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These sites cover the full gamut of mathematical topics, and cater both to total beginners and career mathematicians.
The American Mathematical Society is a great institution for painting a good picture about different happenings in the math community. They have great information on math in the media and different educational resources.
Additional Info: Math Mentoring Network
Encyclopedia of Mathematics is an open-access resource for gaining knowledge into many different subjects. It’s a great way to sift through a bunch of different data and find some useful information.
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NRICH promotes the learning of mathematics through problem solving and provoking mathematical thinking. Rich activities are offered for students, teachers and parents.
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Math Notations works to help convey the best understanding of math possible, since it is largely the foundation of how we function in the world. Most of the material focuses on math between grades 4 and 12, along with AP calculus, so whether you’re looking for a refresher course or preparation material for an examination, the site is invaluable.
Additional Info: So is 75 the Avg of the pos integers from 50 to 100 Inclusive?
X Bubbler: Very Stylish Math is great because of its straightforward nature and easy-to-understand posts. Many of the posts look at prime numbers, so it’s a great place to get more information on that as well.
Additional Info: How Many Prime Numbers Are There?
(x, why?) is a blog with different math-related jokes and keeps a casual, fun tone for students to easily stay engaged while still pulling useful information away.
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When it comes to combining math problems and research topics, Beni Bogosel’s Blog is a great source for looking at all sorts of problems and trying to discern clear solutions.
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David Bressoud is a professor at Macalester College and is the former president of the Mathematical Association of America. His site, Launchings, is an incredibly useful tool that looks at different aspects of math and brings it all under a singular umbrella.
Additional Info: MAA Calculus Study: Effects of Calculus in High School
Math Drudge centers on the musings of two mathematicians as they look at different facets of math and science. The posts are very captivating, each focusing on an area within education.
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The Pi Search Page started merely with intentions to let individuals search the infinite numbers of pi for their birthday. Over the years, it has grown to allow for searching of any chain of numbers within Pi, so it’s a fun way to see what you can find in Pi.
Additional Info: Why? Why?
A Friendly Introduction to Number Theory provides parts of a book of the same title online so that readers can best understand if this is the book that they need for advancing their understanding of advanced mathematics.
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The Boyer-Moore Theorem Prover was started in Scotland in 1971 with the intention of being an automatic theorem prover that makes researching much more efficient.
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The On-Line Encyclopedia of Integer Sequences allows for users to search for different sequences of integers are they need to do research as to the circumstances in which those integers appear.
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Run by a professor of mathematics in London, Peter Cameron’s Blog showcases an ability to convey useful information, but underlines his experience as an educator by being very approachable.
Additional Info: Symmetry Versus Regularity
Check out the entire list at http://onlinemathdegrees.org/prime-resources/