By John Allen Paulos
ISBN: 067973807x (pbk)
From the writer of the nationwide bestseller Innumeracy, a pleasant exploration and rationalization of mathematical ideas from algebra to 0 in simply available alphabetical entries. "Paulos . . . does for arithmetic what the enjoyment of intercourse did for the boudoir. . . ."--Washington submit publication global. First time in paperback.
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This quantity comprises the court cases of the AMS-IMS-SIAM Joint summer season learn convention mostly Relativity, held in June 1986 on the college of California, Santa Cruz. common relativity is likely one of the such a lot winning alliances of arithmetic and physics. It presents us with a idea of gravity which has the same opinion with all experimentation and commentary so far.
This e-book is for college kids who didn't stick with arithmetic via to the top in their college careers, and graduates and execs who're searching for a refresher path. This new version includes many new difficulties and in addition has linked spreadsheets designed to enhance scholars' realizing. those spreadsheets is also used to unravel the various difficulties scholars are inclined to come across throughout the rest of their geological careers.
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Additional resources for Beyond Numeracy: Ruminations of a Numbers Man
5). 5 Power series, two variables The idea of a power series can be extended to more than one variable. One way to develop it is to use exactly the same sort of brute-force approach that I used for the one-variable case. Assume that there is some sort of infinite series and successively evaluate its terms. f (x, y ) = A + Bx + Cy + Dx2 + Exy + F y 2 + Gx3 + Hx2 y + Ixy 2 + Jy 3 · · · Include all the possible linear, quadratic, cubic, and higher order combinations. Just as with the single variable, evaluate it at the origin, the point (0, 0).
This is not a handicap, as there are many circumstances for which this is all you need. I derived this assuming that n is large, but notice that the result is not too bad even for modest values. The error is less than 2% for n = 5. There are even some applications, especially in statistical mechanics, in which you can √ make a still cruder approximation and drop the factor 2πn. That is because in that context it is the logarithm of n! that appears, and the ratio of the logarithms of the exact and approximate numbers goes to one for large n even without this square root factor.
The double factorial of an even integer can be expressed in terms of the single factorial. Do so. What about odd integers? 20 Evaluate this integral. Just find the right substitution. 21 A triangle has sides a, b, c, and the angle opposite c is γ. Express the area of the triangle in terms of a, b, and γ. Write the law of cosines for this triangle and then use sin2 γ + cos2 γ = 1 to express the area of a triangle solely in terms of the lengths of its three sides. The resulting formula is not especially pretty or even clearly symmetrical in the sides, but if you introduce the semiperimeter, s = (a + b + c)/2, you can rearrange the answer into a neat, symmetrical form.