Open Source Math Software For Education?

Rui Carmo writes "Now here's something you don't get asked every day, but which a friend happens to need for her kids: If you had to suggest Open-Source software for mathematics - somewhere from high-school to freshman level, and not merely for 'pure' mathematics, but also applicable to physics and statistics (the kids are considering going into Applied Maths and Engineering), what would you point people toward, assuming they have access to both Linux and Windows? I know this is a niche thing and that there is nothing out there that even comes close to Wolfram's excellent Mathematica (which I used on my old NeXTCube), but surely something along the lines of (or simpler than) Calculation Center exists?" The Knoppix-based Quantian might be a good place to start; what math software do you recommend?

Octave?

What about octave (free Matlab clone)?

Re:Octave?

Octave is a really nice piece of software! Also check out Scilab [scilab.org].

Re:Octave?

Every time a discussion of math packages comes up, Octave is always mentioned right away, but Euler [sourceforge.net] gets ignored. I'm curious why people seem to prefer Octave over Euler so much that Euler is virtually unknown.

Re:Octave?

Here's a link:

http://www.octave.org/

I've used Matlab extensively and can tell you that Octave and Matlab aren't perfectly compatible. However, a student who learns Octave can switch to Matlab without any effort whatsoever.

Re:Octave?

Call that a link?

Octave [octave.org]

That, my friend, is a link.

Re:Octave?

Maybe he doesn't know how to write HTML. Most people don't. [w3.org]

Re:Octave?

You call that a link?

this: http://images.google.com/images?q=this%20is%20a%20 link&hl=en&lr=&sa=N&tab=wi [google.com] is a link.

Re:Octave?

You call that a link? THIS is a link:

http://www.hugeurl.com/?ODg1M2YwMDM0NzNjMDgyNmJlM2 VkYWVkYWYwZTUxMzMmMTImVm0wd2QyUXlVWGxXYTJoV1YwZG9W Vll3Wkc5alJsWjBUVlpPV0Zac2JETlhhMUpUVmpGYWMySkVUbG hoTWsweFZqQmFTMk15U2tWVWJHaG9UVmhDVVZadGVGWmxSbGw1 Vkd0c2FsSnRhRzlVVjNOM1pVWmFkR05GZEZSTlZUVkpWbTEwYT FkSFNrZGpTRUpYVFVad1NGUlVSbUZqVmtaMFVteFNUbUY2UlRG V1ZFb3dWakZhV0ZOcmJGSmlSMmhZV1d4b2IwMHhXbGRYYlVacl VsUkdXbGt3WkRSVk1rcElaSHBHVjJFeVVYZFpWRVpyVTBaT2Ns cEhjRlJTVlhCWlZrWldhMVV5VW5OalJtUllZbFZhY1ZscldtRm xWbVJ5VjI1a1YwMUVSa1pWYkZKRFZqQXhkVlZ1V2xaaGExcFlX a1ZhVDJOdFNrZFRiV3hYVWpOb1dGWnRNSGRsUjBsNFUydGthVk 5GV2xSWmJHaFRWMVpXY1ZKcmRGUldiRm93V2xWb2ExWXdNVVZT YTFwWFlrZG9jbFpxU2tabFZsWlpXa1prYUdFeGNGaFhiRnBoVk RKT2RGSnJhR2hTYXpWeldXeG9iMWRHV25STlNHaFBVbTE0VjFS VmFHOVhSMHBJVld4c1dtSkhhRlJXTUZwVFZqRmtkRkp0ZUZkaW EwcElWbXBKZUUxR1dsaFRhMlJxVWtWYVYxWnFUbTlsYkZweFUy dGthbUpWVmpaWlZWcGhZVWRGZUdOSE9WZFdSVXBvVmtSS1QyUk dTbkpoUjJoVFlYcFdkMVp0Y0V0aU1XUlhWMWhvWVZKRlNtRldi WE40VGtaa2NsWnRkRmhTTUhCNVZHeGFjMWR0U2toaFJsSlhUVV p3VkZacVJtdGtWbkJHVGxaT2FXRXdjRWxXYlhCS1pVWkplRmRz YUZSaVJuQnhWV3hrVTFsV1VsWlhiVVpzWWtad2VGVXlkR3RoYl VwV1lucEtWbFl6YUROWmEyUkdaVWRPU0dGR2FHbFNia0p2Vm10 U1MxUnRWbGRUYmtwb1VqTm9WRmxZY0ZkWFZscFlZMFU1YVUxWF VraFdNalZUVkd4YVIxTnRPVlZXTTFKNlZHdGFWbVZYVWtoa1Jt UnBWbGhDU2xac1pEUmpNV1IwVWxob2FsSkZOV0ZhVjNSaFlVWn JlRmRyZEd0U2EzQjZWbGQ0VDJGV1RrWlRhM1JYVFc1b1dGZFdX bEpsUm1SellVWlNhRTFzU25oV1Z6QjRUa1phYzFWc1pGaGhNMU p2VlcxNGQyVkdWblJOVldSWFRVUkdlVlJzVm05V01VbzJVbXRv VjFaRldreFdha3BQVW14YWMxcEhiRk5OVlZZelZteGFVMUl4Yk ZkWGJrcE9WbXh3V0ZsWWNGZFdSbFp5Vm10YVQxVlVNRGs9 [hugeurl.com]

For statisticians...

There is R
R Project [r-project.org]

Re:Octave?

Educational versoin is around $150/yr which includes the symbolic toolbox. That, I must say, is a darn good deal for MATLAB, considering it does a whole helluva lot. Everything that a high schooler would ever need to do, and a lot more. If you want math software, shell out the $150 (less than the cost of a textbook) and get Matlab, it's the best math software possible

That being said, the best software for math is no software at all. Paper and pencil, that's it. Over at my college, all engineers are required to go through four semesters of math (2 calc, diff eq. and linear algebra), and no calculators or tech tools are allowed for either course. And yes, we did need to plot slope fields, draw 3d representations of functions, etc... It's more important to know the concept of doing a problem than crunching numbers. The only time I use MATLAB is when I'm working on my design project-- I do the design, I setup the equations, MATLAB crunches the numbers for me.

Remember, number crunching != real math. Theory is the most important thing to learn.

Re:Octave?

Blockquoth the poster:

I've never been allowed to use a calculator and I'm much better off for it.

How do you know you're better off for it? Maybe, if calculators had been allowed, you'd've been able to get to deeper concepts faster. Maybe you'd have been able to play with function and form and plots, and discovered chaos.

'Course, maybe not. But it seems to me that a blanket statement like yours is essentially unsupportable, and generally counterproductive. There's room for pen-and-paper, or even just brain work, but IMHO, there's room for integrators and plotters.

Put another way: When I took math in grade school, I had a teacher who also didn't believe in "high tech" -- like the pencil. We did everything in ink. Her theory was, if it was in ink, you couldn't correct a mistake -- so you wouldn't make any. It was an insane educational theory, of course, and bore no relation to what actually occured.

Re:Octave?

Oh, geez, does no one understand the difference between a symbolic mathematics package (like Mathematica, Maple, or Calculation Center) and a numerical mathematics package (like Octave and Matlab)?

The guy's looking for a symbolic mathematics package. Why don't you recommend Excel for him why you're at it? Heavens.

Re:Look again

Rui Carmo: I'm looking for a good solid, off-road vehicle.

mvdw: Have you considered a Toyota Camry?

Anonymous Coward: Oh, geez, does anyone know the difference between an off road vehicle and a sedan?

cameldrv: High-end off road vehicles have become more sedan-like lately.

Rui Carmo: WTF?

R (GNU S)

R statistical language [ucla.edu]

Re:R (GNU S)

Dangit, you beat me to it!

I was going to suggest R.

To the person who claims it is a poor choice for High Schoolers, I disagree, especially if statistics is of interest. It forces you to actually THINK about what you are doing with your models instead of being able to run, willy nilly, any old analysis on any old data (vis-a-vis SPSS).

It is also good because it is VERY robust in its data import capabilities (excel, spss, etc), and is very strong at doing correct analyses.

There are some caveats:
Need to program
Need to be willing to really learn
Poor documentation
Memory intensive for large datasets.

This last item needs some explanation: R, unlike other statistical packages, loads the entire data set into memory, and performs all analyses there, instead of accessing the disk more frequently. This results in large datasets taking some serious memory, especially once you start working on complex analyses. If you plan to be using 5,000+ observations (which isn't all that uncommon in some fields), you should plan on having a fairly beefy computer.

The upside is that it can provide much more information than spss could ever hope for. Now, if someone would just finish the plugin for kalc or gnumeric that would allow direct access, that would be awesome.

(For R afficianados who aren't aware, check out ESS-Emacs Speaks Statistics--it's great for unix coders, but unnecessary for win32 stats folks).

Maxima

Look at http://maxima.sourceforge.net/ [sourceforge.net].

Re:Maxima

I have played with Maxima a little bit. I think it is a decent peice of software. It started out as a government research app that was later open sourced. Unfortunately development is slow (if even existent)...

It is being actively developed [sourceforge.net]. While William Schelter was maintaining it (for 19 lonely years), development was very slow indeed. I gather that most of the work was done by him, and some of his graduate students. Since his death in 2001, a number of other people have come on board, and there is a lot of catching up to do.

Some documentation [sourceforge.net]has been rewritten, a great many bugs have been squashed, the package has been ported to several Lisps (yes, it does matter to users), there has been at least one new Emacs mode written for it, it can be used with Texmacs, and so on. Some of the people who are working on it are big names in their spheres, like Richard Fateman [berkeley.edu], who worked on the original Macsyma.

Version 5.9.1 was released in September '04, and the next big step will be the GREAT SOURCE DOWNCASING. Maxima is so old that most of it is written in all caps. There is a lot to do to bring it into the 21st century, and most of what's being done right now is behind-the-scenes stuff.

As you say, it's decent software now. It's fully usable, with a useful GUI for Windows (developed on Schelter's watch, as I recall). It is probably better for memory intensive work than Maple or Mathematica; that's what initially got me started using it.

Re:Maxima

My dad was a physicist at ORNL who started using the DOE MIT version of Maxima in the early 1970s. He thought Maxima was the greatest thing since sliced bread. His division hired a new Phd at one point whose dissertation had taken 18 months to derive by hand. When he joined ORNL, he ran the problem through Maxima. Only took an afternoon and he was quite relieved when Maxima got the same answer he had gotten by hand.

GraphCalc is good

GraphCalc [graphcalc.com] is a good graphing program. It might not do everything in math, but it graphs pretty nicely.

Math Software?

The whole technology upgrade the schools have been getting doesn't seem to be making learning more efficient. It seems like a big waste of money.

If a kid doesn't spend time studying his books, why would he start studying his software?

Re:Math Software?

Actually its totally appropriate. Highschools that want to do CalculusI thru DiffEq for their advanced students use Mathematica and Calculus Remote from The Ohio State University [ohio-state.edu] (CROSU), or University of Illinois at Urbana-Champaign's Netmath program. I believe Harvard does the same.

I think a problem might be that you associate highschool math with trig. Using Mathematica in a self-based course of instruction they can move as fast as is natural for them. Why not let the kids move past dull rote mechanical skills and learning by doing something useful?

Is there really any reason why (the undergrad intro) QM can't be taught in HS using visualization and moderate Linear Algebra skills? I mean, if they can get as far as DiffEq? Isn't it more the *style* of instruction (chalk vs. powerpoint), and what we have them do for homework that holds them back more than the concepts?

gnuplot

What are these "kids" trying to learn?

They can explore lots of stuff just with gnuplot.
bc is also pretty good - simple to learn and use.

Who needs all the flashy stuff?

Stephan

Why software?

There were no computers in my middle/high school math classes and I learned math just fine. What is your friend trying to do that couldn't be done better with pen and paper and old fashioned teaching? Computers aren't a panacea.

Re:Why software?

Fractals and strange atractors were only unleashed once computers were available.

Fractals are merely a novelty at a high school level. What can students struggling with pre-calc do with fractals other than gawk at pretty pictures? To appreciate them beyond "hey, it's glittery...oooh, color cycling....drool" takes a motivation and interest not present in most students.

Re:Why software?

But, those shiny colors can motivate them.

In the worst way. "Hey, those fractals look pretty cool, I think I'll sign up for this advanced fractals course." --semester begins-- "Holy flying fluke, Batman, where did these equations come from?!?" --drops class, ends with less motivation than before--

bc

bc [gnu.org]

For a high school freshman . . .

I wouldn't recommend software at all. I would recommend something we call "pencil and paper." Learning mathematics (and reading music, and a number of other such undertakings) is as much a mechanical skill as an intellectual one and the quickest way to the brain is through the fingers.

Come back when they're in college and ask again.

KFG

Math.com?

I hate to state the obvious, but Math.com [math.com] is where I've spent some time brushing up on all the math I've forgotten.

I'd love a math tutor style of program that would fluidly walk you through from basic math all the way to calc and trig, automatically adjusting to your rate of learning based on little exercises.

You want Maxima

Maxima [sourceforge.net]:

It's the closest thing I know of to an OSS Mathematica. It is to Mathematica what The Gimp is to Photoshop. Namely, it's a fair way behind the front runner but still very usable.

OT: Learn the math, then use the tools

I know this is a bit off-topic, but it can't be overemphasized:

If possible, students should learn the principles behind the math before they are allowed to use fancy tools like calculators and computers.

My high school teacher made us learn logarithms and trigonometry using a pencil, graph paper, and tables, THEN we got to use a calculator. As for calculus, we did all our graphs by hand, sub-$200 graphing calculators weren't available back then.

I hope you get some good answers in this thread.

a good question deserves a good answer.

I'd like to recommend the very exellent GNUWin project [gnuwin.epfl.ch]. They are a great collection (consisting entirely of GNU software) of applications for not only scientific computing, but also just basic general computing on the Windows platform. Check out the list [gnuwin.epfl.ch] of applications on the two CD set as well as the current wishlist. It includes many of the programs already named. Latest ISO is the Nov 30 release package.

P.S. I think they're looking for new leadership to continue to project. Please help if you can.

I've always loved this quote

I know this is a niche thing and that there is nothing out there that even comes close to

Insert excellent software that does just what you want , but surely something along the lines of (or simpler than) Insert Open source project here

So, what is wrong with people doing a good job and creating value, getting a little bit of that value back so they can pay rent ?

Just wondering

Have you checked out the pricing on math products

Have you checked out the pricing on math products lately? I have. It's freakin' stratospheric, and then they nickel and dime you for extensions.

My main issue with this pricing structure is that a hobbyist like myself simply can't justify the expense. And that's very unfortunate.

Re:I've always loved this quote

So, what is wrong with people doing a good job and creating value, getting a little bit of that value back so they can pay rent ?

Nothing. Exactly like there's nothing wrong with telling people that there's something out there that does exactly what they want and is expensive, and that there is something with some/much/most/all of the functionality but it's Free, Open Source or Cheap.

Maxima

At National Mu Alpha Theta this summer (a math tournament), I had brought my OS X laptop which happened to have Maxima [sourceforge.net] on it. I use Mathematica at home, but I only have the Win32 version. Maxima is difficult to learn (not user-friendly, but it's almost as powerful as Mathematica -- in fact, its predecessor, Macsyma, was one of the first CASes, predating Mathematica. I used Maxima to verify some lengthy integrals after one test when the answer posted differed significantly from my answer.

Oh, and it's GPL, and it works on Windows, Linux, and Mac OS X (via Fink).

BTW, you probably know this, but if you can afford Mathematica or a Math'ca-based product, or at least a student license, it's going to be a lot better and more powerful than any OSS math product today. Math'ca is really an excellent product. Unfortunately, the price matches its quality.

Mathematica, of course

Full disclosure: I work for Wolfram Research [wolfram.com]. But oh -- the irony! I am also a columnist for Math Games at maa.org [maa.org], and I wrote an article about the Quantian Distribution [maa.org]. I didn't want a spammer to start using quantian.org just as the distro was getting popular, so I bought it, and provided a redirect to the main Quantian site. So now, I'm getting doubly Slashdotted. Huzzah. A student should definitely be getting Mathematica for Students [wolfram.com] -- but check with the college first. They might be on a Mathematica Campus [wolfram.com], and can get it for free.

Pari-gp, Lisp and interfaces

No-one's mentioned the superb pari-gp [u-bordeaux.fr] yet. It'll draw graphs using gnuplot and unlike much other software of it's type it has excellent documentation.

Lisp is also prominently absent but I agree with what Chaitin [auckland.ac.nz] says about it being the natural computer language for mathematically minded computer users. Actually I'm surprised it isn't more popular with other software developers - it seems to me to make any kind of programming easier and more pleasurable.

People who've mentioned Maxima also haven't said anything much about graphical (non-plotting) interfaces to it. I like imaxima in emacs and also TeXmacs - which will act as a graphical front end to many other mathematical programs.

Maxima is your best bet

I lead the Maxima project, http://maxima.sourceforge.net/ [sourceforge.net]. Maxima is a full-featured GPL'd computer algebra system under active development. We don't hear much from people who want to use Maxima for high school mathematics, but we would welcome the input.

Quantian article

I own the quantian.org domain. The following is from my article on the Quantian Distribution [maa.org]. Here is a brief run down of links, programs, and other goodies in Quantian.

• R [r-project.org], including several add-on packages (such as tseries [r-project.org], RODBC [r-project.org], coda [www-fis.iarc.fr], mcmcpack [wustl.edu], gtkdevice [r-project.org], rgtk [omegahat.org], rquantlib [eddelbuettel.com], qtl [jhsph.edu], dbi [bell-labs.com], rmysql [r-project.org]), out-of-the box support for the powerful ESS [r-project.org] modes for XEmacs [xemacs.org] as well as the Ggobi visualisation program [ggobi.org];
• A complete teTeX [tug.org], TeX [upenn.edu], and LaTeX [latex-project.org] setup for scientific publishing, along with TeXmacs [texmacs.org] and LyX [lyx.org] for wysiwyg editing;
• Perl [perl.org] and Python [python.org] with loads of add-ons, plus ruby [ruby-lang.org], tcl [www.tcl.tk], Lua [lua.org], and Scientific and Numeric Python [scipy.org];
• The Emacs [gnu.org] and Vim [vim.org] editors, as well as Gnumeric [gnome.org], kate [kde.org], Koffice [koffice.org], jed [jedsoft.org], joe [freshmeat.net], nedit [nedit.org] and zile [sourceforge.net];
• Octave [octave.org], with add-on packages octave-forge [sourceforge.net], octave-sp [debian.org], octave-epstk [debian.org], and matwrap [usc.edu];
• Computer-algebra systems Maxima [sf.net], Pari/GP [parigp-home.de], GAP [st-and.ac.uk], GiNaC [ginac.de] and YaCaS [sf.net];
• the QuantLib [quantlib.org] quantitative finance library including its Python [python.org] interface;
• GSL [redhat.com], the Gnu Scientific Library (GSL) including example binaries;
• The GNU compiler suite comprising gcc [gnu.org], g77 [gnu.org], g++ [wm.edu] compilers;
• the OpenDX [opendx.org], Plotmtv [ornl.gov], and Mayavi [sf.net] data visualisation systems;
• it includes apcalc [halcyon.com],aribas [uni-muenchen.de],autoclass [nasa.gov],

Perl Data Language

http://pdl.perl.org/

If you're already teaching your kids perl (for some strange reason), pdl adds vector numeric features and access to all sorts of numeric libraries.
It's good for number crunching and data display.