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I thought the exact same thing you thought about the textbook, and I thought I would do it sort of like a professor does--start out with a set of notes that evo
by brentr 18y ago
I thought the exact same thing you thought about the textbook, and I thought I would do it sort of like a professor does--start out with a set of notes that evolve into a textbook over time.
I agree with the "cut the crap" out of textbooks. I think modern textbooks spend a lot of pages showing fluff. When I look at historical books, like Hardy's A Course on Pure Mathematics, I am amazed at how concise yet rigorous they are compared with today's textbooks.
- me2i81 18y agoSchaum's Outlines are usually a good source of cheap (~$15) "cut the crap" textbook alternatives. Brief explanations, then many worked problems, then more problems with answers elsewhere.
- brentr 18y agoI'm not so sure Schaum's is that great. I want to "cut the crap" but replace it with a deeper study of whatever the student is studying. I really dislike when a mathematics textbook states something like "The proof is too complicated and therefore not included." Let me be the judge of that. At least indicate where I may find a proof of a theorem if it's not included in the text. I also believe that logic and proofs should be taught much earlier in the curriculum than at present, and I don't consider the simple geometric proofs learned in high school to be a firm basis on which to start. Under my plan, something like Rudin should be what is taught as a last math class in high school. Some may say that is too ambitious. I don't think so.