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  • What is Mathematics, An Elementary Approach to Ideas and Methods - Courant, Robbins, Stewart
  • How to Solve It, A New Aspect of Mathematical Solving - Polya
  • Introductory Mathematics, Algebra and Analysis - Smith
  • A Transition to Advanced Mathematics - Smith, Eggen, St. Andre
  • An Introduction to Mathematical Reasoning - Eccles
  • A Book of Proof - Hammack
  • How to Prove It, A Structured Approach - Velleman

By "Transitional", I mean a book that can take the reader from college Mathematics to the more rigorous and abstract Mathematics taught to Math Majors.

By "college Mathematics", I mean all the scientific majors that include Mathematics in the curriculum, Mathematics Major excluded. Honors Math programs, with their rigour and proofs, quite differ from other Math courses that are generally more problem-solving-based. Although Cambridge and Oxford use these books, I am asking about books used by the US education system - more than the European or any other system in the world.

ex0plan
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    How to prove it. – Git Gud Jun 04 '14 at 21:50
  • I would suggest this book. http://www.amazon.com/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0321797094/ref=sr_1_3?ie=UTF8&qid=1401918682&sr=8-3&keywords=a+transition+to+advanced+mathematics. It is by far one of the best books ive seen to get you introduced to proofs without overwhelming you. – user60887 Jun 04 '14 at 21:51
  • I don't think a book especially about proofs is required, Spivak is a good candidate I think. – Asinomás Jun 04 '14 at 21:54
  • Umm, I'm pretty sure college mathematics is exactly the mathematics taught to math majors, being that math majors are in college and all... – Ephraim Jun 04 '14 at 22:04
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    @Ephraim, actually "college math" is often the name for a course or textbook aimed at non-majors. – StumpyLeg Jun 04 '14 at 22:14
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    You really need to be more specific about where you are coming from - "college mathematics" can mean a lot of things. – Thomas Andrews Jun 04 '14 at 22:14
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    I've done problems from Spivak's Calculus, and many were even tougher than the book I used for real analysis. I would say that some book that primes your proof techniques maybe necessary rather than jumping into it. – user60887 Jun 04 '14 at 22:24
  • Spivak's are always recommended, but the question isn't about suggesting what's the best Calculus textbook may be. However the level of difficulty of problems isn't an indication of how much it was good as a problem to be asked at that particular time or in that specific form. Real Analysis has a vastly different scope and approach from "regular" college Calculus (i.e. non-math mayor Calculus) – ex0plan Jun 04 '14 at 23:17
  • I like the Courant one. – Bennett Gardiner Jun 05 '14 at 04:28
  • Pólya's is more on solution strategy in elementary settings than what you are looking for. Hammack's is free, you should take a look on it in any case. – vonbrand Jun 05 '14 at 09:47
  • @Ephraim no... There are plenty of students taking math courses that aren't math majors at any specific school – vonbrand Jun 05 '14 at 09:49
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    Feel free to add to the presented list of books if you deem it absolutely necessary. Like "Mathematical Proofs, A Transition to Advanced Mathematics - Chartrand Polimeni Zhang" which I haven't mentioned. @vonbrand Thanks. I do have access to all the books I've enumerated – ex0plan Jun 05 '14 at 10:39
  • I would add to those, Fridberg and Insell's Linear Algebra. Did magic for me. – shooting-squirrel Jun 06 '14 at 16:34
  • Wow, a zoombie. – copper.hat Dec 20 '21 at 04:51
  • Does this answer your question? Book covering introduction to mathematical proofs – Jacob Manaker Dec 20 '21 at 05:17
  • For me, it was Linear Algebra by Friedberg et al. – NicNic8 Dec 26 '21 at 15:32

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