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?

Comments

Octave?

[mvdw]

What about octave (free Matlab clone)?

Re:Octave?

[hotchai]

Octave is a really nice piece of software! Also check out Scilab.

Re:Octave?

[Anonymous Coward]

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?

[Anonymous Coward]

If you go with octave you might want to check out octaviz (http://sourceforge.net/projects/octaviz/) too. It is a 3D visualization system for octave that will let you do in octave everything that VTK (www.vtk.org) can do.

Re:Octave?

[rjstanford]

Call that a link?

Octave

That, my friend, is a link.

Re:Octave?

[beefstu01]

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?

[Safety Cap]

Maybe he doesn't know how to write HTML. Most people don't.

Re:Octave?

[aussie_a]

You call that a link?

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

Re:Octave?

[spacecadetglow]

I see you've played linkey spooney before.

Re:Octave?

[Anonymous Coward]

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:Octave?

[sketerpot]

If you want something like Maple, but open source, try getting Maxima. It runs on Windows and Linux, can do algebra, calculus, and a good amount of other stuff, and you can use TeXmacs as a front end.

Re:Octave?

[gilroy]

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?

[Anonymous Custard]

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

Re:Octave?

[altstadt]

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

Re:Octave?

[N1XIM]

As somebody whom has had to correct the work of students before, I can tell you that it is enormously frustating work when you know that the student has down the concept that you are currently working on but is making mistakes (often of the simple careless type) in less complex or related concepts--causing the student to get the wrong answer, become frustated, and often fail to realize (now matter how much you reassure them) that they did it right the first time and messed something else up--not the concept that they were trying to learn (and therefore the concept that they assume is the source of all errors).
Calculators can help, if used properly, to lessen the number of arithmetic errors that the students make in the hurried frenzy to get the problem done and find out if the answer they have devised (but not yet calculated the numeric value of) is correct. Working slower would be a solution to the problem if it were not for the fact that students in general are being assigned more homework in the very conceptual and complicated classes (that we are talking about) than ever before (while the students in less advanced classes are doing a lot less homework than in the past, despite the fact that it would actually benefit them more). Allowing the students to use technology is a way around the perceived need to drown students in work to teach them new concepts.

Re:Octave?

[Anonymous Coward]

Because Octave is actually Matlab compatible, and there are thousands of lines of Matlab code out there? Also, Octave has been around for some time. I discovered it in 1996 and has been using it ever since.

Re:Octave?

[le_jfs]

because I don't like all the windows of Matlabs gui
Try

matlab -nodesktop

R (GNU S)

[Neil Blender]

R statistical language

Re:R (GNU S)

[Kludge]

R is very good for statistical coding. A good number of professional statiticians code for the project and an even greater number actually use it, and it will run almost any S code written.

I've used it since graduate school and in my two subsequent professional research jobs. Currently I use it for running statistical simulations in parallel across our 45 node cluster.

Re:R (GNU S)

[DarkSarin]

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

[Anonymous Coward]

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

Re:Maxima

[willy134]

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) but on windows it did a fairly good/fast job of calculating funny integrals. They plotting features are decent also.

It is much closer to mathematica than matlab. I don't know how it compares to mathcad.

Hey it is free so at least give it a try.

Re:Maxima

[YGingras]

I'd like to add that Maxima support formated output when run inside GNU TeXmacs. You get top quality homeworks with really little effort.

Re:Maxima

[RealAlaskan]

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. 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 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, 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

[antiMStroll]

"I don't know how it compares to mathcad."

Is there GPL software comparable to MathCAD? Due to the pioneering work of Martin King (http://www.quarter-wave.com/) the latter has become popular among DIY builders for modeling transmission lines speakers. Most though can't justify the ~$1000 for hobby software and use MathCAD's crippled demo, Explorer 8.

Re:Maxima

[Skjellifetti]

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

[theteenager]

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

Math Software?

[jtbauki]

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?

[upsidedown_duck]

You don't even know what Mathematica is, don't you?

Actually, Mathematica is completely inappropriate for high school math courses. It is very complex, insanely powerful, and just way too much for simple stuff like plotting approximations of integrals or whatever. For high school math, there is nothing more fruitful than just working it out by hand. Plotting even a few points is sufficient to show a concept. Are students and teachers so damn insecure that they feel they need 3-D 24-bit color plots of data with animations and full-blown programming languages...for trig?!?!

Re:Math Software?

[DanteBlack]

I am aware of the United States' failing academic standing. It's sad really because we were once great leaders. The problem in schools now is that students don't really want to learn, they've simply become complacent. Worse it seems like too many teachers have fallen pray to this as well, they don't want to teach. This sounds like a completely opposite sittuation however, more power to them.

As for computers in comp sci, math, and other I don't know how much I can argue that they should be in "soft" classes. If they help, great. If they're not, perhaps it's a failing of the use of the tool not the tool itself. I can't really say, I didn't have computers in my classes but I wasn't using a slide rule either.

Tools for learning are important and if they're not working properly examination of why is equally, if not more, important. Kids that don't care are fairly well doomed, but kids that do should be given every chance and tool to help them along be it "hard" or "soft" course work.

Re:Math Software?

[civilizedINTENSITY]

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 (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?

Re:Math Software?

[bobscealy]

A package like Mathematica might be inappropriate to present to everybody on a high school math class, but for somebody who is likely to become involved in mathematics at a tertiary level surely there is some utility in them being familiar with this kind of package, and at very least there is no harm in it.

Plotting a few points might be suitable for many concepts, like displaying the behaviour of a low order polynomial, but what about the behaviour of a function like sin(1/x) as it approaches 0? I tutor quite a few first year mathematics courses, and based on many students understanding of the behaviour of quite simple functions I would encourage anyone in late highschool who was interested to play with a math package.

Re:Math Software?

[upsidedown_duck]

LOL, what kind of math did you take in High School? I was taking A.P. classes in High School.

So was I. I even got a 5 on the AP test (like it ever mattered). Mathcad was a drag. Mathematica would have been hell. We spent so much time dicking around with the computers, we could probably have covered half a chapter in that time! Computers add so much complexity that they are really only a benefit for very large problems, like CFD over an airplane wing. High school students really don't need a computer, unless the class is specifically for programming, which is not math (don't confuse programming with Comp Sci, please).

Re:Math Software?

[hobbesmaster]

Well, a lot of high schools teach the AP Calculus AB and BC courses, which are the equivalent of a first and second semester calculus course respectively at the college level. In my school of 2000 there are 3 sections (each of about 25 students) in AP calculus 1, and about 20 in AP calculus 2. Additionally, 2 students maxxed out with Cal2 in their junior year and are taking 3rd and 4th semester calculus at the local university. Total for all students in Calculus then would be about 4.85% of the school population. DE are covered in the cal2 course at my school, so about 1.1% of the student population would have use of mathematica by your reasoning. Still not very many, but still a far cry from 0.001%.

That said, a computer algebra system period is useful in learning calculus if you're at all of the curious sort. Taking AP Cal 1 I've used my 89 to answer all sorts of questions I have about why you can't do things. And its faster than looking up the answer in the back of the book usually. :)

Re:Math Software?

[Mooncaller]

Not only was I, but almost all of my friends, were doing Diff. Eq. by their Senior year. Of course, we were teaching ourselves because High School only gets to Calc II. I was the math geek of my crowd and I was into Calc III, Abstract Algebra, and just getting into Tensors. BTW, when tested in HS, my IQ was only 145. Don't tell me that High Schoolers can't hand the stuff. High School students can and will be able to learn advanced math if they know that they can access it. Math software may be just the thing. I have found when tutoring, that being able to visualize the math, is the key to understanding it. Almost all of the programs I wrote ( in the mid 70's) were for exploring math. Access to a good library ( my dad was an EE), computors, and a few really awsome instructors did it for me.

gnuplot

[sugarmotor]

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?

[Hatta]

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?

[Zangief]

Because there are things that simply cannot be done without a computer. Fractals and strange atractors were only unleashed once computers were available.

Plus, there are other cool things you can do. Long equations can be simnplefied, you don't have to write so much, and you can concentrate in the mathematics, instead of in the often tedious mechanics.

Re:Why software?

[spac3manspiff]

Yeah, and guys in the stone age did math with rocks and did fine too.

But I think progress education of younger generations if we allow them to use new technology. Introducing math to kids in middle school allows them to become more familiar with the technology. Like, my dad can do math perfectly with pen and pencil but can use a computer or graph on a calculator. That shows the difference in generations.

Re:Why software?

[upsidedown_duck]

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?

[upsidedown_duck]

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--

Re:Why software?

[Morganth]

While I agree that technology in Math helps for some things, especially visualization of otherwise abstract concepts, technology can also really impede Math learning.

I know this. I'm a public high school graduate who is now in Computer Science and feels as if his Math background is lacking, to say the least.

Yet, I got a 5 on AP Calculus exam, got As in my Calc class, but don't remember a damn thing from Calculus. Why? I mastered the fucking calculator.

Armed with a graphing calculator (TI-89 preferred), I can do anything from Calculus. Armed with a pen, paper, and my own brain, I'm as useless as a monkey throwing darts at a dartboard (sometimes, I feel even more useless).

How can this be, you ask? AP has a section without the Calculutor too! Answer: lots of long-night review the night before the exam. I barely remember that week, let alone the material I crammed into my head for the exam.

Sure, it didn't help that my Calc teacher wasn't stellar, and that it was senior year (so I was busy with college applications and all that nonsense), but nonetheless, I wish I had gotten a real Calculus education. And I could have, if it weren't for that damned calculator.

People learn what interests them. If you love Math and hate technology, then you'll learn math and the calculator will help you out in tough spots. If you don't really love Math but do love technology, then you'll do what's logical: master the device, the graphing calculator. Little did I know I'd actually need the concepts I used my technological know-how to work around!

Now I have to audit a Calc I class to catch up, since I feel so embarassed for myself.

More and more kids are excited by technology. That means less and less will learn math, especially if they are using stuff like Mathematica in their classrooms, instead of working out the derivatives or whatnot.

I take the same view as my algorithms Professor nowadays. On the second day of class, he took away the graphing calculator from a student he saw using it to calculate whatever, then he brought it up to his desk, pulled out a hammer from his drawer, and smashed it to pieces.

Or so we thought; he actually smashed an old, broken calculator to pieces that he switched with the brand-new one. We were all shocked, and amused when he revealed the trick, but then he said, "If you want to learn something, throw away your calculator, unless that thing you want to learn is your calculator."

That student he embarassed was me.

python

[viva_fourier]

As an avid Matlab user, octave would be a good realm for lower dimensional mathematics. But, there's a nice foundation being set for python as an interpretive math environment. For the matlab lackies, matplotlib provides Matlab-like plotting support. For windows, grab the enthought compilation -- for linux, piecemeal together your environment starting with SciPy, MayaVi, and Matplotlib.

bc

[bbh]

bc

For a high school freshman . . .

[kfg]

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

Re:For a high school freshman . . .

[Neil Blender]

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.

Word to that. When I was in school, we couldn't even use calculators. I could calculate the cube root of large numbers to several significant digits with paper and pencil.

Re:For a high school freshman . . .

[Geoffreyerffoeg]

No.

Software is useful. As a freshman in trig, I was learning calculus on my own, and Mathematica helped. There was one derivative in particular which I couldn't figure out; after using Mathematica to find the answer, the method whereby you reach that answer came to me a few days later -- it was much more obvious from the answer than from the question. There have been countless discussions between my friend and I as to how Mathematica arrived at a certain solution.

You try doing large integrals with pencil-and-paper and then come back and tell me that mathematics software isn't worth it for highschoolers. The only thing I can see is "useful" is the handwriting practice.

the quickest way to the brain is through the fingers

Software which shows you how to work a problem gets to the brain a lot quicker than fingers which have no idea what to do. Besides, I have seen countless cases of classmates in physics who have no idea what they're doing but can write down the examples that the teacher gives without fail.

The problem, of course, is software which devolves to mindless number-punching. I frown upon that - except when you would be punching in the same numbers into a calculator, surrounded by some function signs that are relatively obvious, or when you'd be sitting there for 2 hours working the problem by hand. Apart from stupid programs, it's hard to claim that writing out things helps you work better than using calculators and computers.

Re:For a high school freshman . . .

[ltbarcly]

Of course some integrals are hard. That is why there is a table of integrals in the front (and back) cover of almost every calculus book. However, that does not mean you don't have to learn the method to solve those integrals.

Learning is MUCH more complicated than simply absorbing the ability to do certain well defined tasks. There are abilities gained when working hard math problems that are far more important than the math problems themselves, at least in the case of difficult integrals.

Having done 'large integrals' by hand (and having slid through using my TI-89) I can tell you that using a table (or math software) will come back to bite you.

Learning is SUPPOSED to be hard (see Pinker: The Blank Slate or How the Mind Works) because if it isn't hard then you aren't learning anything. You cannot find an easy way ('no royal road' -Euclid) and you cannot trick people into learning using gimmicks. You just have to sit down and work at it until you get it.

Your example of not being able to do a derivitive is CRAP. Everywhere in America are libraries, and every library has a calculus book. These will not be checked out, trust me. Go get one. Also, there is a publisher called "Dover" which sells fairly decent books for like 10 bucks. So the 100 dollars for a student edition of mathematica (I know I know it was free for you because you stole it) is hardly worth the money compared to what is available free or cheap. Note: If you are doing 100 or 200 level mathematics then you aren't doing anything that is really hard enough to require mathematica to do it, (except for diffyQ where they sometimes give assignments which require Matlab or Mathematica for charts and stuff).

Re:For a high school freshman . . .

[lakeland]

I was learning calculus on my own
If you're learning calculus on your own, you're going to expect things to be different. For people who have the luxury of a class where they learn calculus, I think you'll find your argument doesn't hold. Certainly I recall that in second and third year calc, when asked to compute a derivative or an integral we would usually be given the answer. That way the lecturer could ask a more complex problem that tested more techniques and still expect the right percentage of students to get it correct. Naturally, the answer is not always given to ensure the technique of working backwards is not always available.

Re:For a high school freshman . . .

[sketerpot]

Word to that. When I was in school, we couldn't even use calculators. I could calculate the cube root of large numbers to several significant digits with paper and pencil.

It can be done by someone who can do arithmetic---and knows how. I don't know how, but I know Newton's method of root solving, so I can come up with a way quickly.

To find the cube root of c (which I'll call x), we need to solve x^3 - c = 0. We can do this by coming up with a guess t[0] and recursively saying that t[n+1] = t[n] - (x^3-c)/(3x^2).

I might have learned this in school, but I would have forgotten it. I'd say I was better served by understanding of concepts than overemphasis on calculation.

Maxima and Axiom

[metalogic]

Maxima and Axiom.

Paper?

[csubear]

How about a book, paper, and pen? Maybe a white board to write examples on?

Really, why do you need software to teach kids math, engineers where trained with out the aid of computer software for years.

This may spark your interest

[bmzf]

I've seen this but haven't yet used it. It seems pretty cool:

Genius Math Tool

Scilab

[Anonymous Coward]

Scilab http://scilabsoft.inria.fr/ is an open source clone of matlab available for both Linux and Windows. I use it almost daily. 99.9% of what you do in Matlab can be done in Scilab for free.

Math.com?

[DigitalRaptor]

I hate to state the obvious, but 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.

Best open source math software = ...

[cdsr]

Pencil + graph paper + ruler + eraser + brain

You want Maxima

[cabraverde]

Maxima:

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

[davidwr]

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.

For statisticians...

[Gentlewhisper]

There is R
R Project

Re:For statisticians...

[ClaytonianG]

R is actually better than a lot of non open source out there. I actually prefer it over S, SPSS, and mini-tab(I haven't used any other major stats software).
There is even a nifty web interface. Check out Rweb

Re:For statisticians...

[transib]

and for education purposes there is the Statistical Lab http://www.statistiklabor.de/ - a working and learning environment designed for elementary studies in statistics. statistical engine is R. freeware at the moment, open source later next year...

I don't get it...

[hexcentric1]

There are any number of ways to learn math; most of them involve exploring the relationships between numbers and the physical world. This means teaching someone how to think about things. Math software does not teach anyone how to think; it is a tool for accomplishing a goal. First the student learns arithmetic, then algebra, geometry, trig, calculus, and so on. Once the concepts are understood, the foundation is sound, and the student *knows* math, then, and only then, does math software become useful. It becomes a shortcut, a means to an end. It is a tool used to solve a problem. You have to know how to use the tool to get to the answer. You can train someone to input numbers into some piece of software and watch other numbers get spit out, but that person won't *understand* what they are doing. If the person already understands the math, and is looking for a tool to accomplish some problem solving, then the programs mentioned in this topic become useful. As far as using software to learn math, I don't think any piece of software, open source or otherwise, can currently take the place of a good math teacher. And by that I don't mean someone who drills you in math problems, but someone who can help you discover for yourself the power and elegance of mathematics.

a good question deserves a good answer.

[tloh]

I'd like to recommend the very exellent GNUWin project. 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 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.

Re:Second Octave and R

[civilizedINTENSITY]

NumAnalII was taught in MatLab, but Octave worked for me. Never had any problems. Loved the emacs modes! Write scripts in one emacs window, run an octave process in another emacs window...send the current line (or function, or selected text...etc) to the process for evaluation. Very sweet.

I've always loved this quote

[MerlynEmrys67]

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

Re:I've always loved this quote

[dougmc]

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.

Re:I've always loved this quote

[asuffield]

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 ?

That would be the part where they make it impossible for anybody else to develop the thing any further, so that it suits their needs when the original developer has no interest in them. There's a reason why proprietary software sucks.

Re:I've always loved this quote

[kevinrbing]

I've never heard marx defend propriety software... kudos!

Maxima

[Geoffreyerffoeg]

At National Mu Alpha Theta this summer (a math tournament), I had brought my OS X laptop which happened to have Maxima 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.

University of Arizona

[asscroft]

The UofA has some great titles, from rurfc1, the r u ready for calculus program, to slopes and other diffeq titles. All free, all good.

The rur series is GOLD! I've installed in on all computer I own and made CDs just because its the kind of thing some new math dept head could take off the website and you'll never see it again.

http://math.arizona.edu/~www_main_2002/software/ ua sft.html

Why Pencil and Paper may not be appropriate

[lilmouse]

I will grant: Pencil and Paper are great if you're working on learning math skills. Even then, however, there are times you're going to want something to do the arithmetic and/or graphing and/or solve the integral for you. If I've know how to add already, I don't want paper and pencil, I want an open source calculator so I don't have to. If I know how to do Integration by Parts already, I don't need to do it every time...of course, studying math won't mean you have to do Integration by Parts all the time (unless you're in DiffEQ or something), which brings me to my "But":

But: Paper and Pencil aren't gonna cut it as far as taking an engineering course is concerned. Nor as far as a physics course is concerned. If I'm trying to "learn the concepts" of a non-calculus class, then having to do all these pesky integrals isn't going to help any! It's just taking up my time. Even better, there are going to be cases where you can't do the work without some hefty numerical computations that would take you faaar too long to do by hand. Sure, you should do the first one on paper, but do you want to do every calculation of magnetic field by hand? Want to do this line integral for the 7th time? Not yet bored of 2 page solutions? Really want to follow Newton's method by hand?

Furthermore: The age when everything could be done on paper and pencil is now part of the "good old days(TM)", and such technology is no longer the only mainstay.

Finally: I was in a graduate program for mathematics, and yes, even doing "pure" mathematics, we used software. The programs that pop immediately to mind were Maple (cheaper than mathematica) and McCauley (it's algebra. I don't know much else). I also wrote a C program to handle card shuffling, so we could look at various results - sure, you could do it by hand, but it'd take a *lot* longer. In one course, I even wrote Public Key Encryptioni/Decryption software in Maple - an easy way to get a hands-on feel for the concepts, and you don't even have to handle arbitary-length modular multiplication by hand...

Don't get me wrong, Paper and Pencils are great, but so are math packages!

--LWM

Have you checked out the pricing on math products

[melted]

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.

Mathematica, of course

[Ed Pegg]

Full disclosure: I work for Wolfram Research. But oh -- the irony! I am also a columnist for Math Games at maa.org, and I wrote an article about the Quantian Distribution. 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 -- but check with the college first. They might be on a Mathematica Campus, and can get it for free.

Re:Maxima history

[xtermin8]

Macsyma was actually started at MIT, written in lisp, part of Project MAC. At least two different versions came out, Maxima was from the Department of Energy's version, which has been open sourced. Another version was owned by Symbolics, then was spun off into its own company. I beleive there's still another version and MIT still retains the rights to it. Feel free to correct me on any of this- but for sure the software has a long and tangled history.

dc

[kisielk]

uh.. comes in the same package as parent, but its RPN :)

Re:No Math Software

[shobadobs]

You haven't seen high school girls pull out their TI-83 PLUSes so they could discover that 40 + 8 equals 48. (This actually happened. In an honors math class.)

There is no reason students shouldn't have a basic scientific for say, things like calculating pe^(rt), but graphing calculators are unnecessary. They cause students to learn how to do a sequence of operations for finding the answer to a question which they'll get on next week's test, not how the problem actually gets solved. If the kids are being taught concepts and not arithmetic, wouldn't the problems and scenarios be designed to make the arithmetic trivial anyway?

Do it the old fashioned way - p&p

[GomezAdams]

For years the Russians and Indians have turned out some of the best theoretical mathematicians on the planet because they have always done math The Old Fashioned Way(tm). Pencil and paper were available for everyone, computer time was not. The Chinese and other asians are great at computational concepts because they learn to use arithmetic rules to work the abacus. The abacus only holds the result of each step the of the operations. Machines are only good when you know that the questions and answers are correctly mapped.

It's still GIGO unless you know what you're doing without the use of the machines.

Pari-gp, Lisp and interfaces

[Wolfbone]

No-one's mentioned the superb pari-gp 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 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.

From the front lines.

[kevinrbing]

I'm a high school senior and I would love to have software like this.

There are times in my high school calculus course where I would love to be able to see practical applications of the things I learn in class. Or get extra help on a difficult concept I didn't quite understand in class.

I've tried to use recouces like wikipedia, open course ware (though MIT is a bit out of my leauge), and Sparknotes; but, its hard to learn a concept without a good explanation and instruction.

In conclusion, software that could achually teach or at least tutor math would be a godsend to me and thousands of other confused math students.

P.S. Please don't complain to me about getting better math teachers - thats an issue you'd have to take up with the union. Also, bad students isn't always their fault.

Maxima is your best bet

[amundson]

I lead the Maxima project, http://maxima.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.

Haskell

[sleepingsquirrel]

Haskell is also a great language for performing math. It'd be hard to get a nicer notation for the factorial than something like this...

fac n = product [1..n]

Re:Haskell

[Wolfbone]

Yes - it looks conceptually attractive and it appears possible to have the all-important (to me anyway) interpreter mode. I always found doing any kind of programming but especially mathematical work a real drag until I discovered these kinds of language: CMUCL and SLIME radically improved every aspect of any kind of programming for me.

Quantian article

[Ed Pegg]

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

• R, including several add-on packages (such as tseries, RODBC, coda, mcmcpack, gtkdevice, rgtk, rquantlib, qtl, dbi, rmysql), out-of-the box support for the powerful ESS modes for XEmacs as well as the Ggobi visualisation program;
• A complete teTeX, TeX, and LaTeX setup for scientific publishing, along with TeXmacs and LyX for wysiwyg editing;
• Perl and Python with loads of add-ons, plus ruby, tcl, Lua, and Scientific and Numeric Python;
• The Emacs and Vim editors, as well as Gnumeric, kate, Koffice, jed, joe, nedit and zile;
• Octave, with add-on packages octave-forge, octave-sp, octave-epstk, and matwrap;
• Computer-algebra systems Maxima, Pari/GP, GAP, GiNaC and YaCaS;
• the QuantLib quantitative finance library including its Python interface;
• GSL, the Gnu Scientific Library (GSL) including example binaries;
• The GNU compiler suite comprising gcc, g77, g++ compilers;
• the OpenDX, Plotmtv, and Mayavi data visualisation systems;
• it includes apcalc,aribas,autoclass,

Re:mathematical tools

[fishbowl]

[whiteboard]

I cannot stand them. Chalkboards seem to have completely disappeared. And now all these stupid empty Expo markers are going to landfills. There was nothing, NOTHING wrong with chalk, except that it was cheaper, and that the Sanford corp wasn't getting money for it.

Whiteboards made sense in some environments, such as where it was absolutely crucial not to have chalk dust (but in those environments, you should not use alcohol pens either; they also make dust).

I hate whiteboards. I also hate the fact that I'm basically forced to have white backgrounds on my os windows, since there is invariably some app, and *many* websites, which hardcode the textcolor to black, but assume you have a light background. grr.

Blackboards are absorptive and whiteboards are reflective. Black windows on a computer screen are neutral, white windows radiate.

Pari/GP

[dfinney]

I often use Pari/GP:

http://pari.math.u-bordeaux.fr/

Pari is a command line calculator with graphing capabilities. It was developed by Henri Cohen, a number theorist. It has an incredible number of functions, plus it can calculate really big numbers.

From the FAQ:

PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers, etc., and a lot of transcendental functions.

Java Educational software

[darkone]

The company I work for creates open source educational software from federal grants. Most of our software is Physics or Chemistry based, but most of it is Java and written and tested on MacOSX, Linux, and Windows. Some of our software is written more for classroom use (with tests and all) but some is standalone. Here is a link to our download center.

Maxima, Octave, R, Sclilab and Gnuplot

[183771]

Maybe one of these could be interesting for you:

Maxima 5.9.0
Maxima is a fairly complete computer algebra system with an emphasis on symbolic computation.

Octave 2.1.42
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.

R 1.8.0
R is `GNU S' - A language and environment for statistical computing and graphics. R is similar to the award-winning S system, which was developed at Bell Laboratories by John Chambers et al. It provides a wide variety of statistical and graphical techniques (linear and nonlinear modelling, statistical tests, time series analysis, classification, clustering, ...).

Scilab 2.6
Scilab is a scientific software package for numerical computations in a user-friendly environment.

Gnuplot 3.7.x
gnuplot is a command-driven interactive function plotting program. It can be used to plot functions and data points in both two- and three-dimensional plots in many different formats, and will accommodate many of the needs of today's scientists for graphic data representation.

Source: http://gnuwin.epfl.ch/classes/en/sciences.html

For 3D fun

[Kludge]

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

I agree here. Many people are posting that these mathematical sorts of programs aren't for high schoolers. While it is true that such programs shouldn't be used as a crutch for passing math class, it is also important to teach students programming, in particular mathematical programming. For this R would be good.

Poor documentation

I'll have to disagree here. R is an implementation of the S language standards. There a number of good S language references out there. Also the help.search() facility is great and the R-help mailing list archives are google searchable.

Perl Data Language

[Kludge]

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.

Re:Look again

[Bingo Foo]

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?

Symbolic maths toolbox?

[buchanmilne]

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)?

There might not be such a great difference in functionality between Mathematic/Maple and Matlab, if you have the symbolic math toolbox (although the UI is totally different ...).

Of course, I don't think Octave has a symbolic math toolbox or equivalent at present ...

Re:Symbolic maths toolbox?

[gnalle]

The next question is whether or not a symbolic math package is useful at highscool/freshman level. Maple and Mathematica can look really flashy when you see them for the first time, but after half an hour you end up asking a question that can only be solved if you spend a lot of time looking through the manual, trying to understand all the list operations.(I don't know if Maxima is advanced enough to create this kind of problems) When using Matlab or Octave it is easier to guess what is possible and what is not. This way the students have a better chance of trying to do something on their own hand.So even if Octave cannot integrate it may still be the better education tool in a highscool computer lab. If I understand correctly the the poster just wishes to give his students a glimpse of what computers can do in mathematics. Therefore I would advice him to use Octave. By the way you can also find a great deal of very specialized java applet on the web. Perhaps they are more accessible to the students than Octave.

Symbolic math - Maxima

[gr8_phk]

"The guy's looking for a symbolic mathematics package."

Use Maxima. It does symbolic math very well. And if you're over in Linux, you can use Maxima as a plugin for TeXmacs for really pretty mathematical documents.

I always site Octave and Maxima when people ask about math software. One for numeric and one for symbolic.

Mod parent up - very informed comment, re: Axiom.

[mapnjd]

I wrote my PhD thesis using Axiom's source - Axiom has had c. 300 man-years work done on it. It is an unbelievable piece of work.

(It started in the early 1970's at IBM and was called Scratchpad, later Scratchpad 2 before being "sold" to NAG and rebranded).

Axiom 2 included a new compiler and a new language called Aldor (which was going to be called A# but apparently Sharp objected to the name. WTF about C# then?) and ran on other platforms than AIX 3.x. Solaris, Irix and in the end even Win32.

Unlike the "M'n'M" systems (Maple, Mathematica, etc). it is strongly typed and has its roots in Category theory and/or Universal Algebra - which is pretty much a necessity for and Algebra system to even make any sense. (OK, that's a loaded point - obviously Maple is a very good product without this basis).

Some things are currently missing from Axiom: Aldor - the re-implementation of Axiom's language by Pete Broadberry et al.; HyperTex - the online documentation browser with hyperlinks predating HTML! which are all loaded from the source files); and I believe the pretty GUI bits for graphs, 3D trefoil knots, etc.

Debian and Ubuntu users can just download it, the rest of us have to build it. (It takes about 2 hours on my 1133MHz box).

It is good. If you can grab a copy of Jenks and Sutor's manual then even better.