Physics based programming problem sets

[hudsonj]

TL;DR Summary

Looking for resources similar to the website "Project Euler" but based around physics topics.

Was wondering if anyone knew of any good resources with programming challenges akin to the website "Project Euler" (about page found here). To be more specific, I'm looking for something consisting of problems centred around physics topics that would require some level of problem solving and programming to solve in a reasonable time frame, i.e. deriving and algorithm for finding the nth prime number instead of just listing them off.

 

[pbuk]

TL;DR Summary: Looking for resources similar to the website "Project Euler" but based around physics topics.

I don't think there are any. This is because we can categorise problems in Physics as follows:

• Problems with an analytic solution
  These do not need programming skills to solve.
• Problems with a deterministic solution
  These are described with differential equations so the programming skills required to solve are "write an algorithm to solve differential equations". This is an interesting and complicated problem in its own right, but it would not make a very interesting series of challenges. If you are interested in writing programs to solve differential equations you should study this topic, not try to work out algorithms yourself.
• Problems without a deterministic solution
  Techniques do exist to model these, however as there is no deterministic solution how would the website check your results?

I am confused by your reference to

deriving and algorithm for finding the nth prime number instead of just listing them off.

This is not a problem "centered around a physics topic". Also note that it is an unsolved (and generally believed to be unsolvable) problem in mathematics.

 

[hudsonj]

I don't think there are any. This is because we can categorise problems in Physics as follows:

• Problems with an analytic solution
  These do not need programming skills to solve.
• Problems with a deterministic solution
  These are described with differential equations so the programming skills required to solve are "write an algorithm to solve differential equations". This is an interesting and complicated problem in its own right, but it would not make a very interesting series of challenges. If you are interested in writing programs to solve differential equations you should study this topic, not try to work out algorithms yourself.
• Problems without a deterministic solution
  Techniques do exist to model these, however as there is no deterministic solution how would the website check your results?

I am confused by your reference to

This is not a problem "centered around a physics topic". Also note that it is an unsolved (and generally believed to be unsolvable) problem in mathematics.

That's a shame.

The reference I gave was the description of one of the problems found on the websites archive, which you can find here, and is very much solvable.

My intention was to give an example of the type of problem(s) I was looking for, being the creative application of the user's understanding of programming and the relevant topic(s) to solve a problem that would otherwise be cumbersome or even impossible to solve without a computer.

So really, I'm looking for physics themed problem solving activities that require or at least heavily encourage some level of programming to solve in a reasonable time span, as is the intention of Project Euler but with an emphasis on topics within maths, sorry for any misunderstanding.

Thanks anyway for your response.

 

[jedishrfu]

We had a problem one time in Classical Mechanics class that called for a numerical solution and everyone was of the opinion that there was no analytic one until a student produced it. Everyone was amazed but looking back some years earlier, the prof found that another person had discovered it first.

The suspicion was that the authors of the book knew it but felt this particular problem was ideal for teaching numerical problem solving and so never mentioned that one existed.

 

[pbuk]

The reference I gave was the description of one of the problems found on the websites archive, which you can find here, and is very much solvable.

Yes I am familiar with Project Euler. Problem 7 is of course solvable: we find the Nth prime by counting primes until we get to N, in other words by listing them off. But you suggested that you could find

[an] algorithm for finding the nth prime number instead of just listing them off.

My intention was to give an example of the type of problem(s) I was looking for, being the creative application of the user's understanding of programming and the relevant topic(s) to solve a problem that would otherwise be cumbersome or even impossible to solve without a computer.

Yes, there are lots of such problems in Maths. (Deterministic) Problems in Physics fall into the following categories:

• finding the root(s) of an equation
• finding eigenvalues of a matrix
• finding the solution to a set of simultaneous equations
• integrating a set of ordinary differential equations
• integrating a set of partial differential equations

None of these require any "creative application of the user's understanding of programming", they just require the abilities to know which algorithm to apply from a library and to configure the problem to fit the library's API.

If you disagree, perhaps you could give an example of a problem in Physics that suits your criteria, and we can suggest somewhere you might find other such problems.