joecamel + algebra   12

Is “the theory of everything” merely the ultimate ensemble theory?
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
"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
"In this instalment we’ll take a further look at Monoid morphisms to try to cement our understanding of this concept." HN:
algebra  programming  functional  intro  monoid  morphism  examples 
september 2016 by joecamel
Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics
"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 
september 2016 by joecamel
Modern Algebra | Mathematics | MIT OpenCourseWare
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
"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
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
"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
"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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