Especailly the topics like the binomial theorem in mathematics
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I have some but it is impossible to show them to you so go to these sites:\n\nhttp://www.palgrave.com/science/mpc/\n\nhttp://www.alibris.com/search/search.cfm?S=R&qwork=4235746&qsort=p&siteID=KLVmR9fE2yU-giJdIkKGIBX1NUraLFkp1g\n\nhttp://www.palgrave.com/science/mpc/
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Try this, maybe?\n\nhttp://mathforum.org/library/drmath/drmath.elem.html
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http://mathforum.org/library/drmath/sets/high_calculus.html
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http://mathforum.org/dr.math/\n\nThis is a good site where people ask questions and the questions are answered by volunteer professors.  May not have pictures but there are very good explanations.
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better than a book:\nhttp://www.math.com
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4.2\n\nfor a binomial distribution the mean is the number * the probability
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I like to use C(n,k) for the combiniation of n things taken k at a time.\nUse the binomial theorem to expand (1+k)^n\n\n(1+k)^n = C(n,0) (1^n)k^0 + C(n,1)(1^(n-1))k^1 + C(n,2)(1^(n-2))k^2 + ... + C(n,n-1)(1^1)k^(n-1) + C(n,n)(1^0)k^n\n\n1 ^ of anything is 1 , and if we set k=1, then we get\n\n(1+1)^n = 2^n = C(n,0) + C(n,1) + C(n,2) + ... + C(n,n-1) + C(n,n)\n\nif this sum =2048, then 2^n=2048 or n=11
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Yes, and this is because of Binomial theorem.\n\nAccording to Binomial theorem\n(a+b)^n = sum(k=0 to k=n)[(a^k) * (b^(n-k))]\n\nSo, with each term in your expantion, we observe 3 things\n\n1. Power of one of the variable increases from zero to n.\n2. Power of remaining of the variable decreases from n to zero.\n3. The coefficient of each term from starting to last will have coefficient (n perm k), where n is the power of (a+b) on RHS and k is the number of the term you are evaluating.\n\nI hope this answers your question.\n\nAll the best.
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This theorem has an amazing number of proofs but this theorem(like many other mathematical concepts) as you said was known way before pythogorean times but only to INDIANS who didnt share it on the global scale!!
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"The Calculus of One Variable" by I. A. Maron is a good book for self-study.
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binomials-A polynomial with two terms. \n\ntrinomials-An algebraic expression consisting of three terms connected by plus or minus signs
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Go to Google scearch you will find lot of papers on this.\nCopy with changes from all the papers.\nIncluding whatever Mathamatical figures you find
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Without knowing the relationship between successive elements, I think the best you can do is this:\n[k=0, n-1]∑(x_(k+1) - x_k)²\n[k=0, n-1]∑(x_(k+1)² - 2x_k*x_(k+1) + x_k²)\n[k=0, n-1]∑x_(k+1)² - 2[k=0, n-1]∑(x_k*x_(k+1)) + [k=0, n-1]∑x_k²\n[k=1, n]∑x_k² - 2[k=0, n-1]∑(x_k*x_(k+1)) + [k=0, n-1]∑x_k²\n\nx_0 + x_n + 2[k=1, n-1]∑x_k² - 2[k=0, n-1]∑(x_k*x_(k+1))
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Check out http://math.mit.edu/research/index.html
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math, physics, astronomy
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It never occured to me that this could be a potential subject for study.  Hmm. Fascinating subject. I can just imagine the subject coming up , lets say 2 years from now, when a group of friends would describe their break ups with their boyfriends and the conversation will go like this;\n"Hmmph, he was only a one ml. episode in my life"\n"Really?, ____ was at least a fiver".\n\nI have to say it will vary from each person to the next , all proportionate to the duration. If a mathematician will just come up with an equation, you can start your study!
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I suggest you go to this site http://www.math.com/students/practice.html and take one of their quizzes