Calculus without limits
September 17, 2014 5:23 PM Subscribe
Hyperreal numbers: infinities and infinitesimals - "In 1976, Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers. Now it's free, with a Creative Commons copyright!" (pdf—25mb :)
also btw :P
also btw :P
- The logic of real and complex numbers - "The cool part is that in some ways the complex numbers are simpler than the real numbers! The ultimate reason is that you can't talk about one complex number being greater than another. This avoids some nonstandard number systems where you have a number that's greater than all the ones you wanted to talk about."
- Science, models, and machine learning - "Machine learning is the art of getting computers to learn, so you don't have to explicitly tell them what to do. People use it in spam filters, search engines that guess what you're trying to find, optical character recognition, cars that drive themselves, and many other things. But how does it work?"
- Neural Networks and Deep Learning - "Inspired by the topics discussed in this earlier post, I've been reading Michael Nielsen's online book on neural nets and deep learning."
- Introduction to Statistical Computing - "At an intersection of Enigmas of Chance and Corrupting the Young."
- Higher Algebra & Topos Theory - "Mathematician Jacob Lurie, who was honored for redefining models in algebraic geometry, negotiated with his publisher to make his book on math principles available for free download on his personal website. While academics sometimes place papers online free, putting a whole book online isn't yet standard practice, according to the 36-year-old Harvard University professor. 'From my point of view, the benefit of writing a book is for people to look at it. I would like as many people as possible to look at it', he said."
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