what does game theory have to do with mathematics?
153504
Game theory (link: http://en.wikipedia.org/wiki/Game_theory) is not typical mathematics as you would normally consider it.\n\nIt was invented by a mathematician who was also a computer pioneer John Von Neumann (link http://en.wikipedia.org/wiki/John_von_Neumann).\n\nIt does not necessarily have equations as you would typically think of in the field of mathematics. It is more of a way to consider a situation (called a game) where competing/cooperating members have choices to make that can affect the outcome of the game.\n\nGame theory has wide ranging implications, from business, computer software, investing, biology, sociology and even law enforcement.
12607
There is indeed a thread in philosophy that treats mathematical truth as representing some kind of eternal fixed world.  However, there are plenty of mathematical objects other than numbers that have a rich field of mathematics associated with them.\n\nFor example, one defines a group as being a set of elements and an operation between them, denoted '+' (a bit like 'addition', but not restricted to acting on numbers) such that:\n1) If a and b are elements in our group then there is an element c such that a + b = c\n2) There exists an element of our group O such that for every element a in our group, a + O = a.\n3) For every element a in our group, there is also an element b such that a + b = 0.\n4) If we pick three elements in our group, then (a + b) + c = a + (b + c).\n\nThis is an abstract definition, and doesn't prescribe what the underlying elements actually are.  All it says is that they must satisfy (1)-(4) to be called a group.  You can probably check for yourself that numbers do satisfy these rules, although there are many particular examples of groups where numbers don't provide enough flexibility to be considered as the underlying elements.\n\nNow, mathematicians spend a lot of time studying these, and other, mathematical objects, and there are many beautiful theorems associated with them.  These objects, and the theorems about them, should be considered as eternal as the numbers whilst at the same time being different to the numbers.
480448
there were a few games we played with cards. in one you use a deck of cards 1-10 no face cards. each person got a hand of cards. the target card was turned over from the stock pile, play went around they table, each person put a series of cards down to reach the number, if you could not play you  drew and the play passed. lets say the number this hand was 7, you can lay 5+2 or 3+4 or 9-2 or 9+10-8-4 you get the idea. you can try other sites for math type games also. you can do math bingo. you can make a board game and depending on the square they land on they do +,-,* and roll 2 die for the numbers to use. You can get 10 and 20 sides dice also, in game shops or book stores. you can do something like this with dominoes also.   See the UCSMP site below.
1169384
The previous responders are incorrect. \n\nLet the expected length of the game (in tosses) be L. We can classify each game into one of three starting sequences (in the following table P=probability,E=expectation value for total length of game):\n\nH --> P = 1/2 , E = L+1\nTH --> P = 1/4 , E = L+2\nTT --> P = 1/4 , E = 2\n\nThe first two cases are equivalent to starting the game over after 1 and 2 tosses respectively.\n\nSumming P*E for these three events gives L:\n\nL =(1/2)*(L+1) + (1/4)*(L+2) + (1/4)*(2)\n= (3/4)L + 3/2\n\n--> L = 6
358575
Mathematics in medicine starts with enzyme kinetics, introducing the ideas of the Law of Mass Action, nondimensionalisation, and perturbation analysis. It also briefly introduces autocatalysis, and cooperative reactions. A pregnancy testing kit can be mathematically modelled and analysed: this will introduce the use of Laplace transforms in partial differential equations and asymptotic results. The vascular system can be discussed and solutions for pusatile blood flow will be derived. This in turn can be applied in the analysis of a catheter in the pulmonary artery which is heated one degree above blood temperature. Knowing the power input we deduce the cardiac output. Finally Infectious diseases can be discussed. In particular the SIR model is dealt with; this is followed by an analysis of a sexually transmitted disease and then the spread of rabies is considered.\n\nDavid Bernoulli was famous for his mathematics applied to medicine
403923
I don't think it's so much a method of calculation as it is a follow the leader thing.  SI did an article a year or two ago in which they talked about the guy who sets the line for one of Vegas' big sportsbooks.  He researched the teams, etc,, but ultimately sort of set it by feel.  An interesting note: his concern was to put the line where the money would flow evenly to each side rather than to actually predict the game's outcome.  After he set his, other sportsbooks followed his lead and came out with similar/identical numbers.  Then, of course, they move it according to which way the action is going so that their odds of losing money are reduced.
912698
Do the game when the students can make one, two or three tally marks.  The object of the game is to make the last mark without going over.    The team gets a choice of going first, or choosing the number the game will go to.  \n\nThere is a pattern to the madness, but I want you to figure it out.
1117732
What mathematical topics to you want discuss ?
691646
Expanding on the above response on the Pareto principle, you can also demonstrate fractals, e.g. if 80% of the sales come from 20% of the customers, 80% of the sales from those 20% will come from 20% of those 80% assuming a large enough set.  Confusing?  I love fractals and think your question is awesome.
227726
Yes, almost all freecell games are winnable. I believe that there are only about 6 games that aren't, but in the version that comes with Windows, they only have 32k different hands and only hand #11982 is (known to be) unwinnable. \n\nWhen it comes to "standard" solitaire (klondike) it gets tricky and very interesting. While no one has proven the exact odds, the best method someone has thought of analyzing it with is the same method used in quantum physics and a possible proof of the Reimann zeta function. The Reimann zeta function is used to figure out prime numbers, but has yet to be proved to be correct or incorrect and is one of the most biggest mysteries in mathematics since it was proposed over 140 years ago.\n\nLook at the source for more info -- I personally find it amazing that prime numbers are somehow related to quantum energy states and that solitaire probability of all things could be similar as well.
516893
Fundamentals of Mathematical Economics -- Chang
724427
1024 matches. This should be on the mathematic section. Everyone know that an elimination match would always require <number of player> - 1 to finish. \n\nThe simple logic is actually: We're gonna create 1024 losers, how could we create 1024 losers with less than 1024 match? Can't have 1024 losers with only several matches.\n\nEach player would play the match 10 times (2^10 = 1024), and exactly one player would play 11 matches. (to complete up the 1025 players)
11041
Philosophy of mathematics is the study of the nature of mathematics, including underlying assumptions of the discipline and its scope. \nHope this helps.
448915
Mathematics is the only 'pure' form of communication and information that exists. 2+2=4, always has, always will.\nThere are many opinionated forms of knowledge such as History, Religion, Evolution, etc. Math is the only exact form that cannot be left to speculation. You can debate an answer to a problem but the answer never changes from its own truth.  40 divided by point 5 equals 80. Always has, always will.
209670
Mathematics is used whenever one has to analyze relationships between exact quantities. Since a scientific theory or hypothesis must be associated with an empirical measurement (thus the theory must be associated with measurable quantities), the language of mathematics is inseparable from most science.
667274
What economists call game theory psychologists call the theory of social situations, which is an accurate description of what game theory is about.\n\nSee the reference for much more information.
459396
This question is asking the EXPECTATION for this game, which can be found by summing the product of each outcome with it's respective probability:\n\np1x1 + p2x2 + ... + pnxn\n\nThis gives the theoretical winnings or losings for the game.  If it's a negative number (loss) it's high risk, while a positive number (gain) would mean you're expected to win.  Of course, with any probability problem, the actual results will match up with the theoretical results only over the long term.