Mathematics book that's not a textbook, but for intuition?

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  • Thread starter ColtonCM
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Does anyone know of any mathematics books that are not textbooks? Something that has problems but is more focused on building mathematical intuition rather than just laying out formulas and what not.

This is a pretty vague question/descriptor for a book, my apologies. If you need more clarification just ask me.

Thanks,

Colton
 

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  • #2
Stephen Tashi
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This is a pretty vague question/descriptor for a book, my apologies. If you need more clarification just ask me.
What level of mathematics? What subject matter? Linear Algebra? Calculus? Or do you merely want an interesting math book?
 
  • #3
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What level of mathematics? What subject matter? Linear Algebra? Calculus? Or do you merely want an interesting math book?
I think Calculus would be a good bet for right now as my mathematical knowledge does not extend beyond that.
 
  • #4
kith
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Try "What is mathematics?" from Courant.
 
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Try "What is mathematics?" from Courant.
Thanks!
 
  • #6
mathwonk
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try experiencing geometry by david henderson. and anschaulich geometrie, [or intuitive geometry], by david hilbert, english title: geometry and the imagination.
 
  • #7
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Even tho serge lang books are considered textbooks. They have given me intuitive insight in some fields of mathematics. Polya," How to Solve It," is very insightful. Helps you think in a pedagogical way how to solve problems.

Morris Kline Calculus is also intuitive. However, the author can be a bit verbose.
 
  • #8
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Even tho serge lang books are considered textbooks. They have given me intuitive insight in some fields of mathematics. Polya," How to Solve It," is very insightful. Helps you think in a pedagogical way how to solve problems.

Morris Kline Calculus is also intuitive. However, the author can be a bit verbose.
I added the Serge Lang calculus book to my wishlist as well as the other two books you mentioned. Thanks a bunch!
 
  • #9
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Hmm do you know calculus already? Before you buy please answer this question.
 
  • #10
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Hmm do you know calculus already? Before you buy please answer this question.
I've taken Calculus I and II at the college level, but I am far from possessing a "mastery" of this area of mathematics. I could benefit from reviewing certain chapters at a time from a book like this.

I want to truly develop a mastery of mathematics as a language as I work towards my astrophysics PhD (still undergraduate right now). I'm ready to commit for the years-long journey this is going to be. I've transitioned from that pre-college mindset of "ewww math problems" to actually enjoying the process of solving them.
 
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I've taken Calculus I and II at the college level, but I am far from possessing a "mastery" of this area of mathematics. I could benefit from reviewing certain chapters at a time from a book like this.

I want to truly develop a mastery of mathematics as a language as I work towards my astrophysics PhD (still undergraduate right now). I'm ready to commit for the years-long journey this is going to be. I've transitioned from that pre-college mindset of "ewww math problems" to actually enjoying the process of solving them.
Not sure if I can answer this. To understand calculus you have to work from a book like spivak or Apostol. However, as a physics major it may be too much.

I believe Kline book would be to easy for you since you have done calculus 2. The book that gave me a better understanding of calculus was the 3rd ed of thomas calculus with analytic geometry. It is a textbook, however the author explains the why in good fashion. For instance his derivation of the shell method is very easy to follow and understand, where stewart made the the proof look uggly and messy.

Not sure if you are trying to understand the application side of the math in regards to physics. Many people recommend Boas mathematical methods, however since I am a math major I have no knowledge of boas. Lang calculus book goes a bit more into detail, however having seen calculus 2 working through Spivak would be a better idea. But Spivak is more an introductory to analysis book.
 
  • #12
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I would recommend looking into multivariable calculus and differential equations after having a solid understanding of calculus. These will reinforce your understanding of calculus in general. (Definitely multivariable calculus (i.e. calc 3) before doing differential equations).

I do not know any books for these kinds of reads, however, you can look up calculus notes, calculus 2 notes, calculus 3 notes, and differential equations notes online. The ones I use are Paul's Online Notes. He has great explanations of the concepts, clear but not too rigorous proofs, plenty of worked out examples/illustrations, and all of his pdf notes are available online for free. They are categorized by chapter and are very organized. He made the set of notes for the classes he teaches, so they are geared with that in mind.

I would recommend briefly reviewing over his calculus 1 / calculus 2 notes and then moving onward.
 
  • #13
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I would recommend looking into multivariable calculus and differential equations after having a solid understanding of calculus. These will reinforce your understanding of calculus in general. (Definitely multivariable calculus (i.e. calc 3) before doing differential equations).

I do not know any books for these kinds of reads, however, you can look up calculus notes, calculus 2 notes, calculus 3 notes, and differential equations notes online. The ones I use are Paul's Online Notes. He has great explanations of the concepts, clear but not too rigorous proofs, plenty of worked out examples/illustrations, and all of his pdf notes are available online for free. They are categorized by chapter and are very organized. He made the set of notes for the classes he teaches, so they are geared with that in mind.

I would recommend briefly reviewing over his calculus 1 / calculus 2 notes and then moving onward.
I like that Paul's Notes website. Thanks.
 
  • #14
33
2
Not sure if I can answer this. To understand calculus you have to work from a book like spivak or Apostol. However, as a physics major it may be too much.

I believe Kline book would be to easy for you since you have done calculus 2. The book that gave me a better understanding of calculus was the 3rd ed of thomas calculus with analytic geometry. It is a textbook, however the author explains the why in good fashion. For instance his derivation of the shell method is very easy to follow and understand, where stewart made the the proof look uggly and messy.

Not sure if you are trying to understand the application side of the math in regards to physics. Many people recommend Boas mathematical methods, however since I am a math major I have no knowledge of boas. Lang calculus book goes a bit more into detail, however having seen calculus 2 working through Spivak would be a better idea. But Spivak is more an introductory to analysis book.
Added all those books to my wishlist too. Going to do more research before buying any of them. Thanks for the suggestions.
 

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