By Steven G. Krantz
This ebook is ready the concept that of mathematical adulthood. Mathematical adulthood is imperative to a arithmetic schooling. The aim of a arithmetic schooling is to remodel the scholar from an individual who treats mathematical principles empirically and intuitively to an individual who treats mathematical rules analytically and will keep watch over and control them effectively.
Put extra without delay, a mathematically mature individual is one that can learn, research, and assessment proofs. And, most importantly, he/she is one that can create proofs. For this is often what smooth arithmetic is all approximately: arising with new principles and validating them with proofs.
The ebook offers history, information, and research for knowing the concept that of mathematical adulthood. It turns the assumption of mathematical adulthood from an issue for coffee-room dialog to a subject for research and critical consideration.
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Extra resources for A Mathematician Comes of Age
The way they had been handling the task before I came along was a two-stage process. ” The machinists would make the machine dies in five sizes—some obviously too small, some too large, and some in between. ” Clearly the mathematicians had not become involved yet, and the problem languished. After personal computers became available, the machinists took a new view of the matter. They purchased a very expensive computer-aided design (CAD) system from McDonnell-Douglas. This software came with about 200 thick volumes of documentation, and required considerable computer power to run.
1 So there are several things that need to be explained to the students: What is the meaning of an approximate solution? How does one measure how accurate an approximate solution is when one does not know the precise solution? How do we compare? Why is an approximate solution often adequate for the task at hand? How does one calculate an approximate solution? How does one calculate an approximate solution with a pre-specified degree of accuracy? What is accuracy to within k decimal places? What are significant digits?
The novice is, in effect, asking for a proof. And a proof is a rather sophisticated entity, accessible only to a certain intellectual elite. ” then he/she is beginning to exhibit mathematical maturity. When a college freshman says, “I don’t know why the fundamental theorem of ✐ ✐ ✐ ✐ ✐ ✐ “master” — 2011/11/9 — 15:21 — page 12 — #30 ✐ ✐ 12 1. Introductory Thoughts calculus should be true. ”, we know that this student is headed towards the good stuff. When a graduate student says to his/her thesis advisor, “I didn’t like the proof that the author gave of this result, so I created my own proof,” we know we are talking to a future mathematician.