100 Great Problems of Elementary Mathematics (Dover classics of science & mathematics)
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ISBN-10: 0-486-61348-8
ISBN-13: 9780486613482
Publisher: Dover Publications
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Year: June 1, 1965
Size: 13.72 x 21.34 x 2.29cm
Number of pages: 393
Weight: 476gr
Binding: Paperback
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Problems that beset Archimedes, Newton, Euler, Cauchy, Gauss, Monge and other greats, ready to challenge today’s would-be problem solvers. Among them: How is a sundial constructed? How can you calculate the logarithm of a given number without the use of logarithm table? No advanced math is required. 100 problems with proofs.
reviews
Elementary algebra and ingenius ideas are combined to solve some of the most difficult problems in the history of math.This book helped me solve several difficult technical problems . The concise treatment and cross reference to other solutions is outstanding . This is the finest treatment of advanced mathematical treatments I have ever seen. First published in 1932, it represents the best from the masters and can be used to discover tricks which were helpful to me in algorithm development . The treatment of astronomical problems alone is worth the price .
Perhaps the stress given to geometry gives evidence to the age of the book, but it still represents an example of how a collection of problems should be written. It is too entangled with mathematics to be defined an issue about mathematical games, but also fans of games can find out some enjoying items. Because, if much room has been given to proofs and resolutions, the boundary of elementary curiosity never goes out of sight, even if it can sometimes look like a far horizon. It is surely the best book about elementary problems, mathematical games and jokes I have ever read till now, and I have found its language as clear and straight as a non-English reader (like me) usually finds a non-English writer.
I love this book, and recommend it very highly, if you're the type who would like to understand, say, why the Fundamental Theorem of Algebra (every polynomial equation as a (possibly complex) root, is true. Yes, it takes intellectual effort to follow the proofs, but that can be incredibly rewarding, once you finally understand. But this review is mostly to clarify the term »Elementary« in the title. This is used in a technical sense. Many (most?) of the theorems have multiple proofs. And sometimes the clearest proofs involve calculus, and often the calculus of complex variables. But if a proof doesn't involve calculus, then mathematicians refer to these as »elementary«. It is in this sense that the title uses the term.
100 Great Problems of Elementary Mathematics is such a goldmine of ingenuity that it is hard to comprehend how it could be sold for so low a price. Ten dollars is practically a steal.
This publication, which was translated into English back in 1965, is a concise summary of some of the greatest works of mathematics throughout mankind's history. The problems contained are quite challenging. Many are such that if you understood any one of them, then you would probably know something that even the best math professor nearest you would not. This may sound like an overstatement, but in a day and age where some PhD's in math have either forgotten or never really learned how to determine so little as the square root of a number by just pencil and paper, it is probably not.
It is from analyzing the book's passages of Bernoulli's Power Sum Problem that I was able to achieve a great mathematical triumph after discovering the following challenge found in William Dunham's The Mathematical Universe: determining a precise mathematical formula to figure out how Jakob Bernoulli could take all the positive integers from 1 to 1000, raise each of them to the tenth power, and then add them up to where the sum came up to over 30 digits! I tried to develop algorithms that would work but failed each time, until I, once again, read this volume.
The situations presented are quite difficult to grasp, but once you get to where you know how to apply any one of them in solving mathematical puzzles, you feel elated. I know I did.
For the individual who enjoys looking at mathematics in a historical context and who wants to approach problems that are perhaps not entirely solvable with the use of the calculator and/or the computer, I recommend this book.
What does boat-sailing have to do with mathematics? Perhaps it is not mainstream mathematics, but apparently some think it is Elementary Mathematics, along with other easy things, say the Hermite-Lindemann theorem and the Abel Impossibility theorem. D"orrie apparently shares this view, but with whom?
Not everything in the book is so bizarre or non-elementary, though it does have full sections on Projective Geometry and Astronomy. There are some nicer problems, but the solutions seem to be a hard read –-- and sometimes they seem to be incorrect (as in the proof of the fundamental theorem of algebra).
But the worst problem is the translation –-- the book still has a German look and feel. While this may be considered a feature by some, I find it very annoying. For example, did you know that putting an overbar over a number denotes factorial? Have you heard of Fermat's Prime Number Theorem? (solution in the book)
So I can recommend it for the German audience –-- unless they can find the original, which they will probably prefer …
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