Free Math Software
From IAE-Pedia
Contents |
Readers interested in this page will likely want to browse the list of specific software packages available at http://iae-pedia.org/Open_Source_Software_Packages.
This is a work in progress. Readers are encouraged to help write this document.
Introduction
This document focuses on free math and math education software. In some cases the software is available free for online use, but a fee is charged for downloading copy to one's personal computer.
My June 2011 search of free math software returned over 67 million hits. Such a broad-based search provides a good example of the information overload that one can face when doing a Web search.
This document will provide you a little help in your search for free math software to fit your specific needs. However, please be aware that you need to reasonable level of knowledge of your needs to succeed in your search.
You may also find that some of your math software needs are satisfied by programs built into software programs or systems that you already have on your computer. For example, perhaps you are using a Macintosh computer. Quoting from from the Help Menu:
About Calculator and Grapher
- Use Calculator to solve basic, scientific, and programmer’s calculations. You can also perform many types of conversions, such as changing currency values or units of measure. As you perform calculations, you can display a list of your calculations, and then print the list or save it for your records.
- Grapher graphs curves, surfaces, inequalities, differential equations, discrete series, and vector and scalar fields. You can also create movie files of your graphs.
Perhaps you have the spreadsheet Excel on your computer. Excel has quite a list of built-in functions for processing data or creating charts or graphs from data you have entered into your spreadsheet. In addition, quoting from Excel:
- Formulas are equations that perform calculations. Excel provides various ways to enter formulas on a sheet. The best format depends on the kind of calculation that you want to perform. All formulas begin with an equal sign (=).
- You can type formulas into a cell manually. Use a formula that refers to a range of cells when you work with data that is located in different parts of a sheet or on another sheet—for example, to divide the sum of the numbers in column A by the sum of the numbers in column B. When your formula refers to other cells, you can change the data in any of the cells, and Excel recalculates the results automatically. Functions are predefined formulas that simplify entering calculations.
Even Microsoft Word has some calculation capabilities provided by built-in formulas.
Computer Algebra Systems
Quoting from the Wikipedia:
- A computer algebra system (CAS) is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.
The symbolic manipulations supported typically include:
- simplification to the smallest possible expression or some standard form, including automatic simplification with assumptions and simplification with constraints
- substitution of symbols, functions, or numeric values for expressions
- change of form of expressions: expanding products and powers, partial and full factorization, rewriting as partial fractions, constraint satisfaction, rewriting trigonometric functions as exponentials, etc.
- partial and total differentiation
- symbolic constrained and unconstrained global optimization
- solution of linear and some non-linear equations over various domains
- solution of some differential and difference equations
- taking some limits
- some indefinite and definite integration, including multidimensional integrals
- integral transforms
- series operations such as expansion, summation and products
- matrix operations including products, inverses, etc.
- add-ons for use in applied mathematics such as physics packages for physical computation
- statistical computation
- theorem proving and verification
Many people have suggested that a modern math education includes students learning to make use of a relatively general purpose Computer Algebra System. However, our overall math eduction system has made only limited movement in that direction. Perhaps the best example of such movement is the requirement of graphing calculators in many math courses at the high school and college level.
Some calculators are powerful enough to contain a fairly comprehensive CAS. Quoting from the Wikipedia:
- In 1987 Hewlett-Packard introduced the first hand held calculator CAS with the HP-28 series, and it was possible, for the first time in a calculator, to arrange algebraic expressions, differentiation, limited symbolic integration, Taylor series construction and a solver for algebraic equations.
- The Texas Instruments company in 1995 released the TI-92 calculator with an advanced CAS based on the software Derive [a CAS]. This, along with its successors (including the TI-89 series and the newer TI-Nspire CAS released in 2007) featured a reasonably capable and relatively inexpensive hand-held computer algebra system.
SAGE: Open Source CAS Software
Sage is a free open-source computer algebra mathematics software system licensed under the GPL. SAGE is available free for Windows, Macintosh, and Linux. It can also be run online.
Quoting from the SAGE Website:
- Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.
- General and Advanced Pure and Applied Mathematics. Use SAGE for studying a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra.
- Use an Open Source Alternative. By using SAGE you help to support a viable open source alternative to Magma, Maple, Mathematica, and MATLAB. SAGE includes many high-quality open source math packages.
Maxima, a Computer Algebra System
Quoting from http://maxima.sourceforge.net/:
- Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. Maxima yields high precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers. Maxima can plot functions and data in two and three dimensions.
- The Maxima source code can be compiled on many systems, including Windows, Linux, and MacOS X. The source code for all systems and precompiled binaries for Windows and Linux are available at the SourceForge file manager.
- Maxima is a descendant of Macsyma, the legendary computer algebra system developed in the late 1960s at the Massachusetts Institute of Technology. It is the only system based on that effort still publicly available and with an active user community, thanks to its open source nature. Macsyma was revolutionary in its day, and many later systems, such as Maple and Mathematica, were inspired by it.
Other Free CAS
The Website http://www.sigsam.org/software/index.phtml contains links to many free CAS. Here is their list, without the links.
Broad purpose free computer algebra systems
- Axiom: a general-purpose, strongly typed, computer algebra system.
- CoCoA: a computer algebra system for doing computations in Commutative Algebra.
- Fermat: a computer algebra system oriented towards polynomial and matrix algebra over the rationals and finite fields.
- GAP: a System for Computational Discrete Algebra.
- KASH/KANT: computer algebra system for sophisticated computations in algebraic number fields and global function fields.
- Macaulay2: a system for research in algebraic geometry and commutative algebra.
- Reduce: an interactive system for general algebraic computations of interest to mathematicians, scientists and engineers.
- SAGE: an open-source general purpose computer algebra system.
- SINGULAR: a Computer Algebra System for polynomial computations with special emphasis on the needs of commutative algebra, algebraic geometry, and singularity theory.
- PARI/GP: a computer algebra system designed for for fast computations in number theory.
Special Purpose Systems, Packages and Libraries
- ACE : a Maple library providing tools useful in algebraic combinatorics.
- Albert: an interactive program to assist the specialist in the study of nonassociative algebras.
- ANUNQ: a GAP package for the computation of nilpotent factor groups of finitely presented groups.
- ANUPQ: an interactive interface to the p-quotient, p-group generation and standard presentation algorithms of the ANU pq C program.
- CALI: a REDUCE package for computational commutative algebra.
- CASA: a Computer Algebra System for Algebraic Geometry.
- CHEVIE: a computer algebra system for symbolic calculations with generic character tables of groups.
- EinS: a Mathematica package allowing one to perform symbolic calculations with indexed objects.
- Felix: a special computer algebra system for the computation in commutative and non-commutative rings and modules.
- FeynArts: a Mathematica package for the generation and visualization of Feynman diagrams and amplitudes.
- GiNaC: a system to allow the creation of integrated systems that embed symbolic manipulations together with more established areas of computer science.
- GRAPE: a GAP package for constructing and analysing graphs related to groups, finite geometries, and designs.
- GUAVA: a GAP package for computing with error-correcting codes.
- LiDIA: A C++ Library For Computational Number Theory.
- LiE: A Computer algebra package for Lie group computations.
- MOLGEN: a system for the computation of all structural formulae that correspond to a given molecular formula.
- ORME: a package for equational theoreies.
- SONATA: a system for the construction and the analysis of finite nearrings.
Wolfram Alpha
I believe that Wolfram Alpha deserves to be in a category by itself. Quoting from the Website
- [Use the free] Wolfram Alpha computational knowledge engine to: answer questions; do math; instantly get facts, calculators, unit conversions, and real-time quantitative data and statistics; create plots and visualizations; and access vast scientific, technical, chemical, medical, health, business, financial, weather, geographic, dictionary, calendar, reference, and general knowledge—and much more.
The site is based on the Mathematica software developed by Wolfram. Mathematica is a commercially available CAS system. Thus, the site can do many of the things that Mathematica can do. However, it can do a great deal more—both in math and in other areas.
Geometry
GeoGebra is a free dynamic mathematics software for all levels of education that joins arithmetic, geometry, algebra and calculus. On the one hand, GeoGebra is an interactive geometry system. You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterward. On the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum. These two views are characteristic of GeoGeb.
Statistics Software
A wide range of statistical software packages are available. Many of the packages are operating system dependent, with many more being available for Windows than for Mac or Linix. Here are some starting points:
- As an example, take a look at the Statistical Software available from Altervista.
- Remember, this page is a Work in Progress. Please make suggestions of your favorite free statistical packages.
Mathematical Computation Software
A typical Computer Algebra System does both symbolic and numerical mathematics. Contrast this with a calculator that does only numerical calculations.
Octave
Octave is a multi platform software package. Quoting from http://www.gnu.org/software/octave/:
- GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab. It may also be used as a batch-oriented language.
- Octave has extensive tools for solving common numerical linear algebra problems, finding the roots of nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations.
Math Education Software
There are a variety of good sources for various types of math-related and math education-related free or inexpensive software. Some are briefly discussed in the following subsections.
Virtual Manipulatives
The Web document Virtual Manipulatives maintained by Southern Oregon University contains an extensive collection of virtual manipulative links.
In addition, the National Library of Virtual Manipulatives Websiteis an excellent resource. Quoting from the Website:
- The National Library of Virtual Manipulatives (NLVM) is an NSF supported project that began in 1999 to develop a library of uniquely interactive, web-based virtual manipulatives or concept tutorials, mostly in the form of Java applets, for mathematics instruction (K-12 emphasis). The project includes dissemination and extensive internal and external evaluation.
- Learning and understanding mathematics, at every level, requires student engagement. Mathematics is not, as has been said, a spectator sport. Too much of current instruction fails to actively involve students. One way to address the problem is through the use of manipulatives, physical objects that help students visualize relationships and applications. We can now use computers to create virtual learning environments to address the same goals.
The materials are available for free online use. These materials come in a free trial (seven day) downloadable version and a $39.99 downloadable version. There are over a hundred interactive virtual manipulatives. They are divided into four different grade level categories and five different math subject area categories.
Graph
Create a Graph: This software graphs data, providing Bar, Line, Area, Pie, and XY graphs. It also contains a tutorial. Quoting from this US Federal Government Website:
- Graphs and charts are great because they communicate information visually. For this reason, graphs are often used in newspapers, magazines and businesses around the world.
- NCES constantly uses graphs and charts in our publications and on the web. Sometimes, complicated information is difficult to understand and needs an illustration. Graphs or charts can help impress people by getting your point across quickly and visually.
The Peanut Software: Winplot for Windows is available free at http://math.exeter.edu/rparris/default.html. Examples of components include:
- Winplot [2-D and 3-D graphing, even implicit function graphing]
- Wincalc [exact arithmetic with hundreds/thousands/more digits]
- 2^100 = 1267650600228229401496703205376
- 123456789*987654321 = 121932631112635269
- Winmat [matrix algebra]
- Wingeom [geometry constructions]
Math Forum @ Drexel
The Math Forum @ Drexel is a large and steadily growing collection of aids to the teaching and learning of math. Quoting from the Website:
- The Math Forum is the leading online resource for improving math learning, teaching, and communication since 1992.
- We are teachers, mathematicians, researchers, students, and parents using the power of the Web to learn math and improve math education.
- We offer a wealth of problems and puzzles; online mentoring; research; team problem solving; collaborations; and professional development. Students have fun and learn a lot. Educators share ideas and acquire new skills.
The Math Tools component of the Math Forum is described as:
- A community library of technology tools, lessons, activities, and support materials for teaching and learning mathematics.
To explore what is available, one starting point is the Getting Started page. Another useful starting point it the Math topics by Course page.
Dare to Compare
The Dare to Compare Website is a free site provided by the US Federal Government. It contains a data bank of a large number of questions in a variety of subject areas (including math) and grade levels. The system will generate a test and administer it online. After a person completes providing test answers, the computer system will grade the test. For each question, the user can request a comparison with answers provided by other people. Some of the data is international, and some in national.
Calculators
There are a huge number of "virtual" calculators available on the Web. Such virtual calculators provide the Web user with a computer simulation of a calculator. Many of the types of calculators available are quite specialized.
For example, recently I was reading about the Commodore-64 microcomputer that was first produced in 1982 and solve at retail for $595. What would this be in today's dollars? My Google search of the expression "inflation calculator" returned a number of hits. I just provide that year (1982), the amount ($595) and the year (2009) and it provides me with the answer according to whatever measure of inflation happens to have been built into the computer program. Of course, there are many different measures of inflation. Thus, there are different possible answers to my question.
What about math? The site http://www.math.wvu.edu/~ef/150/calc/jcalc.html provides an example of a generic scientific calculator.
Interested in a specific brand of of calculator? My Google search of virtual TI calculator returned about 317,000 hits.
How about a metric calculator? My Google search of virtual metric calculator returned about 25 thousand hits.
Looking for still more? Go to Martindale's Calculator On-line Center at http://www.martindalecenter.com/Calculators.html. It has well over 23,000 different calculators and spreadsheets.
Math-Related Games
There are a huge number of free games and puzzles available on the web. Many are math-related. The free games and puzzles vary considerably in their quality of instructions. Sometimes persistence added to trial and error is needed to learn to play the game.
- 34 games.
- Quality computer games for ages 5-12. The English counterpart of the Dutch RekenWeb, started in August 2000. The goal of the Rekennet project is to support primary school teachers in their task to teach realistic mathematics. The Rekennet consists of 2 components: a social network and a website with games. Experts from the Freudenthal Institute participate in online meetings between teachers and offer direction. The site also contains printable activity sheets and practical suggestions.
Links to Other IAE Resources
This is a collection of IAE publications related to the IAE document you are currently reading. It is not updated very often, so important recent IAE documents may be missing from the list.
IAE Blog
Our Analog Human Brain in an Increasingly Digital World.
IAE Newsletter
Visualizing the medical data explosion.
IAE-pedia (IAE's Wiki)
Open Source Software Packages.
Presenting statistical data in meaningful, dynamic, and colorful manner.
I-A-E Books and Miscellaneous Other
David Moursund' Learning and Leading with Technology Editorials.
Author or Authors
The original version of this document was developed by David Moursund.
