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> Focusing on relationships, not mechanical formulas. The focus on formula memorization in schools is tragic. Once upon a time, I too have learned everything a
by weiming 8y ago
> Focusing on relationships, not mechanical formulas.
The focus on formula memorization in schools is tragic. Once upon a time, I too have learned everything about imaginary numbers ... everything, other than why the heck they are actually useful. Can do all the calculations, don't know why I am doing them.
Are there other great math textbooks/websites (Calculus level and higher, Stats, Linear Algebra, etc.) that try to do this better? For someone older than school level who wants to learn again.
- corysama 8y agoEveryone loves: 3Blue1Brown, Khan Academy, No Bullshit Guide to Linear Algebra, Linear Algebra Done Right
- chess19 8y agoYou could look for a math history book (such as "An Imaginary Tale" by Nahin) or something like the Princeton Companion to Mathematics or frankly any other popular math book written by established mathematicians.
- tangentspace 8y agoGravitation, by Misner, Thorne, Wheeler (http://a.co/dczH4eS http://a.co/dczH4eS) Fully understanding the math in this book requires a solid background in linear algebra, calculus, differential equations. But I find it an incredibly interesting book even without understanding all the math: the engaging writing style and numerous illustrations capture the intuitions behind differential geometry and relativity, but without sacrificing the rigorous mathematical formulations underlying it.
- kevin_thibedeau 8y agoThey are only really useful in the science and engineering fields that need them. That is why they remain opaque to most people. High school level pedagogy doesn't deal effectively with the useful applications of these concepts (matrices are also poorly introduced). Most of our modern technology would not be achievable without the use of complex numbers as a tool.
- tangentspace 8y agoI always liked how Feynman dealt with complex numbers in 'QED: The Strange Theory of Light and Matter'. He focuses on the intuitive concept of a particle having a spinny arrow attached, the arrow rotates as the particle flies through space. He only casually mentions that this is in fact a complex number, whereas the bulk of the text focuses on developing intuition around arrows. I read that book in high school, and it certainly influenced the direction I took in university. It helped to understand that the physical universe often appears to behave in extremely non-intuitive ways, but using mathematics we can develop a model that transforms the phenomenon into something that actually does make intuitive sense. I think some of the harder concepts in math are difficult because they act like stepping stones into aspects of our world that just don't make sense based on day-to-day experiences. But modern technology depends on this! Pedagogy is improving, but it still lags advances in technology.
- apricot 8y agoVisual Complex Analysis by Tristan Needham.