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by chalmette
2934 days ago
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Studying math is the most direct and easiest route to get the human tendency to believe what's psychologically expedient beaten out of you. Any rigorous intro to math (abstract algebra, analysis, topology, whatever) book will do. But the easiest, most varied and funnest would be intro to discrete math or the so called "transition" books. For example, check out [1] Discrete Math by Susanna Epp, [2] Transition to Advanced Math by Gary Chartrand et al, [3] How to Think about Analysis by Lara Alcock, [4] Learning to Reason by Nancy Rodgers [1] https://books.google.com/books?id=PPc_2qUhXrAC&pg=PA1&source... [2] https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... [3] https://books.google.com/books?id=n0tuBAAAQBAJ&pg=PA4&source... [4] https://books.google.com/books?id=J9RLuhDRWGQC&pg=PR6&source... If you're on a budget, check out the free ones like [1] Book of Proof by Richard Hammack, [2] Math Foundations of Computing by Keith Schwarz [1] https://www.people.vcu.edu/~rhammack/BookOfProof/ [2] https://web.stanford.edu/class/cs103/notes/Mathematical%20Fo... |
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Its made me realize that critical thinking is just breaking down logic to its smallest component form. And having some means of expressing different ways of organizing those components. Logic applies to all things, so time spent learning math is always useful.
I'm trying to make math derivations / critical thinking something I can do without trying, so its easier for me to pick up more complex topics and actually understand what's going on.