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A professor asked me to help making a specification for a college project. By the time the students should know the basics of programming.

The professor is a mathematician and has little experience in other programming languages, so it should really be in MATLAB.

I would like some projects ideas. The project should

  1. last about 1 to 2 months
  2. be done individually
  3. have web interface would be great
  4. doesn't necessary have to go deep in maths, but some would be great
  5. use a database (or store data in files)

What kind of project would make the students excited?

If you have any other tips I'll appreciate.

UPDATE: The students are sophomores and have already studied vector calculus. This project is for an one year Discrete Mathematics course.

UPDATE 2: The topics covered in the course are

  1. Formal Logic
  2. Proofs, Recursion, and Analysis of Algorithms
  3. Sets and Combinatorics
  4. Relations, Functions, and Matrices
  5. Graphs and Trees
  6. Graph Algorithms
  7. Boolean Algebra and Computer Logic
  8. Modeling Arithmetic, Computation, and Languages

And it'll be based on this book Mathematical Structures for Computer Science: A Modern Approach to Discrete Mathematics by Judith L. Gersting

+8  A: 

General Suggestions:

There are many teaching resources at The MathWorks that may give you some ideas for course projects. Some sample links:

Specific Suggestions:

One of my grad school projects in non-linear dynamics that I found interesting dealt with Lorenz oscillators. A Lorenz oscillator is a non-linear system of three variables that can exhibit chaotic behavior. Such a system would provide an opportunity to introduce the students to numerical computation (iterative methods for simulating systems of differential equations, stability and convergence, etc.).

The most interesting thing about this project was that we were using Lorenz oscillators to encode and decode signals. This "encrypted communication" aspect was really cool, and was based on the following journal article:

Kevin M. Cuomo and Alan V. Oppenheim, Circuit Implementation of Synchronized Chaos with Applications to Communications, Physical Review Letters 71(1), 65-68 (1993)

The article addresses hardware implementations of a chaotic communication system, but the equivalent software implementation should be simple enough to derive (and much easier for the students to implement!).

Some other useful aspects of such a project:

  • The behavior of the system can be visualized in 2-D and 3-D plots, thus exposing the students to a number of graphing utilities in MATLAB (PLOT, PLOT3, COMET, COMET3, etc.).
  • Audio signals can be read from files, encrypted using the Lorenz equations, written out to a new file, and then decrypted once again. You could even have the students each encrypt a signal with their Lorenz oscillator code and give it to another student to decrypt. This would introduce them to various file operations (FREAD, FWRITE, SAVE, LOAD, etc.), and you could even introduce them to working with audio data file formats.
  • You can introduce the students to the use of the PUBLISH command in MATLAB, which allows you to format M-files and publish them to various output types (like HTML or Word documents). This will teach them techniques for making useful help documentation for their MATLAB code.
gnovice
A: 

You might look here: http://www.mathworks.com/academia/student_center/tutorials/launchpad.html on the MathWorks website. The interactive tutorial (second link) is quite popular.

--Loren

Loren
+3  A: 

I have found that implementing and visualizing Dynamical systems is great for giving an introduction to programming and to an interesting branch of applied mathematics. Because one can see the 'life' in these systems, our students really enjoy this practical module.

We usually start off by visualizing a 1D attractor, so that we can overlay the evolution rule/rate of change with the current state of the system. That way you can teach computational aspects (integrating the system) and visualization, and the separation of both in implementation (on a simple level, refreshing graphics at every n-th computation step, but in C++ leading to threads, unsure about MATLAB capabilities here).

Next we add noise, and then add a sigmoidal nonlinearity to the linear attractor. We combine this extension with an introduction to version control (we use a sandbox SVN repository for this): The students first have to create branches, modify the evolution rule and then merge it back into HEAD.

When going 2D you can simply start with a rotation and modify it to become a Hopf oscillator, and visualize either by morphing a grid over time or by going 3D when starting with a distinct point. You can also visualize the bifurcation diagram in 3D. So you again combine generic MATLAB skills like 3D plotting with the maths. To link in other topics, browse around in wikipedia: you can bring in hunter/predator models, chaotic systems, physical systems, etc.etc.

We usually do not teach object-oriented-programming from within MATLAB, although it is possible and you can easily make up your own use cases in the dynamical systems setting. When introducing inheritance, we will already have moved on to C++, and I'm again unaware of MATLAB's capabilities here.

Coming back to your five points:

  • Duration is easily adjusted, because the simple 1D attractor can be done quickly and from then on, extensions are ample and modular.
  • We assign this as an individual task, but allow and encourage discussion among students.
  • About the web interface I'm at a loss: what exactly do you have in mind, why is it important, what would it add to the assignment, how does it relate to learning MATLAB. I would recommend dropping this.
  • Complexity: A simple attractor is easily understood, but the sky's the limit :)
  • Using a database really is a lot different from config files. As to the first, there is a database toolbox for accessing databases from MATLAB. Few institutes have the license though, and apart from that: this IMHO does not belong into such a course. I suggest introducing to the concept of config files, e.g. for the location and strength of the attractor, and later for the system's respective properties.

All this said, I would at least also tell your professor (and your students!) that Python is rising up against MATLAB. We are in the progress of going Python with our tutorials, but I understand if someone wants to stick with what's familiar.

Also, we actually need the scientific content later on, so the usefulness for you will probably depend on which department your course will be related to.

+1 for physics.
Joey Robert
+2  A: 

A lot of things are possible.

The first example that comes in mind is to model a public transportation network (the network of your city, with underground, buses, tramways, ...). It is represented by a weighted directed graph (you can use sparse matrix to represent it, for example).

You may, for example, ask them to compute the shortest path from one station to another one (Moore-dijkistra algorithm, for example) and display it.

So, for the students, the several steps to do are:

  • choose an appropriate representation for the network (it could be some objects to represent the properties of the stations and the lines, and a sparse matrix for the network)
  • load all the data (you can provide them the data in an XML file)
  • be able to draw the network (since you will put the coordinates of the stations)
  • calculate the shortest path from one point to another and display it in a pretty way
  • create a fronted (with GUI)

Of course, this could be complicated by adding connection times (when you change from one line to another), asking for several options (shortest path with minimum connections, take in considerations the time you loose by waiting for a train/bus, ...)

The level of details will depend on the level of the students and the time they could spend on it (it could be very simple, or very realist)

ThibThib
A: 

I always thought the one I was assigned in grad school was a good choice-a magnetic lens simulator. The math isn't completely overwhelming so you can focus more on learning the language, and it's a good intro to the graphical capabilities (e.g., animating the path of an off-axis electron going through the lens).

ChrisC
+2  A: 

You want to do a project with a web interface and a database, but not any serious math... and you're doing it in MATLAB? Do you understand that MATLAB is especially designed to be used for "deep math", and not for web interfaces or databases?

I think if this is an intro to a Discrete Mathematics course, you should probably do something involving Discrete Mathematics, and not waste the students' time as they learn a bunch of things in that language that they'll never actually use.

Why not do something involving audio? I did an undergraduate project in which we used MATLAB to automatically beat-match different tunes and DJ mix between them. The full program took all semester, but you could do a subset of it. wavread() and the like are built in and easy to use.

Or do some simple image processing like finding Waldo using cross-correlation.

Maybe do something involving cryptography, have them crack a simple encryption scheme and feel like hackers.

endolith
+2  A: 

MATLAB started life as a MATrix LAB, so maybe concentrating on problems in linear algebra would be a natural fit.

Discrete math problems using matricies include:

  1. Spanning trees and shortest paths
  2. The marriage problem (bipartite graphs)
  3. Matching algorithms
  4. Maximal flow in a network
  5. The transportation problem

See Gil Strang's "Intro to Applied Math" or Knuth's "Concrete Math" for ideas.

duffymo
A: 

db I/O and fancy interfaces are out of place in a discrete math course.

my matlab labs were typically algorithm implementations, with charts as output, and simple file input.

how hard is the material? image processing is really easy in matlab, can you do some discrete 2D filtering? blurs and stuff. http://homepages.inf.ed.ac.uk/rbf/HIPR2/filtops.htm

Dustin Getz