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Is there a sort of "axiomatic high school maths" course, that builds up from the basics without handwaving? i.e. that covers the actual reasons and proofs for
by hyperpallium 8y ago
Is there a sort of "axiomatic high school maths" course, that builds up from the basics without handwaving? i.e. that covers the actual reasons and proofs for things, not just the mechanics/tricks/techniques. The way geometry is taught.
Some might be beyond high school level, like fundamental theorems of arithmetic (unique prime factorization) and algebra (polynomial factors/zeros). There's also non-integer exponents, defining reals etc.
All this stuff is used in High School but must be taken on faith. Good for believers, bad for skeptics.
Or is this just Mathematics 101? [my engineering maths didn't cover it]
- rjblackman 8y agoNot a course but I believe Mathematics: Its Content, Methods and Meaning by A.D. Aleksandrov, A.N. Kolmogorov , M.A. Lavrent'ev may cover this in book form. (FWIW I have not read this, but intend to at some point)
- sonabinu 8y agoIt’s an amazing book! And very well written. Totally understandable!
- psyklic 8y agoI highly recommend the courses on brilliant.org. They are not axiomatic, but they heavily focus on building up deep insight rather than mechanical problem solving -- https://brilliant.org https://brilliant.org. That said, for a rigorous proof-based approach to high school math, you may enjoy "Basic Mathematics" by Lang: https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877 https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/03879...