What is a good language to develop in for simple, yet customizable math programs?

Question

I'm writing to ask for some guidance on choosing a language and course of action in learning programming.

I've seen thread after thread with questions from newbies, asking, "What is the best language to start with?" and then it always starts a flame war or someone just answers, "There's no best language, it's best to pick one and start learning it." My question is a little bit more focused than that.

First off, I've been programming my whole life, in very limited capacities. My deepest training was in C++. Whilst in my EECS degree program, I resolved to never be a software developer because I couldn't stand not interacting with people for such long periods of time. Instead I realized I wanted to be a math teacher, and so that is the path I have taken.

But now that I'm well down that path, I've started to realize that perhaps I could develop my own software to help me in the classroom. If I want to demonstrate the Euclidean algorithm, what better way than to have a piece of software that breaks down the process? Students could run that software as part of their studies, and the advanced students might even develop programs for themselves. Or, with an Ipad in hand, why not have an app that lets students take their own attendance? It would certainly streamline some of the needs of classroom management.

There's obviously a lot of great stuff already out there for math, and for education, but I want a way to more directly create things specific to my lectures. If I'm teaching a specific way of calculating a percent, I want to create an app that aligns with my teaching style, not just another calculator app that requires the student to learn twice.

The most I use in class right now is iWork Numbers/Microsoft Excel for my stats class. Students can learn the basic statistical functions, and turn some of their data into graphs.

I have dabbled a bit with R, and used Maple in college. I've started the basic tutorials for OS X/iOS development and have actually made good progress making an OS X app that takes a text string, converts it to numbers, and performs encryption using modular addition and multiplication. I sometimes use Wolfram|Alpha to save myself some time in getting quick solutions to equations or base conversions. I know of MatLab, Mathematica, and recently people have been telling me to check into Python or Ruby. I also know basic HTML, and while it's forgotten now, learned Javascript and PERL in college.

If I keep on the path of Obj-C/Cocoa, I think it will have great benefits. Unfortunately, anything I produced for Mac would only be usable on a Mac, so it wouldn't be universal for all of my students. Perhaps then learning a web language would be better. Second, I'm wondering if the primary use is mathematical, then perhaps my time would be better spent learning Mathematica Programming Language, or R, or something based less on GUI and more on simple coding of algorithms, maybe Python or Ruby?

It seems that Mathematica already has a lot of demos for different math concepts, so why reinvent the wheel is also a question I have. I think overall, it would be good to have more control and design things the way I need. And then, if I do want to make an "Attendance" app or something else, I would already have the programming experience to more easily design something for my iPad or MacBook.

The related question to this is what is a good language to teach to my students? In his TED talk, Conrad Wolfram says one of the best ways to check the understanding of a student is have them write a program. But if Mathematica does the math virtually automatically for them, then I'm not sure that will get the deeper experience of working out logic for themselves, like you do when you're writing C, or a traditional procedural language.

I know that programming takes time to learn, but I also know that at this point, my goal is not to be able to make an app like "Tiny Wings." With the app store ease, some of my work may be an extra revenue stream, but I see myself as more of a hobbyist, and now teacher looking to software development specifically for its ability to help me demonstrate mathematical concepts.

I think I will push ahead with Obj-C/Cocoa for OSX/iOS, but if anyone has some better guidance regarding all of the other available stuff, it would be much appreciated. I don't think I would want to go fully to the web (I like apps), but perhaps someone could suggest a nice way of bridging what I produce in XCode to a universal web version. For example, if you come up with an algorithm in obj-c is it easiest to transition that to ruby and run it online, or is there another approach that works better?

Answer 1

As others have advised you, I also recommend python. It's a nice development from C++ and will open your eyes to more programming concepts - the results you can achieve (per line of code) is remarkable!

For maths features and scientific computing, the well-known numpy package cannot be looked past.

Answer 2

If you can afford it: Matlab.

If you want free stuff: Octave (a decent Matlab clone). Some people also love R, AFAIR it has a statistics bent.

I wouldn't necessarily jump into Python as first choice. It's a general-purpose language, not specialized for maths applications.

If you really care about performance: Fortran.

Answer 3

Pick something that has nice plotting and visualization capabilities. Mathematica and some of the open source alternatives like Octave, SciPy, Sage, SymPy, etc. Most of this stuff can be found at http://en.wikipedia.org/wiki/Category:Free_mathematics_software.

Answer 4

If I were in your position as a teacher I would investigate SAGE. It is an open source Python based piece of mathematical software that is written for Linux, runs natively on OS X and through a pre packaged virtual machine on Windows; it is also available online so any of your students can try it out easily.

The project is lead by William Stein who is currently the world's the leading mathematical computer scientist (or however you want to classify him), so it is a serious project. What is nice about it is that it brings together all of the various mathematical packages and software available and allows you to access it in one place; for example, if you have Maple installed, then you can use Maple functions inside it, but via Python syntax. There are lots of tutorials, there is an active development community who would probably be willing to provide some help and support, it uses Python so the language it uses is actually useful and well designed and it's free. Enough said.

One word of warning: on pain of death Do Not Use Mathematica. It is the worst programming language in the world. (Why? No concept of scope anywhere - yep that for loop with an i variable is the same i variable in every other for loop everywhere: No ability to debug - the standard error message is "error", useful! There are more reasons, but those should be enough)

Answer 5

Consider Maxima. http://en.wikipedia.org/wiki/Maxima_(software)

Descendent of Macsyma, if you ever heard of that.

Runs on Windows. Open-source.

LISP-like programming language, if I recall correctly (bonus, imo).

Answer 6

It depends quite a bit on the level of math you are teaching. Is it highschool algebra, or college level problem solving? I have two sons taking CS at university, and use a combination of C plus OpenGL to give them enrichment courses. But here the goal is understanding of computation/algorthims, so writing say a sort from scratch is preferred over finding someone elses implementation, because learning how to think alogorthmically, and to program, and to use graphics to debug your coding etc, is the point of the excercise. I do like JohnLs suggestion of using maxima, as it is nice to compliment numerical solution methods, with computer algebra. I do feel that easy coupling to graphics is important, so that partial results can be visualized. A lot of insight/intuition can be developed if good pictures can be made relatively painlessly.

Answer 7

I would recommend PHP. The syntax is as simple as python, and you're completely free in how big or small of a program you want to make, whether you use OOP or functional programming, etc. The documentation is very good, and there's a vaaaaast community available for when you run into problems.

An added bonus is that PHP uses the same syntax as C, C++, Javascript, and Java (in most ways). Learning PHP made it very easy for me to later learn Java and Javascript, and vice versa someone familiar with C++ would find PHP's syntax easier to grasp.

Installing PHP is a piece of chicken these days via WAMP if you're on windows. You simply run the setup and its installed, and later you can customize the configuration files just as easily, where needed.