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www.pvk.ca | ||
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dvt.name
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| | | | | Gödel's incompleteness theorems have been hailed as "the greatest mathematical discoveries of the 20th century" - indeed, the theorems apply not only to mathematics, but all formal systems and have deep implications for science, logic, computer science, philosophy, and so on. In this post, I'll give a simple but rigorous sketch of Gödel's First Incompleteness ... | |
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fbeedle.com
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| | | | | This book provides a distinct way to teach discrete mathematics. Since discrete mathematics is crucial for rigorous study in computer science, many texts include applications of mathematical topics to computer science or have selected topics of particular interest to computer science. | |
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www.jeremykun.com
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| | | | | In our last primer we saw the Fourier series, which flushed out the notion that a periodic function can be represented as an infinite series of sines and cosines. While this is fine and dandy, and quite a powerful tool, it does not suffice for the real world. In the real world, very little is truly periodic, especially since human measurements can only record a finite period of time. Even things we wish to explore on this blog are hardly periodic (for instance, image analysis). | |
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www.jeremykun.com
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| | | The first step in studying the sorts of possible computations (and more interestingly, those things which cannot be computed) is to define exactly what we mean by a "computation." At a high level, this is easy: a computation is simply a function. Given some input, produce the appropriate output. Unfortunately this is much too general. For instance, we could define almost anything we want in terms of functions. Let $ f$ be the function which accepts as input the date of California Super Lotto drawings, an... | ||
