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www.jeremykun.com | ||
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peterbloem.nl
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| | | | | [AI summary] The text provides an in-depth explanation of the Fundamental Theorem of Algebra, which states that every non-constant polynomial of degree $ n $ has exactly $ n $ roots in the complex number system, counting multiplicities. It walks through the proof by first establishing that every polynomial has at least one complex root (using the properties of continuous functions and the complex plane), then using polynomial division to factor the polynomial into linear factors, and finally addressing the nature of roots (real vs. complex) and their multiplicities. The text also touches on the conjugate root theorem, which explains why complex roots of polynomials with real coefficients come in conjugate pairs. | |
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www.themathdoctors.org
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www.oranlooney.com
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| | | | | R, like many scientific programming languages, has first-class support for complex numbers. And, just as in most other programming languages, this functionality is ignored by the vast majority of users. Yet complex numbers can often offer surprisingly elegant formulations and solutions to problems. I want to convince you that familiarizing yourself with R's excellent complex number functionality is well worth the effort and will pay off in two different ways: first by showing you how they are so amazingly useful you'll want to go out of your way to use them, and then by showing you how they are so common and fundamental to modern analysis that you couldn't avoid them if you wanted to. | |
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www.johndcook.com
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| | | RSA encryption as a group automorphism. Lagrange's theorem applied to the group. Carmichael's totient function applied to RSA. | ||
