I hope you don't mind if I ask for a bit of advice regarding modelling robotic systems. I've recently become rather interested in using inverse kinematics (IK) to control a 5 dof robotic manipulator. I have a solid foundation in IK but what I'm having trouble with is a way to visualize how the manipulator moves with respect to joint angles.
I've looked into using 3D toolkits (such as Blender, Panda3D, vPython) to create a 3d model of the arm, but I'm not sure if I should be looking something with physics support. I'm also not sure how well I can model motion with these packages. Anyone have any suggestions? What I'm NOT looking for is a full blown robotic simulator like Microsoft's Robotic Studio, I'd like to start with the basics and learn how everything works first, ie code the IK in Python, then visualize the motion in 3D. I'm very familiar with Python, so something that interfaces with Python would be preferable.
Thanks!
Well the great thing about Blender is that its API is actually in python!
In addition, it supports inverse kinematics (IK) quite well in addition to many other modeling tools.
Blender Cookie is a great resource.
Here is a tutorial on making IK rigs in Blender.
Blenders python api is documented quite extensively, and it even has an interactive python shell built right in so that you can see the effects of your script as you go along.
The physics engine that blender uses is the popular bullet physics engine, which has been used in many commercial games as well as a few feature films (2012 among them).
This isn't really a hard problem, is it? Presumably you're working out the math on your own; so if your robotic arm is visualized as, say, a few rectangular solids then all you need is something that will render these at the x,y,z coordinates and with the orientation vector you supply, updating when need be. OpenGL should do just fine for this, you could probably do it in <50 lines.
Python-Ogre is a wrapper around the very mature C++ engine OGRE 3D. I have used it for a pretty significant project and I would give the Python wrapper a mixed but mostly positive review. It's very capable and does a good job of wrapping all C++ functionality in a mostly Pythonic interface. You can get the physics support through one of the many OGRE extension modules which provide those capabilities.
The biggest negative is that the documentation for the Python interface is poor, and you will have to rely on the C++ library's documentation to make sense of some things. To give you a sense of what's possible, I was able to implement a scripting language around OGRE using Python and PyV8 (the language was Javascript), as I prototyped a C++ project.
The resulting prototype was very mature and robust, and I was able to wrap the internals of OGRE with high-level Javascript. With the scripting language I was able to script animation, materials, rendering and physics.
I took a scientific programming course this semester that I really enjoyed and experimented with a lot. We used python, and all the related modules. I am taking a physics lab next semester and I just wanted to hear from some of you how python can help me in ways that excel can't or in ways that are better than excel's capabilities. I use Mathematica for symbolic stuff so I would use python for data purposes.
Off the top of my head, here are the related things I can do:
All of the things you would expect in a intro course (loops, arrays, slicing arrays, etc).
Reading data from a text file.
Plotting scatter, line, and bar graphs.
Learning how to plot linear regression but haven't totally figured it out.
I have done 7 of the problems on Project Euler (nothing to brag about, but it might give you a better idea of where I stand in skills).
Looking forward to hearing from some of you. You don't have to explain how to use the things you mention, I could look up the documentation.
The paper Python all a scientist needs comes to mind. I hope you can make the needed transformations from Biology to Physics.
Scipy will also be useful to you, as it includes many more advanced analysis tools. For example, Scipy includes a linear regression, and gets more interesting from there. Along with the other tools you mentioned, you'll probably find most of your needs covered.
Other notes on tool selection:
Mathematica is a great tool, if you can afford it. I've played around with the other options, like Sympy, and sadly, they don't come close to being as useful as Mathematica.
I can't imagine using Excel for any serious scientific work. If you're planning to continue forward using the tools that you learn in class, you might as well start with tools that offer you that potential.
Don't reject Excel outright. It's still great for doing simple data analysis and plotting. Excel also has the considerable advantage of being installed on most engineer and scientist's computers, making it a lot easier to share your work with colleagues.
That said, I do use Python when Excel just won't cut it; times when I've had to:
color the points in a scatter plot based on a third column
plot a field of vectors
extract a few values from each of several thousand data files to do statistical process control
generate dozens of scatter plots over different dimensions of a large data set to find which variables are important
solve a nonlinear equation at several intermediate points of a calculation, not just as the final result.
accept variable length input from a user to define a problem
VBA in Excel can do a lot of those things too, but it becomes painful fast in such a primitive language. I dream that Microsoft will make IronPython a first-class scripting language in the next version of Excel. Until then, you might want to try Resolver One
I can recall 2 presentations by Jan Martinek on EuroScipy 2008, he's PhD candidate and presented some fun experiments with Physics in the background. Abstracts are here and I'm sure he would't mind to share more if you contact him directly. Also, take a look at other presentation from EuroScipy, there are some more Physics-related ones.
It would not be my intention to put a link on my blog, but I don't have any other method to clarify what I really mean. The article is quite long, and it's in three parts (1,2,3), but if you are curious, it's worth the reading.
A long time ago (5 years, at least) I programmed a python program which generated "mathematical bacteria". These bacteria are python objects with a simple opcode-based genetic code. You can feed them with a number and they return a number, according to the execution of their code. I generate their genetic codes at random, and apply an environmental selection to those objects producing a result similar to a predefined expected value. Then I let them duplicate, introduce mutations, and evolve them. The result is quite interesting, as their genetic code basically learns how to solve simple equations, even for values different for the training dataset.
Now, this thing is just a toy. I had time to waste and I wanted to satisfy my curiosity.
however, I assume that something, in terms of research, has been made... I am reinventing the wheel here, I hope. Are you aware of more serious attempts at creating in-silico bacteria like the one I programmed?
Please note that this is not really "genetic algorithms". Genetic algorithms is when you use evolution/selection to improve a vector of parameters against a given scoring function. This is kind of different. I optimize the code, not the parameters, against a given scoring function.
If you are optimising the code, perhaps you are engaged in genetic programming?
The free utility Eureqa is similar in the sense that in can create fitting symbolic functions (much more complicated than simple linear regression, etc.) based on multivariate input data. But, it uses GA to come up with the functions, so I'm not sure if that's exactly what you had in mind.
See also the "Download Your Own Robot Scientist" article on Wired for a breakdown of the general idea of how it works.
Nice article,
I would say you're talking about "gene expression programming" rather than "genetic programming", btw.
Are you familiar with Core Wars? I remember there were a number of code evolvers written for the game which had some success. For example, MicroGP++ is an assembly code generator that can be applied to the Core Wars assembly language (as well as to real problems!).
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I've been recently asked to learn some MATLAB basics for a class.
What does make it so cool for researchers and people that works in university?
I saw it's cool to work with matrices and plotting things... (things that can be done easily in Python using some libraries).
Writing a function or parsing a file is just painful. I'm still at the start, what am I missing?
In the "real" world, what should I think to use it for? When should it can do better than Python? For better I mean: easy way to write something performing.
UPDATE 1: One of the things I'd like to know the most is "Am I missing something?" :D
UPDATE 2: Thank you for your answers. My question is not about buy or not to buy MATLAB. The university has the possibility to give me a copy of an old version of MATLAB (MATLAB 5 I guess) for free, without breaking the license. I'm interested in its capabilities and if it deserves a deeper study (I won't need anything more than basic MATLAB in oder to pass the exam :P ) it will really be better than Python for a specific kind of task in the real world.
Adam is only partially right. Many, if not most, mathematicians will never touch it. If there is a computer tool used at all, it's going to be something like Mathematica or Maple. Engineering departments, on the other hand, often rely on it and there are definitely useful things for some applied mathematicians. It's also used heavily in industry in some areas.
Something you have to realize about MATLAB is that it started off as a wrapper on Fortran libraries for linear algebra. For a long time, it had an attitude that "all the world is an array of doubles (floats)". As a language, it has grown very organically, and there are some flaws that are very much baked in, if you look at it just as a programming language.
However, if you look at it as an environment for doing certain types of research in, it has some real strengths. It's about as good as it gets for doing floating point linear algebra. The notation is simple and powerful, the implementation fast and trusted. It is very good at generating plots and other interactive tasks. There are a large number of `toolboxes' with good code for particular tasks, that are affordable. There is a large community of users that share numerical codes (Python + NumPy has nothing in the same league, at least yet)
Python, warts and all, is a much better programming language (as are many others). However, it's a decade or so behind in terms of the tools.
The key point is that the majority of people who use MATLAB are not programmers really, and don't want to be.
It's a lousy choice for a general programming language; it's quirky, slow for many tasks (you need to vectorize things to get efficient codes), and not easy to integrate with the outside world. On the other hand, for the things it is good at, it is very very good. Very few things compare. There's a company with reasonable support and who knows how many man-years put into it. This can matter in industry.
Strictly looking at your Python vs. MATLAB comparison, they are mostly different tools for different jobs. In the areas where they do overlap a bit, it's hard to say what the better route to go is (depends a lot on what you're trying to do). But mostly Python isn't all that good at MATLAB's core strengths, and vice versa.
Most of answers do not get the point.
There is ONE reason matlab is so good and so widely used:
EXTREMELY FAST CODING
I am a computer vision phD student and have been using matlab for 4 years, before my phD I was using different languages including C++, java, php, python... Most of the computer vision researchers are using exclusively matlab.
1) Researchers need fast prototyping
In research environment, we have (hopefully) often new ideas, and we want to test them really quick to see if it's worth keeping on in that direction. And most often only a tiny sub-part of what we code will be useful.
Matlab is often slower at execution time, but we don't care much. Because we don't know in advance what method is going to be successful, we have to try many things, so our bottle neck is programming time, because our code will most often run a few times to get the results to publish, and that's all.
So let's see how matlab can help.
2) Everything I need is already there
Matlab has really a lot of functions that I need, so that I don't have to reinvent them all the time:
change the index of a matrix to 2d coordinate: ind2sub extract all patches of an image: im2col; compute a histogram of an image: hist(Im(:)); find the unique elements in a list unique(list); add a vector to all vectors of a matrix bsxfun(#plus,M,V); convolution on n-dimensional arrays convn(A); calculate the computation time of a sub part of the code: tic; %%code; toc; graphical interface to crop an image: imcrop(im);
The list could be very long...
And they are very easy to find by using the help.
The closest to that is python...But It's just a pain in python, I have to go to google each time to look for the name of the function I need, and then I need to add packages, and the packages are not compatible one with another, the format of the matrix change, the convolution function only handle doubles but does not make an error when I give it char, just give a wrong output... no
3) IDE
An example: I launch a script. It produces an error because of a matrix. I can still execute code with the command line. I visualize it doing: imagesc(matrix). I see that the last line of the matrix is weird. I fix the bug. All variables are still set. I select the remaining of the code, press F9 to execute the selection, and everything goes on. Debuging becomes fast, thanks to that.
Matlab underlines some of my errors before execution. So I can quickly see the problems. It proposes some way to make my code faster.
There is an awesome profiler included in the IDE. KCahcegrind is such a pain to use compared to that.
python's IDEs are awefull. python without ipython is not usable. I never manage to debug, using ipython.
+autocompletion, help for function arguments,...
4) Concise code
To normalize all the columns of a matrix ( which I need all the time), I do:
bsxfun(#times,A,1./sqrt(sum(A.^2)))
To remove from a matrix all colums with small sum:
A(:,sum(A)<e)=[]
To do the computation on the GPU:
gpuX = gpuarray(X);
%%% code normally and everything is done on GPU
To paralize my code:
parfor n=1:100
%%% code normally and everything is multi-threaded
What language can beat that?
And of course, I rarely need to make loops, everything is included in functions, which make the code way easier to read, and no headache with indices. So I can focus, on what I want to program, not how to program it.
5) Plotting tools
Matlab is famous for its plotting tools. They are very helpful.
Python's plotting tools have much less features. But there is one thing super annoying. You can plot figures only once per script??? if I have along script I cannot display stuffs at each step ---> useless.
6) Documentation
Everything is very quick to access, everything is crystal clear, function names are well chosen.
With python, I always need to google stuff, look in forums or stackoverflow.... complete time hog.
PS: Finally, what I hate with matlab: its price
I've been using matlab for many years in my research. It's great for linear algebra and has a large set of well-written toolboxes. The most recent versions are starting to push it into being closer to a general-purpose language (better optimizers, a much better object model, richer scoping rules, etc.).
This past summer, I had a job where I used Python + numpy instead of Matlab. I enjoyed the change of pace. It's a "real" language (and all that entails), and it has some great numeric features like broadcasting arrays. I also really like the ipython environment.
Here are some things that I prefer about Matlab:
consistency: MathWorks has spent a lot of effort making the toolboxes look and work like each other. They haven't done a perfect job, but it's one of the best I've seen for a codebase that's decades old.
documentation: I find it very frustrating to figure out some things in numpy and/or python because the documentation quality is spotty: some things are documented very well, some not at all. It's often most frustrating when I see things that appear to mimic Matlab, but don't quite work the same. Being able to grab the source is invaluable (to be fair, most of the Matlab toolboxes ship with source too)
compactness: for what I do, Matlab's syntax is often more compact (but not always)
momentum: I have too much Matlab code to change now
If I didn't have such a large existing codebase, I'd seriously consider switching to Python + numpy.
Hold everything. When's the last time you programed your calculator to play tetris? Did you actually think you could write anything you want in those 128k of RAM? Likely not. MATLAB is not for programming unless you're dealing with huge matrices. It's the graphing calculator you whip out when you've got Megabytes to Gigabytes of data to crunch and/or plot. Learn just basic stuff, but also don't kill yourself trying to make Python be a graphing calculator.
You'll quickly get a feel for when you want to crunch, plot or explore in MATLAB and when you want to have all that Python offers. Lots of engineers turn to pre and post processing in Python or Perl. Occasionally even just calling out to MATLAB for the hard bits.
They are such completely different tools that you should learn their basic strengths first without trying to replace one with the other. Granted for saving money I'd either use Octave or skimp on ease and learn to work with sparse matrices in Perl or Python.
MATLAB is great for doing array manipulation, doing specialized math functions, and for creating nice plots quick.
I'd probably only use it for large programs if I could use a lot of array/matrix manipulation.
You don't have to worry about the IDE as much as in more formal packages, so it's easier for students without a lot of programming experience to pick up.
MATLAB is a popular and widely adapted piece of a
sophisticated software package. It'd be a mistake to think
it's merely a math software since it has a wide range of
"toolboxes". I recently used Matplotlib to plot some data
from a database and it did the job without needing all the
bells and whistles of MATLAB. However, it may not be proper
to compare Python and MATLAB in every situation. As with
everything else the decision depends on what you need to do.
I used MATLAB in undergrad for control systems design and
simulation and also for image processing in grad school. For
these fields MATLAB makes the most sense because of the
powerful control and image processing toolboxes. As everyone
mentioned, array operations, which are used in every MATLAB
script you'd need to write, are very easy with MATLAB.
Another nice thing about MATLAB is that it's very easy and
fast to do prototyping and trying out ideas using the built
in toolbox functions. For instance, it takes no effort to
import an image and compute it's histogram or do some simple
processing on it. One disadvantage of MATLAB could be it's
speed because of its interpreted nature. However, if one
really needs speed than he can choose to implement the
tested logic in C/C++, etc.
For further comparison with Python, I can say that MATLAB
provides a full package for you to do your work without the
need of looking around for external libraries and
implementing extra functions.
One last point about MATLAB which I see is not mentioned in
the answers here is that it has a very powerful visual
modeling/simulation environment called Simulink. It's
easier to design and simulate larger systems with Simulink.
Finally, again, it all depends on the problem you need to
solve. If your problem domain can make use of one of
MATLAB's toolboxes and you have access to MATLAB then you
can be sure that you'll have the right tool to solve it.
MATLAB, as mentioned by others, is great at matrix manipulation, and was originally built as an extension of the well-known BLAS and LAPACK libraries used for linear algebra. It interfaces well with other languages like Java, and is well favored by engineering and scientific companies for its well developed and documented libraries. From what I know of Python and NumPy, while they share many of the fundamental capabilities of MATLAB, they don't have the full breadth and depth of capabilities with their libraries.
Personally, I use MATLAB because that's what I learned in my internship, that's what I used in grad school, and that's what I used in my first job. I don't have anything against Python (or any other language). It's just what I'm used too.
Also, there is another free version in addition to scilab mentioned by #Jim C from gnu called Octave.
Personally, I tend to think of Matlab as an interactive matrix calculator and plotting tool with a few scripting capabilities, rather than as a full-fledged programming language like Python or C. The reason for its success is that matrix stuff and plotting work out of the box, and you can do a few very specific things in it with virtually no actual programming knowledge. The language is, as you point out, extremely frustrating to use for more general-purpose tasks, such as even the simplest string processing. Its syntax is quirky, and it wasn't created with the abstractions necessary for projects of more than 100 lines or so in mind.
I think the reason why people try to use Matlab as a serious programming language is that most engineers (there are exceptions; my degree is in biomedical engineering and I like programming) are horrible programmers and hate to program. They're taught Matlab in college mostly for the matrix math, and they learn some rudimentary programming as part of learning Matlab, and just assume that Matlab is good enough. I can't think of anyone I know who knows any language besides Matlab, but still uses Matlab for anything other than a few pure number crunching applications.
The most likely reason that it's used so much in universities is that the mathematics faculty are used to it, understand it, and know how to incorporate it into their curriculum.
Between matplotlib+pylab and NumPy I don't think there's much actual difference between Matlab and python other than cultural inertia as suggested by #Adam Bellaire.
I believe you have a very good point and it's one that has been raised in the company where I work. The company is limited in it's ability to apply matlab because of the licensing costs involved. One developer proved that Python was a very suitable replacement but it fell on ignorant ears because to the owners of those ears...
No-one in the company knew Python although many of us wanted to use it.
MatLab has a name, a company, and task force behind it to solve any problems.
There were some (but not a lot) of legacy MatLab projects that would need to be re-written.
If it's worth £10,000 (??) it's gotta be worth it!!
I'm with you here. Python is a very good replacement for MatLab.
I should point out that I've been told the company uses maybe 5% to 10% of MatLabs capabilities and that is the basis for my agreement with the original poster
MATLAB is a fantastic tool for
prototyping
engineering simulation and
fast visualization of data
You can really play with, visualize and test your ideas on a data set very effectively. It should not be regarded as an alternative to other software languages used for product development. I highly recommend it for the above tasks, though it is expensive - free alternatives like Octave and Python are catching up.
Seems to be pure inertia. Where it is in use, everyone is too busy to learn IDL or numpy in sufficient detail to switch, and don't want to rewrite good working programs. Luckily that's not strictly true, but true enough in enough places that Matlab will be around a long time. Like Fortran (in active use where i work!)
The main reason it is useful in industry is the plug-ins built on top of the core functionality. Almost all active Matlab development for the last few years has focused on these.
Unfortunately, you won't have much opportunity to use these in an academic environment.
I know this question is old, and therefore may no longer be
watched, but I felt it was necessary to comment. As an
aerospace engineer at Georgia Tech, I can say, with no
qualms, that MATLAB is awesome. You can have it quickly
interface with your Excel spreadsheets to pull in data about
how high and fast rockets are flying, how the wind affects
those same rockets, and how different engines matter. Beyond
rocketry, similar concepts come into play for cars, trucks,
aircraft, spacecraft, and even athletics. You can pull in
large amounts of data, manipulate all of it, and make sure
your results are as they should be. In the event something is
off, you can add a line break where an error occurs to debug
your program without having to recompile every time you want
to run your program. Is it slower than some other programs?
Well, technically. I'm sure if you want to do the number
crunching it's great for on an NVIDIA graphics processor, it
would probably be faster, but it requires a lot more effort
with harder debugging.
As a general programming language, MATLAB is weak. It's not
meant to work against Python, Java, ActionScript, C/C++ or
any other general purpose language. It's meant for the
engineering and mathematics niche the name implies, and it
does so fantastically.
MATLAB WAS a wrapper around commonly available libraries.
And in many cases it still is. When you get to larger
datasets, it has many additional optimizations, including
examining and special casing common problems (reducing to
sparse matrices where useful, for example), and handling
edge cases. Often, you can submit a problem in a standard
form to a general function, and it will determine the best
underlying algorithm to use based on your data. For small
N, all algorithms are fast, but MATLAB makes determining the
optimal algorithm a non-issue.
This is written by someone who hates MATLAB, and has tried
to replace it due to integration issues. From your
question, you mention getting MATLAB 5 and using it for a
course. At that level, you might want to look at
Octave, an open source implementation with the same
syntax. I'm guessing it is up to MATLAB 5 levels by now (I
only play around with it). That should allow you to "pass
your exam". For bare MATLAB functionality it seems to be
close. It is lacking in the toolbox support (which, again,
mostly serves to reformulate the function calls to forms
familiar to engineers in the field and selects the right
underlying algorithm to use).
One reason MATLAB is popular with universities is the same reason a lot of things are popular with universities: there's a lot of professors familiar with it, and it's fairly robust.
I've spoken to a lot of folks who are especially interested in MATLAB's nascent ability to tap into the GPU instead of working serially. Having used Python in grad school, I kind of wish I had the licks to work with MATLAB in that case. It sure would make vector space calculations a breeze.
It's been some time since I've used Matlab, but from memory it does provide (albeit with extra plugins) the ability to generate source to allow you to realise your algorithm on a DSP.
Since python is a general purpose programming language there is no reason why you couldn't do everything in python that you can do in matlab. However, matlab does provide a number of other tools - eg. a very broad array of dsp features, a broad array of S and Z domain features.
All of these could be hand coded in python (since it's a general purpose language), but if all you're after is the results perhaps spending the money on Matlab is the cheaper option?
These features have also been tuned for performance. eg. The documentation for Numpy specifies that their Fourier transform is optimised for power of 2 point data sets. As I understand Matlab has been written to use the most efficient Fourier transform to suit the size of the data set, not just power of 2.
edit: Oh, and in Matlab you can produce some sensational looking plots very easily, which is important when you're presenting your data. Again, certainly not impossible using other tools.
I think you answered your own question when you noted that Matlab is "cool to work with matrixes and plotting things". Any application that requires a lot of matrix maths and visualisation will probably be easiest to do in Matlab.
That said, Matlab's syntax feels awkward and shows the language's age. In contrast, Python is a much nicer general purpose programming language and, with the right libraries can do much of what Matlab does. However, Matlab is always going to have a more concise syntax than Python for vector and matrix manipulation.
If much of your programming involves these sorts of manipulations, such as in signal processing and some statistical techniques, then Matlab will be a better choice.
First Mover Advantage. Matlab has been around since the late 1970s. Python came along more recently, and the libraries that make it suitable for Matlab type tasks came along even more recently. People are used to Matlab, so they use it.
Matlab is good at doing number crunching. Also Matrix and matrix manipulation. It has many helpful built in libraries(depends on the what version) I think it is easier to use than python if you are going to be calculating equations.
I need to deliver one and half hour seminar on programming for students at the department of mathematics.
I have chosen python as language.
What should be content of my presentation ?
What are good resources available ?
What is necessity of programming for maths students?
How will knowledge of programming will help them?
Thank you !!!
NOTE: I know here is one post but it doesn't solve my problem.
Do the getting started guide to scipy?
http://www.scipy.org/Getting_Started
Sage: http://www.sagemath.org/
Assuming that these students are new to programming (which is quite likely for math students), you'll want to give them a basic introduction to programming (what a function is, what a variable is, how each of these differ from functions and variables in math, etc).
Show them some example programs, with a view to things that will be helpful for math: numerical methods, matrix multiplication, etc.
Wherever possible, wow them so that they'll get excited about using computers for their own projects.
Some Python/Math resources
I would bring up using Python as a free & open source option to replace/augment expensive packages like Matlab, IDL, etc via:
scipy - fft's,
ipython - "shell"/debugger
matplotlib - 2d graphing
MayaVi - 3d graphing/visualization
This video may be helpful.
You are going to have to decide what you want to show them. If you want to show them how to using a computer can be a useful tool in mathematics show them sage and how you can perform numerical methods with it to get answers to hard questions. Then manipulate some algebraic formulas with it. Maybe show how it can whip through hard integrals and derivatives without sweating. They will be nearing the end of some of their first calulus courses after all.
None of this displays why they need to know how to program of course. This just shows how useful other people's programming is for them to use. While you do have the full power of python in sage the reality is the odd "for loop" and some "if statements" is really all of the programming most mathematicians will do with sage most of the time (though there is a significant minority who will do a lot more). If you want to go down this road I would suggest you try to get your hands on one of the Experimental mathematics books(http://www.experimentalmath.info/). These are the guys who (amongst many other interesting results) came up with BBP numbers: which is the way to find arbitrary digits of pi. They mostly use maple and mathematica but most of this work translates to sage.
I would strongly suggest you don't show them how to actually implement numerical methods themselves. Very few mathematicians are writing programs to solve numerical problems. Most just plug their programs into other people's programs. So I don't think showing how they could implement these methods themselves, if only they knew how to program, will excite anyone.
If this were me I think I would probably give a seminar building a simple game plugin for cgsuite (http://cgsuite.sourceforge.net/). I recognize that this is java and not python but their are a lot of advantages to this approach. First young mathematicians always get excited by combinatorial game theory. You are fundamentally showing them how they can use math to always win at certain games. It's like you are giving them a super power.
Second, you are implementing the rules of a game in a program. Game rules are great ways to learn programming idioms because they translate so directly into programming concepts.
And finally, you end up with a tool that can play your game perfectly. 90 minutes is a long time for a seminar as far as I'm concerned. If you can end on a bang, like with 10 minutes of playing a game against a computer, they will leave excited instead of bored and drained.
I would recommend solving a few different kinds of problems from Project Euler in Python and having a discussion about the solutions, how they could have been done differently to be more efficient, etc. as part of the seminar. Python is a very elegant language for solving mathematical problems and should be one of those easier understood than most by mathematics students, so I think you made a good choice there.
I'm assuming this is for Freshmen (only because most higher level Math students will likely know how to program)? If so, do something that is fun and relevant. Go through the basics, but maybe walk them through the logic / basic framework for a Game (which are heavily math oriented) or Python-Based Graphing Calculator.
If you want to get them real geeked though, show them Mathematica. I know, it's not what you selected ... but when I was a Sophomore Math major and first saw what you could do with it, I was in love.
Python will work well, but GNU Octave may be better.
What should be content of my presentation ?
The concept of functional programming with Python.
Some introduction to third party modules like NumPy and SciPy.
What are good resources available ?
Hans Petter Langtangen, Python Scripting for Computational Science, Springer
What is necessity of programming for maths students?
None. Usually maths students will have no problem in programming, since most programming language were developed to solve maths problem.
How will knowledge of programming will help them?
The computer was earlier developed as a tool for scientist to help them solve scientific/mathematics problems efficiently in a very short time, as compared to human.
http://www.sagemath.org
In our wiki is a collection of talks, they may help you! http://wiki.sagemath.org/Talks
Also be aware, that Sage contains NumPy, SciPy and SymPy. Therefore all information about these three python libraries hold for Sage.