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Intersection of Relation with Inverse is Symmetric Relation Theorem Let \mathcal R be a relation on a set S. Then \mathcal R \cap \mathcal R^{-1}, the intersection of \mathcal R with its inverse, is symmetric. Proof Let \left({x, y}\right) \in \mathcal R \cap \mathcal R^{-1}

Related:  Mathematics

A Physics Booklist [Physics FAQ] - [Copyright] Updated 2005. Updated 1994—1997 by SIC, PEG. Original by Vijay Fafat. This article is a compilation of books recommended by sci.physics participants as the "standard" or "classic" texts on a wide variety of topics of general interest to physicists and physics students. As a guide to finding the right book for you, many of the comments from the contributors have been retained. A Gentle Introduction To Learning Calculus I have a love/hate relationship with calculus: it demonstrates the beauty of math and the agony of math education. Calculus relates topics in an elegant, brain-bending manner. My closest analogy is Darwin’s Theory of Evolution: once understood, you start seeing Nature in terms of survival. You understand why drugs lead to resistant germs (survival of the fittest). You know why sugar and fat taste sweet (encourage consumption of high-calorie foods in times of scarcity).

Online texts Professor Jim Herod and I have written Multivariable Calculus ,a book which we and a few others have used here at Georgia Tech for two years. We have also proposed that this be the first calculus course in the curriculum here, but that is another story.... Although it is still in print, Calculus,by Gilbert Strang is made available through MIT's OpenCourseWare electronic publishing initiative. Quaternion group where 1 is the identity element and −1 commutes with the other elements of the group. Cayley graph[edit] The Q8 group has the same order as the Dihedral group, D4, but a different structure, as shown by their Cayley graphs: Cayley table[edit]

10 Coolest Mathematics Results Technology Many people are put off by the obscure symbols and strict rules of math, giving up on a problem as soon as they see both numbers and letters involved. But while math may be dense and difficult at times, the results it can prove are sometimes beautiful, mind-boggling, or just plain unexpected. OSWINS - Mathematics Content: calculators , graphs , computational tools , math games , algebra , courses , tutorials and problem solving Quotes "The understanding of mathematics is necessary for a sound grasp of ethics." - Socrates "Mathematicians do not study objects, but relations between objects. Why Math Works Most of us take it for granted that math works—that scientists can devise formulas to describe subatomic events or that engineers can calculate paths for space­craft. We accept the view, initially espoused by Galileo, that mathematics is the language of science and expect that its grammar explains experimental results and even predicts novel phenomena. The power of mathematics, though, is nothing short of astonishing. Consider, for example, Scottish physicist James Clerk Maxwell’s famed equations: not only do these four expressions summarize all that was known of electromagnetism in the 1860s, they also anticipated the existence of radio waves two decades before German physicist Heinrich Hertz detected them. Very few languages are as effective, able to articulate volumes’ worth of material so succinctly and with such precision.

Polyhedra by Jim McNeill: last updated 23 Apr 2013. Note: If you are having difficulty viewing the VRML files, then download the latest version of Cortona from here. HEDRON: Polyhedron generating software, now at V1.12, available here. Help text here. Hedron Tools (Release 2B). Uniform Polyhedra: Displayed as 'switchable' VRML files, including Skilling's figure, including links to 'molecular' VRML files of all the uniform Polyhedra.