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I recently read about the Moore method for learning mathematics (Moore method Wikipedia) and wanted to apply it to my own learning (undergraduate level). However, I am unable to find any books that follow such a method or something similar.

Specifically, I'm looking for books that introduce the reader to important mathematical concepts through problems/questions rather than blocks of text (for instance, instead of the book proving Lagrange's theorem in group theory, the reader is presented with a question which guides the reader by introducing the definition of cosets etc., so that the reader can prove it themself). I am not very picky about the topic, for I have not been able to find such books on any topic so far. Any recommendations? Thanks.

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  • $\begingroup$ You should also look for "guided inquiry" books $\endgroup$
    – seeker
    Commented Jul 15, 2015 at 9:36
  • $\begingroup$ Elements of Abstract Algebra written by Allan Clark is probably such a book. $\endgroup$
    – user1551
    Commented Nov 3, 2020 at 13:22

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It’s long out of print, but John Greever’s Theory and Examples of Point-Set Topology is such a book. He does prove a few of the most difficult theorems and treat some of the more complicated examples in detail, but for the most part he gives you the definitions and the statements of the theorems, and you have to supply the proofs.

He wrote it because that’s how he taught the undergraduate topology course: at each class meeting he’d simply ask the next student on the roster to present the next theorem, and we were supposed to work far enough ahead to be prepared. (I took the course when the book was still in manuscript; it was one of the most enjoyable courses I’ve ever had, though I suspect that quite a few of my fellow students had a different opinion!)

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Coursera has a course called Introduction to mathematical thinking by Stanford math professor Keith Devlin. He has a book by the same name you can buy it on Abebooks.com, it's print to order for about 12 bucks. Or you can audit the course for free. As an introduction they have a video on inquiry-based learning which is similar to the Moore method but not completely. Video Creativity in Mathematics and the Moore method

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I found the recently published book "Topology Through Inquiry" here: https://math.hmc.edu/su/topology-through-inquiry/

I actually don't know anything about this book (yet) but am posting this answer in case someone else like me finds this question. I continued my internet search and just stopped here to post what I've found.

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