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By Steven G. Krantz

This booklet is set the idea that of mathematical adulthood. Mathematical adulthood is significant to a arithmetic schooling. The aim of a arithmetic schooling is to remodel the coed from a person who treats mathematical rules empirically and intuitively to an individual who treats mathematical principles analytically and will keep watch over and control them effectively.

Put extra without delay, a mathematically mature individual is one that can learn, study, and evaluation proofs. And, most importantly, he/she is one that can create proofs. For this is often what sleek arithmetic is all approximately: bobbing up with new principles and validating them with proofs.

The booklet presents heritage, information, and research for knowing the concept that of mathematical adulthood. It turns the belief of mathematical adulthood from an issue for coffee-room dialog to a subject for research and severe consideration.

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On Proof and Progress in Mathematics 21 One of Thurston’s most incisive ideas is that human thinking and understanding do not follow a single track. There are several different thinking faculties at play. Among these are: (1) Human Language: “Our linguistic facility is an important tool for thinking, not just for communication” [THU, p. 164]. The language that we use reflects both the level and the profundity of our thinking. We learn the quadratic formula, as a simple example, almost as a chant.

But Kepler’s mathematical maturity had the flaw that he could not understand John Napier’s theory of logarithms. In this sense Napier was ahead of Kepler. If collaboration were more the norm in the seventeenth century, as it is today, then perhaps Napier and Kepler could have worked together, and could have produced much more scientific work more efficiently. It is fun to rewrite history, and to speculate on what might have happened. ✐ ✐ ✐ ✐ ✐ ✐ “master” — 2011/11/9 — 15:21 — page 26 — #44 ✐ ✐ ✐ ✐ ✐ ✐ ✐ ✐ “master” — 2011/11/9 — 15:21 — page 27 — #45 ✐ CHAPTER ✐ 2 Math Concepts If we desire to form individuals capable of inventive thought and of helping the society of tomorrow to achieve progress, then it is clear that an education which is an active discovery of reality is superior to one that consists merely in providing the young with ready-made wills to will with and ready-made truths to know with .

And to do so with panache and flair. Someone who is struggling to follow the reasoning step-by-step is not going to be able to do it. Instead the situation calls for someone who is similar to a chess master. That is, it requires someone who can see ahead five or six moves, who knows where the line of reasoning is heading, who can see the forest for the trees. The student sees only the next fallen limb in the path, and likely as not trips over it. The professional sees the long-term goal, and nimbly walks around—or jumps over—that pesky limb.

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