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Ladataan... Euclid in the Rainforest: Discovering Universal Truth in Logic and MathTekijä: Joseph Mazur
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Kirjaudu LibraryThingiin nähdäksesi, pidätkö tästä kirjasta vai et. Ei tämänhetkisiä Keskustelu-viestiketjuja tästä kirjasta. "Whimsical" and mathematically "rigorous" are two concepts that seldom apply to the same book, but they do to Joseph Mazur's "Euclid in the Rainforest." ("Goedel, Escher, Bach" comes to mind.) Mazur develops three separate way of thinking mathematically: the classical logic of the Greek geometers, the weird logic of infinity, and probalistic logic. He takes us through several proofs of the Pythagorean theorem. He distinguishes between logical induction and mathematical induction and then illustrates the latter with proofs that (1) the square root of 2 is irrational; (2) there is not a largest prime number; (3) between every 2 rational numbers there is an irrational number; (4) between every 2 irrational numbers there is a rational number; and (5) that the cardinality of the irrational numbers is greater than that of the rational numbers. He also shows Cantor's proof that the real numbers are uncountable. Finally, he adds some counterintuitive examples of probability theory and a discussion of decision making under uncertainty and the normal curve. Mazur tries to make the rigor painless by illustrating some of the proofs in the context of anecdotes about some of his quirky travel and teaching experiences. That technique can be annoying in the hands of a less skill writer, but I think Mazur pulls it off rather well. All in all, a pleasant read for the non-mathematician. JAB näyttää 3/3 ei arvosteluja | lisää arvostelu
Like Douglas Hofstadter's Godel, Escher, Bach and David Berlinski's A Tour of the Calculus, Euclid in the Rainforest combines the literary with the mathematical to explore logic - the one indispensable tool in man's quest to understand the world. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between maths and the real world. Kirjastojen kuvailuja ei löytynyt. |
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Some of the little stories in the book were ones I found difficult to credit, but perhaps that was a savvy way of giving the reader a motive to further ponder the notion of plausibility!