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Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface.

This slide show demonstrates some techniques that would be suitable for an experimental geometry project. The basic shapes of square and circle are explored using open source Geogebra and Dr Geo geometry software. The examples includes exercises in geometric construction, novel solutions and recursive (spiral) constructions. This is mathematics that can be done without algebra. There is some algebra on slide 18, to calculate the radius and area of a semicircle inscribed in a square.

"MathJax is an open source JavaScript display engine for mathematics that works in all modern browsers. "

"In this article we introduce the free educational mathematics software GeoGebra. This open source tool extends concepts of dynamic geometry to the fields of algebra and calculus. You can use GeoGebra both as a teaching tool and to create interactive web pages for students from middle school up to college level. Specifically designed for educational purposes, GeoGebra can help you to foster experimental, problem-oriented and discovery learning of mathematics. We will illustrate the basic ideas of the software and some of its versatile possibilities by discussing several interactive examples."

The OpenScience project is dedicated to writing and releasing free and Open Source scientific software. We are a group of scientists, mathematicians and engineers who want to encourage a collaborative environment in which science can be pursued by anyone who is inspired to discover something new about the natural world.

An open source "general-purpose" computer algebra system.

"Mathics is a general-purpose computer algebra system. Enter queries and submit them by pressing Shift + Return. See the gallery for some neat examples or the documentation for a full list of supported functions. Mathics uses MathJax to display beautiful math."

"Mathics is a free, general-purpose online computer algebra system featuring Mathematica-compatible syntax and functions. It is backed by highly extensible Python code, relying on SymPy for most mathematical tasks and, optionally, Sage for more advanced stuff. Get Python if you don't have it already (you probably have it if you're on Linux or a Mac)."

Free open source textbook suitable for college juniors and seniors

Fundamentals of Mathematics is a work text that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who (1) have had a previous course in prealgebra, (2) wish to meet the prerequisite of a higher level course such as elementary algebra, and (3) need to review fundamental mathematical concepts and techniques. NOTE: This collection is a work in progress, and the content has not yet been marked up in CNXML. You can download PDF copies of individual chapters in from their respective modules.

"Several of our classes involve students using mathematical expressions, but there was no way for us to automatically check this work. The stated solution to a problem may be x+y, but if a student answers y+x, our system needs to understand that this is also correct." "sympy, an open source Python library for symbolic mathematics," is proposed as a solution.