Read e-book online A Century of Mathematics in America PDF

By Peter Duren

ISBN-10: 0821801309

ISBN-13: 9780821801307

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There will be ten squares on one side, and five cross-products on the other side. . Now that we’ve done this, we have the fundamental tool that we need in order to be able to build our computer. The CPU of that computer is going to have a bunch of hardware registers, just like real computers do. But unlike real computers, each register will hold an unsigned integer, which can be an arbitrarily large number of bits. And the unknowns in our master equation will give the contents of these registers.

Actually, it is a lot of fun if you do it yourself. Like making love, it’s not much fun to hear how somebody else did it. You have to do it yourself! And you don’t learn much by reading someone else’s software. It’s excruciating to have to do that, you’re lost in the maze of someone else’s train of thought! But if you yourself write the program and debug it on interesting examples, then it’s your train of thought and you learn a lot. Software is 38 Meta Math! frozen thought. . So we won’t finish working out the design in detail.

Let me just tell you how far I got playing with this myself when I was a teenager. You can do a fair amount using comparatively elementary methods and the fact that the sum of the reciprocals of the primes diverges: 1/2 + 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/23 + . . = ∞ This was established by Euler, and it shows that the primes cannot be too sparse, or this infinite series would converge to a finite sum instead of diverging to infinity. My Complexity-Based Proof That There Are Infinitely Many Primes Because if there were only finitely many different primes, expressing a number N via a prime factorization N = 2e × 3 f × 5g × .

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A Century of Mathematics in America by Peter Duren


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