"Like music or art, mathematical equations can have a natural progression and logic that can evoke rare passions in a scientist. Although the lay public considers mathematical equations to be rather opaque, to a scientist an equation is very much like a movement in a larger symphony. Simplicity. Elegance. These are the qualities that have inspired some of the greatest artists to create their masterpieces, and they are precisely the same qualities that motivate scientists to search for the laws of nature. Like a work of art or a haunting poem, equations have a beauty and rhythm all their own."
Michio Kaku
"Who in all the world, who enjoys merely some degree of communion with the Muses, ... is there who would not choose to be the mathematician rather than the tyrant?"
William Rowan Hamilton
"Philosophy is written in this grand book -- I mean the universe -- which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures, without which it is humanly impossible to understand a single word of it."
--- GALILEO GALILEI, H Saggiatore (1623)
"The following texts were provided by the International Mathematical Union, which awards the Fields Medals. They do an excellent job of explaining in as accessible language as possible what the four 2014 medallists did to earn their awards." |
"A brief description of the work of the winners is available at the links given below. The laudations for the winners and their talks at the Congress will appear in Volume 1 of the Proceedings." |
"for their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics." |
The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2019 to Karen Keskulla Uhlenbeck of the University of Texas at Austin, USA "for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.", |
The Norwegian Academy of Sciences and Letters has decided to award the Abel Prize for 2015 to the American mathematicians John F. Nash, Jr. and Louis Nirenberg “for striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.” |
This guide covers everything from the different career choices under the IT umbrella, to training seminars, education, and organizations that provide support to women in tech. |
Every course on Coursera is taught by top instructors from the world’s best universities and educational institutions. Courses include recorded video lectures, auto-graded and peer-reviewed assignments, and community discussion forums. Choose from hundreds of courses created by the world’s top educational institutions. Courses are open to anyone, and learning is free. |
FabMarks helps students achieve their academic aspirations. It provides Online test-prep services for standardized tests such as the PSAT, SAT, ACT, GMAT. It provides FREE access to a lot learning resources (Recorded Vidoes, Practice Questions, Tests) and also offers live online instructor-led tutoring services for SAT, ACT and the GMAT. |
American InterContinental University's mission is to provide for the varying educational needs of a career-oriented, culturally diverse and geographically dispersed student body with the goal of preparing students academically, personally, and professionally. |
"You can find more than 500 accredited free online college classes that provide you with the opportunity to make use of research-based academic resources from some of the world’s best universities." |
Learning these concepts can make everyday experiences easier because it enables us to approach problems from different angles, think more efficiently and creatively, process information quickly and accurately, and understand how things work. |
"However, it is important to point out that the mathematical formulation of the physicist's often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena." |
10 Mind Blowing Mathematical Equations | by Sean Li
What is the most beautiful equation? | Quora Forum
The Baffling and Beautiful Wormhole Between Branches of Math | by Lee Simmons - Wired Magazine
The Most Beautiful Equation of Math: Euler's Identity | by Le Nguyen Hoang
Includes 55-minute video
The Mathematics of Planet Earth | John Baez
One of Western civilization's jealously guarded myths is that of Greek cultural supremacy. In this controversial study, William Ivins shows that the limitations of the Greek worldview actually hampered the development of the arts and sciences and gives a stimulating history of the new ideas of the Renaissance, especially in painting and geometry, that freed us from ancient misconceptions. |
Fundamental Theorem of Finite Abelian Groups
Any finite abelian group is isomorphic to a direct product of cyclic groups of prime power order.
Any two such decompositions have the same number of factors of each order.
Analogous to the Fundamental Theorem of Arithmetic.
"The movement of humanity, arising as it does from innumerable arbitrary human wills, is continuous," he [Tolstoy] writes. "To understand the laws of this continuous movement is the aim of history … only by taking infinitesimal units for observation … and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history."
Leo Tolstoy
"The 2016 Nobel Prize in Physics was awarded "for theoretical discoveries of topological phase transitions and topological phases of matter." What does that mean?"
"Thouless later used topology to explain other bizarre behavior, what's now known as the integer Quantum Hall effect. If a semiconducting slab sits at right angles to a magnetic field, a voltage develops across the slab. But instead of increasing smoothly as the strength of the magnetic field increases smoothly, the voltage jumps up at specific intervals. In 1983, Thouless was able to link this phenomena mathematically to topological properties, explaining the jumps."
"Not only are new materials on the horizon thanks to this novel work, but interest in the field of topological physics is exploding. The great contributions of all three of the Nobel Laureates exposed a richness of questions and possibilities, inspiring many other physicists to investigate."
The above graphic represents the evolutionary development of plants from their beginnings to the present.
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Computer Science
Charles Babbage and Alan Turing are each called the "Father of Computer Science."
Turing, however, is considered the originator of the idea of Artificial Intelligence.
This report is an introduction to Artificial Neural Networks. The various types of neural networks are explained and demonstrated, applications of neural networks like ANNs in medicine are described, and a detailed historical background is provided. The connection between the artificial and the real thing is also investigated and explained. Finally, the mathematical models involved are presented and demonstrated. |
This tutorial covers the basics of creating KML files. We will be using Google Earth to create KML files containing points, lines, and polygons, the three basic geometries involved in vector-based GIS. |
Tutorials exist for just about any subject under the sun. If you don't find what you're looking for in that regard, do a search on GOOGLE or any preferred search engine.