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I’m self-studying physics and mathematics out of interest and I am looking for some non-rigorous (text)books on mathematics. Perhaps one book covering all areas relevant to physics or separate books in the areas of non-linear dynamics, differential equations, differential geometry, group theory, etc. I am explicitly looking for non-rigorous, intuitive approaches to these fields. I feel overly rigorous books make the material needlessly difficult (to me often impossible) and slow to read. I am looking for things in the style of student’s guides, such as Dan Fleisch’s “A Student’s guide to vectors and tensors” but then more expanded: https://www.goodreads.com/book/show/11925464-a-student-s-guide-to-vectors-and-tensors?ac=1&from_search=true

Also, a mathematics book that shows the bigger picture on mathematics would be of interest. Something more or less popularising.

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  • $\begingroup$ Have you looked at the answers here? $\endgroup$ – knzhou Mar 30 '19 at 19:17
  • $\begingroup$ Maybe Penrose's Road to Reality? $\endgroup$ – Avantgarde Mar 30 '19 at 19:47
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    $\begingroup$ To be called mathematics, it cannot be nonrigorous. Mathematicians are well aware of the dangers of heuristic/intuitive mathematics since at least the beginning of the 20th century. See the controversies surrounding the italian school of geometry, and recently nonrigorous mathematics such as the grossone numbers $\endgroup$ – yuggib Mar 30 '19 at 20:22
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I would suggest Group Theory: an Intuitive Approach by Ron Mirman. This does a nice job "talking" the reader through a lot of the material and using examples to introduce some concepts sometimes presented completely without context and thus difficult appreciate.

It is not overly rigorous and I do not think Mirman is good enough as a stand-alone text, but as a companion to go with something a little more rigorous - like Cornwell's Group theory in physics, Mirman is very useful to lessen the slope of the learning curve of this topic.

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"The Theoretical Minimum" seems aimed at what you seek. This covers all of the math subjects needed for QM and GR at an introductory textbook level with a minimum of elaboration. It assumes algebra and introductory calculus as prerequisites although it reviews some key points of those.

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  • $\begingroup$ I am looking for something in-between The Theoretical Minimum and actual rigorous textbooks still. I have read (and enjoyed) these books but I would like to dig a little deeper. Thanks for the suggestion though. $\endgroup$ – J VS Mar 30 '19 at 20:16

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