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The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces.

Here is an alphabetical list of online mathematics books, textbooks, monographs, lecture notes, and other mathematics related documents freely available on the web.

Wiki-style site that is intended to develop into a large store of useful mathematical problem-solving techniques. Some of these techniques will be very general, while others will concern particular subareas of mathematics. All of them will be techniques that are used regularly by mathematical problem-solvers, at every level of experience.

"I often sit on a Thursday evening about 2000hrs and watch the ukedchat hashtag. This week it was about physical education. Although this is not one of my strong subjects in teaching (or even in real life) I was interested in the first question which asked how physical education could be related to literacy and/or mathematics. Just like a GSCE multiple choice essay question I chose to answer how it could be related to mathematics. You can see the full tweet chat conversation here - but I thought I would expand my response in this week's waffle."

Math journals provide advantages for students to develop a better understanding of mathematics, with teachers learning their student's views and beliefs regarding math.

Eureqa (pronounced "eureka") is a software tool for detecting equations and hidden mathematical relationships in your data. Its primary goal is to identify the simplest mathematical formulas which could describe the underlying mechanisms that produced the data. Eureqa is free to download and use. Below you will find the program download, video tutorial, user forum, and other and reference materials.

Within this site you will find lesson ideas, examples, and downloads for mathematics that embrace active learning, constructivism, and project-based learning while remaining true to the standards. The initial focus will be for grades 5 and up, but teachers of younger students may be able to find some uses or inspiration from the site. Higher level thinking skills, such as analysis, synthesis, and creativity are encouraged as well as technology skills and social learning. The scope of this site is mathematics, but many lessons lend themselves to interdisciplinary activities also.

Teaching mathematics through inquiry represents a radical departure from traditional mathematics instruction.

Microsoft Mathematics provides a graphing calculator that plots in 2D and 3D, step-by-step equation solving, and useful tools to help students with math and science studies. I wonder if it is as good as the graphing calculator that has been on Mac forever?

Finland is an innovator in education and now they're doing it again. Schools need a facelift. If you're building a new school - rethink school. I'd look at the designs. Also, Ewan McIntosh wrote a great "7 spaces of schools" that is in the "Choice" chapter for those of you have bought my book Flattening Classroom, Engaging Minds - he talked about this on a boat in South Africa with me 2 years a go and is an expert to follow in the area of school design. "Finnish students consistently have placed among the top countries on the Program for International Student Assessment, which gauges 15-year-old students' ability to understand and transfer concepts in reading, mathematics, and science. For example, in the most recent mathematics assessment, in 2009, Finnish students scored 54 points higher than their American peers on a scale of zero to 1,000. Pasi Sahlberg, the director general of the Center for International Mobility and Cooperation at Finland's education ministry, attributes the nation's academic achievement to a three-fold approach: quality of the academic curriculum, equity in educational access, "and the third one is the environment. How the environment and design of the school is supporting students' learning. When we combine these three things we can say something about the overall goodness of the school system."

Presidential Awards for Excellence in Mathematics and Sciences are open. Anyone - principals, teachers, parents, students or members of the general public - may nominate exceptional mathematics or science teachers who are currently teaching grades K-6 for the 2014 award year.

Math and Science fellowships for beginning math and science teachers.

Math and Science teachers -- beginning teachers should consider applying for these fellowships. These are in the United States. Here is what the ocmpany says about the fellowships (applications due Jan 15): "The prestigious KSTF Teaching Fellowship is valued at nearly $150,000 over the course of five-years and supports aspiring teachers of promise as they embark on careers teaching high school science and mathematics. Designed to meet the financial and professional needs of beginning teachers, the Fellowship exposes educators to a variety of teaching resources, new curriculum materials, and research and experts in the field. Most importantly, the program fosters professional development within a community of high school science and mathematics teachers and prepares Fellows to become leaders in their field."

This website provides Logic puzzles, Word problems and other mathematical games. Visitors also have access to videos for explaining mathematical concepts and skills.

Offers interactive demonstrations of anything that can be modeled mathematically - bacteria growth, light refraction, supply and demand, etc. Running a demo requires Mathematica Player, which can be downloaded free, along with the demos

About the Wolfram Demonstrations Project Conceived by Mathematica creator and scientist Stephen Wolfram as a way to bring computational exploration to the widest possible audience, the Wolfram Demonstrations Project is an open-code resource that uses dynamic computation to illuminate concepts in science, technology, mathematics, art, finance, and a remarkable range of other fields. Its daily-growing collection of interactive illustrations is created by Mathematica users from around the world, who participate by contributing innovative Demonstrations. Interactive computational resources have typically been scattered across the web--requiring specialized programming knowledge that's made them difficult and expensive to develop. As a result, their coverage has long been limited, and progress has been slow. In many ways, the Wolfram Demonstrations Project introduces a new paradigm for exploring ideas. The power to easily create interactive visualizations, once in the domain of computing experts alone, is now in the hands of every Mathematica user. Demonstrations can be created with just a few short lines of readable code, powered by the revolutionary advances in Mathematica. This opens the door for researchers, educators, students, and professionals at any level to create their own sophisticated mini-applications and publish them online.

Problem solving in mathematics is critical to understanding geometric concepts and also making connections with other mathematics concepts. Four activities are used for scaffolding an inquiry into SOMA Cubes.

Big list of flash-based activities, games, and interactives that work well for use with an interactive whiteboard in a mathematics classroom. Includes many areas of math including geometry, numeracy, fractions, probability, and more.

Game Classroom is an educational games website catering to the K-6 market. Game Classroom offers mathematics games and language arts games. Games can be found by selecting a grade level and then a subject area. Both the mathematics and language arts categories are subdivided into specific focus areas. Some of the games are unique to Game Classroom and some are games that are used on other sites.

Fascinating cross-curricular project from Jennifer Tan's diigo bookmarks (she joined the educators group tonight.) Mathematics students determine whether Poe's story is mathematically sound using graphing calculators and computers.

Excellent example of cross curricular projects

"Usually, being able to visualise mathematical concepts to students is an important step in helping them understand techniques to illustrate connections with previous learning, helping them master maths notions to progress their skills. The importance of visualising concepts is clearly integral for Peter Mattock who has collected together a valued resource of mathematical activities that can be used with manipulative across the age and ability range."

"New research from Monash University has found that girls in single-sex schools are more likely to study chemistry, intermediate mathematics, advanced mathematics and physics in their senior years when compared to their co-ed counterparts."