INCUMBENT

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Philip Hudson
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Re: INCUMBENT

You are a kinder man than I am, Slava. Although the New Math has come and mercifully gone, detailed proofs are still incumbent, at least in higher math.
It is dark at night, but the Sun will come up and then we can see.

Perry Lassiter
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Re: INCUMBENT

I've read serious posts by mathemeticians who say the practice of making people solve problems only by the book is just wrong. Understanding, they say, is the aim.

I hav eheard teachers say one might solve that particular problem that way, but learning to go by the book will solve others at different times. It also curtails cheating or at least makes it harder.
pl

Philip Hudson
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Re: INCUMBENT

In higher mathematics the question of eloquence comes in. Eloquence is usually translated to the smallest number of steps in a specific proof. The shorter the proof the greater the eloquence, providing the proof is complete. There is more than one way to skin a cat, and more than one way to solve a mathematical problem. I have had classmates who excused themselves from seeing a proof because they thought they could present a more eloquent one tomorrow. I was never energetic enough to do that. But that's not saying I never devised the most eloquent proof. My daughter is a professional musician and she is what is called a "quick study". The first time she plays the piece she gets it right. She never has to practice. I considered myself a quick study in proving mathematical problems. I might be able to do it better if I try again, but the first one was good enough for who it was for. Laziness also played a part.
It is dark at night, but the Sun will come up and then we can see.

MTC
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Re: INCUMBENT

My hat is off to you, Philip, figuratively at least, having no hat suitable to swoosh. You can do something I cannot despite concerted effort. I have written a short essay (still too long to post) about my struggle to overcome the Math Monster. To summarize the story, a grade school kid terrified by Math in time transforms himself into an "A" student through mighty efforts despite a lack of aptitude. The story has a Forrest Gump-like quality to it. Picture Forrest casting off his leg braces. Look, I can walk! The same. Of course, there are limits. The story ends when I--an English major--wisely drop Number Theory in the first week to protest at the Moratorium in Washington. (Also oddly Gump-like.)

misterdoe
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Re: INCUMBENT

MTC, your story reminds me of an old friend of mine, a student in that same eighth-grade math class where I got the 58. He squeaked through four marking periods with a 66 average, and knew he had to do pretty well on the final exam to avoid failing for the year. He wound up with a 91 on the exam, and guess what? He's now a math professor!

Perry Lassiter
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Re: INCUMBENT

My kids started and dropped many math courses before getting by enough to graduate. My second son had an abusive teacher in the sixth grade who liked to pick on him. When he went in to take the standardized test she wondered aloud why he even bothered to take it. That enraged him enough that on the concept half he scored 12th grade, while on the practical half he scored solid grade level. He now teaches school music.

On the proofs, I took a course in mathematical logic that supposedly liked neat proofs. In the last chapter of our WV Quine text, he takes six or seven pages to develop the number 1!
pl

MTC
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Re: INCUMBENT

"(T)he number 1!" is that 1 factorial, or 1, exclamation mark?

About your son, Perry, I give him credit for overcoming his teacher's negativity. Teachers can pour water or acid on your roots with equal ease.

To misterdoe, your friend's experience shows overcoming a deficit can spark a career.

Perry Lassiter
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Re: INCUMBENT

The integer 1. The prof let us stop before that, but I traced it enough to see where he was going then. Couldn't now without reworking the whole book.
pl