Wikipedia:Reference desk/Archives/Mathematics/2012 April 1

= April 1 =

Game Theory Textbook
I'm a mathematics student with no exposure to game theory. I would like to remedy this. Can anyone suggest an introductory textbook on the subject which has been developed with mathematicians as the intended audience? Thanks in advance! Korokke (talk) 03:01, 1 April 2012 (UTC)
 * I found "Game Theory, A Very Short Introduction" by Ken Binmore, Oxford ISBN 978-0-19-921846-2 to be a very readable introduction to the subject.--Salix (talk): 07:25, 1 April 2012 (UTC)
 * Binmore is a great read but not a textbook. "Game Theory" by Webb in the SUMS series is supposed to be good and is aimed at undergraduates. Tinfoilcat (talk) 08:55, 2 April 2012 (UTC)
 * It's a while since I read it, but I remember liking "Games and Information" by Eric Rasmusen (2nd edition, 1994) - Amazon link. AndrewWTaylor (talk) 11:43, 2 April 2012 (UTC)
 * Thank you, I'll investigate those! Korokke (talk) 09:55, 4 April 2012 (UTC)

 Test
(This may well require general mathematical intuition as opposed to any understanding of statistical tests or physical phenomena - I can't say for sure because I don't know what to do - so could anyone who reads this please not be put off by the possibility that it's outside their field of expertise?)

I am attempting to perform a calculation that involves the  test 1 and am unsure of how to proceed. Some (minor) background first though. I wish to test whether a sample of objects has a uniform comoving density that doesn't change with (cosmic) time and I have been told to make use of the  test. We assume that we detect each object with observed flux $$ f>f_0$$ and we determine the observed flux and the redshift for each object. Corresponding to each luminosity L is a maximum redshift $$ z_{max}(L)$$, corresponding to which there is a maximum volume $$ V_{max}(L)$$. I have a formula for computing the comoving volume as $$V=\frac{4\pi}{3}{D_C}^3$$, where D_C is the comoving distance and is a function of z.

I am now meant to determine V and V_max, having been given pairs of data z and $$f/f_0$$. I cannot see how to perform this calculation given the information I have. If someone could point me in the correct direction, I would greatly appreciate it (and if there is more information needed that I haven't provided, please just ask). Thanks. meromorphic  [talk to me]  10:03, 1 April 2012 (UTC)
 * If I understand correctly, it involves a list of all the galaxies above a certain minimum luminosity, each with it's redshift, which basically gives the distance of the galaxy. Then you calculate how much further the galaxy would have to be to exactly match the minimum luminosity, and that gives you V/Vmax for that galaxy ( that's (d/dmax)^3, no?), and if the average of all those values is 0.5 then your sample is complete (assuming a constant space density). So it seems to me you do have enough info, z gives you the distance, the redshift gives you the dmax...
 * what isn't clear for me is why one would need the distance at all, it would seem logical to me that the luminosity on it's own determines the value of d/d max and therefore the value V/V max .... maybe I'm missing something... Ssscienccce (84.197.178.75) (talk) 13:10, 1 April 2012 (UTC)
 * link I found useful: http://www.astro.virginia.edu/class/whittle/astr553/Topic04/Lecture_4.html Ssscienccce (84.197.178.75) (talk) 13:16, 1 April 2012 (UTC)
 * I'm not actually provided with the minimum luminosity. Earlier on in the project that I'm doing, I am provided with a formula (which I may or may not be meant to use for this section, I'm unsure) relating observed flux to luminosity but since I only have the ratio f/f_0 and no absolute values, I can only compute the ratio of two luminosities. Also, at the risk of asking a stupid question, will the minimum luminosity be the same for all galaxies in the sample or will it be different according to the galaxy I'm considering? Thanks. meromorphic   [talk to me]  14:02, 1 April 2012 (UTC)
 * Actually scratch that. On rearranging the formulae I have, I can derive an expression for V/V_max in terms of f/f_0, z and z_max. It's now z_max that is causing the problem. Any suggestions? meromorphic   [talk to me]  14:10, 1 April 2012 (UTC)