Mathematics for Computer Science: a free, CC-licensed MIT textbook

This is indeed an up-to-the-minute text [PDF], dated Mar 7, 2017. It's written by Googler/MIT prof Eric Lehman, MIT/Akamai scientist F Thomson Leighton and MIT AI researcher Albert R Meyer, as a companion to their Mathematics for Computer Science open course. (via 4 Short Links)

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  1. I'm assuming it is this

    Philosophical proof involves careful exposition and persuasion typically based on a series of small, plausible arguments. The best example begins with “Cogito ergo sum,” a Latin sentence that translates as “I think, therefore I am.” This phrase comes from the beginning of a 17th century essay by the mathematician/philosopher, Ren´e Descartes, and it is one of the most famous quotes in the world: do a web search for it, and you will be flooded with hits.

    Deducing your existence from the fact that you’re thinking about your existence is a pretty cool and persuasive-sounding idea. However, with just a few more lines of argument in this vein, Descartes goes on to conclude that there is an infinitely beneficent God. Whether or not you believe in an infinitely beneficent God, you’ll probably agree that any very short “proof” of God’s infinite beneficence is bound to be far-fetched. So even in masterful hands, this approach is not reliable.

    Mathematics has its own specific notion of “proof.”

    It's the only reference to any god I could find in the book.

    Edit: I also found just found this

    The ZFC axioms weren’t etched in stone by God. Instead, they were mostly made up by Zermelo, who may have been a brilliant logician, but was also a fallible human being—probably some days he forgot his house keys. So maybe Zermelo, just like Frege, didn’t get his axioms right and will be shot down by some successor to Russell who will use his axioms to prove a proposition P and its negation P. Then math as we understand it would be broken—this may sound crazy, but it has happened before.

    That's all the references to god in the book. Hardly anything to get worked up over.

  2. null says:

    That was my assumption, but it seems @Karl_Jorgensen is reading far more into it than a mention of Descartes warrants.

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