Hot answers tagged reference-request
25
Short version
I think mathematica is a good first programming language, and Stephen Wolfram has dropped some hints in a few places that it should get even better at being a beginner programming language soon:
It'll probably be related to my goal in the next year or two of making Mathematica definitively the world's easiest to learn language...
More ...
15
I own a copy of Modelling Financial Derivatives with Mathematica by William Shaw. I think it was a ground-breaking book for its time. However, here are some issues you should be aware of:
It was published in 1998 and is based on Mathematica version 3. We are now at 8, anticipating 9. Much of the graphics code he uses is now obsolete (eg Graphics`Graphics).
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15
Mathematica is the best tutorial. It is a discovery tool - just start from something that he knows a bit already and you both take one little step at a time. Just try things.
1st Thing - Try this Link => Hands-on Start to Mathematica
I personally would recommend engaging with him in a project of making an application and submitting it to the Wolfram ...
14
The course material I used to learn Mathematica myself is directed at beginners. You should have no problem following it even if you have next to zero prior programming experience. It is a bit outdated (it was written for an old version of Mathematica), but I think that it is still a very useful learning resource today. Most importantly, it includes ...
13
Update: I described an alternative approach based on built in plotting functions in this answer. That approach is not very practical here though because I need to be able to handle points at arbitrary positions while built in functions work with a rectangle-based mesh. I am still looking for improvements.
I came up with this very naive approach and ...
10
Affirming Vitaliy's suggestions I'll say something beyond his comprehensive answer and to a certain extent more specific.
A great mathematician S.Banach used to say (maybe as a joke) that children shouldn't be taught mathematics early because that would be a too sharp tool for them. There is an obvious analogy and this is why children shoudn't be taught ...
9
I'm a bit late to this party, but I can assure you that it is possible to learn Mathematica as your first and only programming language. I know because I did it. It is also most certainly possible to use Mathematica as your calculation “Swiss Army knife” if you are an economist. I know because I am an economist, too, and I have been successfully using it as ...
9
Vitaliy's suggestion is indeed very good.
What I want to add is that the Documentation is a good place to start. Say he's interested in drawing some graphs to illustrate something, then the Guide page for Graphs is a great place to start and the reference pages have tons of examples to build from.
Once one has solved a problem or two with Mathematica ...
8
I just wrote a book on financial engineering that uses Mathematica heavily. The publisher (World Scientific) says it should be available for purchase within a week or two. I have taught risk management and asset pricing and derivatives with these materials for the past few years at NYU-Poly. The point of the book is precisely to do lots of projects, the ...
8
The methods NDSolve uses are documented in detail here:
Advanced Numerical Differential Equation Solving in Mathematica
This section says that PDEs are solved using the "method of lines", and explains which kinds of problems this method can deal with. There's also a detailed example of how the method works.
The numerical method of lines is a ...
7
In a comment you asked about learning algorithm development and functional programming basics. Take a look at the courses at http://www.wolfram.com/training/ . Wolfram offers many of them as free videos that you can watch any time.
Check out the "General Mathematica" section for some introductory courses. There is also a free Functional Programming: Quick ...
7
One unconventional but possibly very useful approach it to introduce him to Project Euler. While many of the newer questions are completely beyond me (mind you that is not saying much), many of the earlier ones are quite approachable. If your friend has the desire to learn and an interest in puzzles/challenges, this site will grow as he grows.
Most of the ...
6
Here are some links I collected in my answer to the post Where can I find examples of good Mathematica programming practice?. The first link exposes quite well the new functionalities of Mathematica in this field.
Finance (some CUDA examples also)
http://www.wolfram.com/events/chicago2011/nVidiaFinancePresentation.nb
High-Performance Computing in ...
5
I started learning Mathematica a couple of months ago, and all these suggestions are good. I'd also say that, although it's possible to surround yourself with books and tutorials, it's even more important to have some focus or goal to give shape to your learning efforts. You can find yourself bouncing from one interesting corner to the next (particularly ...
5
I've had an interest (as one can see in my other posts) in a wide range of distributed processing and parallel computing approaches and while not seen in any of my posts machine learning approaches as well. I looked at neural networks some years ago, and while they didn't suit the problems I worked on at the time I remembered the article Duncan and Tweney ...
5
You can check here for Function Approximations Package References
References
Hairer, E. and G. Wanner. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer, 1991.
Iserles, A. and S. P. Nørsett. Order Stars. Chapman and Hall, 1991.
Lambert, J. D. Numerical Methods for Ordinary Differential Systems:
The Initial ...
5
Mathematica's documentation is also available online in the pdf format, as a tutorial collection. The place to look for it is here. Also, some books on Mathematica are now available as kindle editions, from Amazon. Finally, for those books which have Mathematica notebook versions, you can probably make a pdf from those notebooks for a personal use, if that ...
4
The GraphUtilities documentation has a whole section that should answer your question: “Algorithms for Finding Community Structure”. The reference for the algorithm it uses is: A. Clauset, "Finding Local Community Structure in Networks," Physical Review E, 72, 026132, 2005 (arXiv mirror).
4
Although exporting x3d format maintains the light sources and exports the mesh, it isn't perfect when used with Blender (the only 3D editor I tried). However, since it's the best solution I have, I wrote some brief instructions for that procedure. It's important to note that I used Blender version 2.60 and Mathematica 9.
Since the instructions are almost ...
4
Introduction to Probability Models by Ross gives good description of stochastic processes.
Applied Intertemporal Optimization by Walde also has easy to follow structure on stochastic models in both discrete and continuous time and it is free to download pdf.
3
The references mentioned in the other answer do not really pertain too much to the problem of minimax approximation; they are more concerned with the other functions in FunctionApproximations` that deal with numerical differential equation solving; that is, the content that was once in the old NumericalMath`packages Butcher` and OrderStar`.
Indeed, a look ...
3
This page could be quite interesting in your case
http://education.wolfram.com/algebra/
The animations here explain some common Mathematica functions in a quite funny way.
http://documents.wolfram.com/flash/
There's a huge list of other resources here where you could pick what you think suits you.
Where can I find examples of good Mathematica ...
3
To show that your expression is real you could use ComplexExpand. By default, ComplexExpand will expand a complex expression into its real and imaginary part under the assumption that all undefined symbols occurring in the expression are real. The only problem here is that as far as I know there is no way to provide extra assumptions to ComplexExpand, ...
2
Building on @Verbeia's observation that the denominator is real:
almostThere = ComplexExpand[1/2 (Numerator[finalnew] - Conjugate[Numerator[finalnew]]),
TargetFunctions -> {Re, Im}];
Then if you can make the assumptions ArcTan[x_, 0] == 0, ω > 0, d > 0 :
Simplify[almostThere /. (ArcTan[x_, 0] -> 0), Assumptions -> {ω > 0, d > ...
1
Here you can find some software to convert Mathematica graphics for input into POVray (untested and rather old, though)
http://www.mathconsult.ch/showroom/pubs/MathProg/htmls/2-11.htm
Edit
Maeder's book and files aren't available for online downloading (you've to purchase the book)
Edit Or perhaps you can find them at the link provided in the comments
1
It depends on how deep you want to go into the details of financial engineering (Multi Factor Models, Complicated Deal Types, ...) - if you intend to work with these things check out the Mathematica based solutions here
http://www.unrisk.com/index.php/products
Also some white papers on the underlying mathematical methods are available there
1
I don't know why you would expect Mathematica to understand that this is a real expression when you have I, (-1)^(1/4) and (-1)^(3/4) at various places in the expression.
(-1)^(1/4) // N
(* Out[1]= 0.707107 + 0.707107 I *)
(-1)^(3/4) // N
(* Out[2]= -0.707107 + 0.707107 I *)
In this particular instance, the denominator is pretty obviously real.
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