product. Set Operations: set operations union and disjoint union, intersection, difference, complement, symmetric difference Functions: domain, co-domain, range; image, pre-image; one-to-one, onto, bijective, inverse; functional composition and exponentiation; ceiling and floor.
Discrete Math Lecture Notes
Pauls Online Math Notes
Algebra Cheat Sheet - This is as many common algebra facts, properties, formulas, and functions that I could think of. There is also a page of common algebra errors included. Currently the cheat sheet is four pages long. Algebra Cheat Sheet (Reduced) - This is the same cheat sheet as above except it has been reduced so that it will fit onto the front and back of a single piece of paper.
Russell's Paradox (Stanford Encyclopedia of Philosophy)
First published Fri Dec 8, 1995; substantive revision Wed May 27, 2009 Russell's paradox is the most famous of the logical or set-theoretical paradoxes.
