General Math Resources & Articles for Students and Teachers
Algebra & Trigonometry || Linear Algebra
Geometry || Algebraic Geometry || Projective Geometry || Differential Geometry
Logic & Set Theory || Number Theory || Fermat's Last Theorem
Modern/Abstract Algebra || Lie Group - Lie Algebra || Representation Theory
Mechanics || Quantum Mechanics || Quantum Field Theory
Calculus || Tensor Calculus & Relativity || Graph Theory & Combinatorics
Topology || Algebraic Topology || Differential Topology
Category Theory || Chaos Theory & Fractals
"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."
"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 CRM-Fields-PIMS prize has become the premier Canadian award for research achievements in the mathematical sciences. It is awarded jointly by the three Canadian mathematics institutes.
October 23, 2015 - Press Release
December 1, 2014 - Pacific Institute for the Mathematical Sciences
"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."
Maryam Mirzakhani is the first woman to ever win the Fields Medal – known as the "Nobel Prize of mathematics" – in recognition of her contributions to the understanding of the symmetry of curved surfaces.
August 12, 2014 - The Guardian
The first woman to win the prestigious Fields Medal prize discusses her life as a mathematician
Maryam Mirzakhani is among four young researchers to win Fields Medals, awarded every four years.
"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."
Scientific American | by John Matson, August 20, 2010
Deccan Herald | by Kalyan Ray, Hyderabad, Aug 20, 2010
The Fields Medal, considered the Nobel Prize of math, has been awarded quadrennially since 1936 by the International Congress of Mathematicians to recognize outstanding mathematics achievement.
Awarded to Jean Bourgain, Institute for Advanced Study, Princeton, USA and Terence Tao, UCLA
This site focuses on help for students of any academic level. Students have access to both guided and independent learning in a unique environment that combines technology and personal interaction. Key areas of the site include Guides, Online Tools, Scholarship Program, and Assignment Help.
There are 7 videos in this category and 5119 videos in 1090 subcategories.
Connexions is a dynamic digital educational ecosystem consisting of an educational content repository and a content management system optimized for the delivery of educational content.
View and share free educational material in small modules that can be organized as courses, books, reports or other academic assignments. Our free textbooks are developed and peer-reviewed by educators to ensure they are readable, accurate, and meet the scope and sequence requirements of your course.
eIMACS, the distance learning division of the Institute for Mathematics & Computer Science (IMACS), gives students a competitive edge by teaching them how to think critically using logic and reasoning.
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."
Financial aid and scholarship information - Guides and tips to help save students money
NetMath is a distance learning program that offers online math courses for college credit. Our mission is to bring the academic resources from one of the nation's top universities to students around the world.
This provides a comprehensive collection of audio/video courses and lectures in mathematics and its applications.
Choose from hundreds of courses created by the world’s top educational institutions. Courses are open to anyone, and learning is free.
The Johns Hopkins University Center for Talented Youth identifies and develops the talents of the most advanced K-12 learners worldwide.
Skwirk is an online interactive learning portal for primary and secondary school students. Covering multiple subjects, we are now used by over 20,000 teachers, 280,000 students and in over 1400 schools.
OEDb is a comprehensive online education directory for both free and for-credit learning options.
Tutor Pace provides effective Math tutoring sessions which are personalized and customized to meet student demands in one to one sessions.
Personally tailored lessons from exceptional tutors in a one-on-one setting. We focus on in-home tutoring that offers flexible scheduling and your choice of locations.
The main content is Excel, Word and PowerPoint tutorials that have corresponding tests.
For children kindergarten through 12th grade
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For over a decade the Global Student Network has provided online education excellence to children in elementary school all the way through high school.
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Global Village School offers a progressive, accredited, customizable K-12 homeschooling program via online and text-based curriculum, complete with individualized teacher services.
Home School Legal Defense Association is a nonprofit advocacy organization established to defend and advance the constitutional right of parents to direct the education of their children and to protect family freedoms.
WHO is committed to making sure that parents interested in homeschooling get accurate and up-to-date information on the homeschooling law, local support, resources, and services.
"We offer a tutorial (Introduction, Basics, Functions, Data Analysis and VBA) on how to use Excel. Want to learn much more about Excel? You can find related examples and features (300 Examples) on the right side of each page. We keep it easy!"
"We’ve recently created a straightforward ‘How to Use Excel’ guide for beginning Microsoft Excel users. This short, comprehensive guide aims to help the Excel beginner master the basics of Microsoft’s most popular software in three easy chapters."
[I've checked out the following sites and they appear valid. Nonetheless, things change abruptly on the web without notice. In general, whenever you download anything--a book, a music video, a documentary, a software program from a third party, a game, an email attachment--you need to be wary. In particular, if a site requests that you first install a special program or utility in order to facilitate download, forget it. There is no technical reason for having to do so.]
Written by a mathematician who had a lively interest in logic, semantics and philosophy, the story of Alice's fall down the rabbit-hole is packed with intriguing problems.
The ESP site is dedicated to the electronic publishing of scientific and other scholarly materials.
offers over 40,000 free ebooks: choose among free epub books, free kindle books, download them or read them online.
The Internet History Sourcebooks Project is a collection of public domain and copy-permitted historical texts presented cleanly (without advertising or excessive layout) for educational use. | Paul Halsall, Editor
We are a nonprofit organization with a mission to improve mathematics and science education in US public secondary schools by building a corps of outstanding STEM teachers and leaders.
AMS, founded in 1888 to further the interests of mathematical research and scholarship, serves the national and international community through its publications, meetings, advocacy and other programs.
Search publications database
The goals of AIM are to expand the frontiers of mathematical knowledge through focused research projects, through sponsored conferences, and through the development of an on-line mathematics library.
AIMS is primarily focused on serving mathematicians and scientists sharing a common interest in differential equations, dynamical systems, and their wide-range applications to sciences and engineering through analysis, modeling and computations.
The Mathematical Association of America is the largest professional society that focuses on mathematics accessible at the undergraduate level. | The mission of the MAA is "to advance the mathematical sciences, especially at the collegiate level."
Project NExT (New Experiences in Teaching) is a professional development program for new or recent Ph.D.s in the mathematical sciences.
Dedicated to increasing and disseminating mathematical knowledge
Applied mathematics, in partnership with computational science, is essential in solving many real-world problems. Our mission is to build cooperation between mathematics and the worlds of science and technology through our publications, research, and community.
Project MUSE is a leading provider of digital humanities and social science content for the scholarly community.
The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field.
The principal mathematical society for the university community in Scotland. Details of the meetings programme, its journals, library, and other facilities.
The Institute of Mathematics and its Applications (IMA) is the UK's learned and professional society for mathematics and its applications.
The purpose of the Association for Women in Mathematics is to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences.
GAMS is an on-line cross-index and virtual repository of mathematical and statistical components of use in computational science and engineering. Some 9,000 problem-solving software modules from nearly 100 packages are indexed, including a large subset of the NETLIB collection [Netlib is a collection of mathematical software, papers, and databases.].
The CodeCogs Equation Editor can be can be used in a wide range of circumstances to create beautifully formatted mathematical equations in either LaTeX or MATHML.
Tutorial Approach to Mastery of Mathematica | James J. Kelly - University of Maryland
Professor of Mathematics - Institute of Mathematics - University of Aberdeen, Scotland
This guide is designed to provide you with sufficient information to allow you to use EES, Elsevier’s electronic manuscript submission and peer-review system.
Zentralblatt MATH (zbMATH) is the world’s most comprehensive and longest-running abstracting and reviewing service in pure and applied mathematics. The zbMATH database contains more than 3.5 million bibliographic entries with reviews or abstracts currently drawn from more than 3,000 journals and serials, and 170,000 books.
Mission: To develop the highest quality knowledge-based products and services for the academic, scientific, professional, research and student communities worldwide.
Founded in 1995 as the central portal for electronic math resources in Europe.
This Directory of Preprint Servers makes available the current homepage URLs and email contacts of mathematical preprint and e-print servers throughout the world.
The Tardis Project - University of Southampton
Welcome to the University of Southampton Institutional Research Repository ePrints Soton.
INED makes a vast body of resources on population available to website users, including the INED library, open to all and accessible on line.
Mathematics documentation portal, providing access to bibliographical databases, book and periodical catalogues, prepublications, theses, digitized collections and directories.
The MIMS EPrints archive is an electronic repository for the papers, preprints and theses produced in the School of Mathematics at the University of Manchester.
"With more than a thousand academic journals and over 1 million images, letters, and other primary sources, JSTOR is one of the world's most trusted sources for academic content."
Eprints: Quick Guide to Open-Access Archives in Science, Technology & Medicine
Core Metalist of Open Access Eprint Archives -- Open access eprint archives are where authors of published research papers and papers destined for peer reviewed publication can self-archive the full texts of their work for all to see.
e-prints, journals, classification, dictionaries, etcetera...
"The Prime Glossary" is your Internet guide to the terminology of prime numbers."
This is a collaboratively edited question and answer site for people studying math at any level and professionals in related fields.
The "Careers in Mathematics" video contains interviews with mathematicians working in industry, business and government.
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
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."
"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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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.
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.