At work I worked an summer intern. I am not too impressed with his programming skills. I expect nicely documented, neat codes. I TOLD him, don't add a lot of Strings in Java, use a StringBuffer. He didn't listen. I haven't seen him come up with anything other than putting together in a rather slopppy way what his collegues told him.
One day calculus was the topic. So it was a couple years ago that this college intern took calculus. I decided to quiz him: so, do you recall the Fundamental Theorem of Calculus?
He doesn't know.
This is like asking "have you heard of 'To be or not to be'" to someone who says who has read Hamlet.
I am not asking for a proof. I didn't ask the intern to do an outrageous difficult asterisk problem, nor recall some little known obscure theorem. It was the fundamental theorem. I am not so impressed. Students take classes and they forget right away. What is the purpose of education?
Speaking of fundamental theorems. There are many (and I only know 3).
Elementary school students (including YOU) know the Fundamental Theorem of Arithmetic: all numbers can be factored uniquely into primes. Take 100 for example, we have one way to factor it: 2252. (Ok, you got a super child prodigy if you find an elementary student who can prove it)
High school students may have heard of the Fundamental Theorem of Algebra: all polynomials of degree n have n roots, where they may be complex. Can't factor a quardratic? The quardratic formula gives you two complex solutions. The proof is easy to state but difficult to prove and it is Gauss's triumph accomplishment. This really is the gateway from real numbers to complex numbers.
I don't see a Fundamental Theorem of Geometry. My vote goes to the Pythagorean Theorem. This is the gateway from rational numbers to irrational numbers.
1 comment:
Calculus is about 2 things:
Crazy desire to find the area of imperfect shapes under a graph (function), with complex techniques.
Crazy desire to tell everybody else how to do use the techniques and explain that the desire is not crazy but noble, with proofs.
I am not surprised that most graduates know nothing about Calculus. Most of them knew that at one point, but after the exams, alcohol wiped all that knowledge out.
Programmers with no programming skills are plenty. They should be fired for incompetence. But that rarely happens, so the few gurus in the organization does the bulk of the work. That's just the way it is.
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