Is “the theory of everything” merely the ultimate ensemble theory?

february 2017 by joecamel

The paper contains an interesting figure that illustrates relationships between various basic mathematical structures.

math
paper
visualization
overview
algebra
february 2017 by joecamel

Clifford Algebra: A visual introduction | slehar

november 2016 by joecamel

"Clifford Algebra, a.k.a. Geometric Algebra, is a most extraordinary synergistic confluence of a diverse range of specialized mathematical fields, each with its own methods and formalisms, all of which find a single unified formalism under Clifford Algebra. It is a unifying language for mathematics, and a revealing language for physics."

algebra
math
clifford
introduction
motivation
november 2016 by joecamel

Badness 10.000 - Algebraic Patterns - Monoid morphisms

september 2016 by joecamel

"In this instalment we’ll take a further look at Monoid morphisms to try to cement our understanding of this concept." HN: https://news.ycombinator.com/item?id=12609247

algebra
programming
functional
intro
monoid
morphism
examples
september 2016 by joecamel

Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics

september 2016 by joecamel

"We can do better! Research on the design and use of

mathematical systems provides a guide for designing a unified mathematical language for the whole of physics that facilitates learning and enhances physical insight. This has produced a comprehensive language called Geometric Algebra, which I introduce with emphasis on how it simplifies and integrates classical and quantum physics."

algebra
math
mathematics
physics
geometric.algebra
2002
paper
talk
lecture
oersted
pdf
read
mathematical systems provides a guide for designing a unified mathematical language for the whole of physics that facilitates learning and enhances physical insight. This has produced a comprehensive language called Geometric Algebra, which I introduce with emphasis on how it simplifies and integrates classical and quantum physics."

september 2016 by joecamel

Modern Algebra | Mathematics | MIT OpenCourseWare

november 2014 by joecamel

This undergraduate course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics.

math
algebra
lecturenotes
mit
ocw
course
november 2014 by joecamel

How to Conquer Tensorphobia | Math ∩ Programming

june 2014 by joecamel

"This post is an attempt to bridge the gap between the elementary and advanced understandings of tensors. We’ll start with the elementary (axiomatic) approach, just to get a good feel for the objects we’re working with and their essential properties. Then we’ll transition to the “universal” mode of thought, with the express purpose of enlightening us as to why the properties are both necessary and natural."

algebra
math
mathematics
programming
tensors
introduction
explanation
blog
cs
june 2014 by joecamel

An Intuitive Guide to Linear Algebra | BetterExplained

october 2012 by joecamel

Some ideas in the article might be used for introductions to Linear Algebra.

algebra
learning
math
linearalgebra
october 2012 by joecamel

Normal subgroups and quotient groups « Gowers's Weblog

december 2011 by joecamel

"In this post, then, I’d like to give a fictitious account of why normal subgroups and quotient groups were introduced into group theory, once some of the more basic concepts were already in place."

introduction
group
theory
gowers
blog
post
method
math
algebra
december 2011 by joecamel

MATH E-222 Abstract Algebra

december 2010 by joecamel

"Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields." // Benedict Gross seems like a great lecturer! Course uses Artin's book "Algebra".

math
course
open
harvard
algebra
video
lectures
benedict.gross
december 2010 by joecamel

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