 | Logic for Mathematicians (International Series in Pure and Applied Mathematics) by J. Barkley Rosser
Buy used from: $17.99 [GET THE 2nd EDITION.] Here's where it starts for me. Rosser goes through the main material of Principia Mathematica illustrating principles of logic using examples from actual mathematics textbooks. This shows that 'mathematical' logic actually has something to do with the practice of mathematics long before the proofs/transition course or Davis and Hersh.
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| Why the professor can't teach: Mathematics and the dilemma of university education by Morris Kline
Buy used from: $93.58 The real reason math students have trouble with the 'transition' (and many other things).
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| A bridge to advanced mathematics by Dennis Sentilles
Buy used from: $3.90 Apparently this was the first published 'transition course' textbook.
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 | How to Read and Do Proofs: An Introduction to Mathematical Thought Processes by Daniel Solow
Buy new: $48.39 / Used from: $29.08 The first edition of this book was my first inkling that other people cared about this.
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 | Proofs and Fundamentals: A First Course in Abstract Mathematics by Ethan D. Bloch
Buy new: $49.45 / Used from: $18.98 I like this one as clear and comprehensive.
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 | Logic, Sets and Recursion by Robert L. Causey
Buy new: $116.95 / Used from: $19.80 More of a computer science approach. Introduction to formal logic and applications in mathematical proof.
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 | Mathematical Proofs: A Transition to Advanced Mathematics (2nd Edition) by Gary Chartrand
Buy new: $88.17 / Used from: $71.40 This one seems to be well respected.
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 | Discovering Higher Mathematics: Four Habits of Highly Effective Mathematicians by Alan Levine
Buy new: $115.67 / Used from: $0.92 A different approach to the transition problem.
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 | How to Prove It: A Structured Approach by Daniel J. Velleman
Buy new: $21.59 / Used from: $18.74 |
 | A Transition to Advanced Mathematics by Douglas Smith
Buy new: $138.11 / Used from: $98.00 Another that seems to be fairly standard.
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 | Reading, Writing, and Proving: A Closer Look at Mathematics (Undergraduate Texts in Mathematics) by Ulrich Daepp
Buy new: $41.90 / Used from: $38.21 I like the idea of emphasizing reading and writing in addition to proving.
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 | Mathematical Reasoning: Writing and Proof (2nd Edition) by Ted Sundstrom
Buy new: $91.18 / Used from: $53.00 |
 | An Introduction to Mathematical Reasoning by Peter J. Eccles
Buy new: $40.17 / Used from: $32.00 |
 | The Nuts and Bolts of Proofs, Third Edition: An Introduction to Mathematical Proofs by Antonella Cupillari
Buy new: $35.54 / Used from: $33.33 Seems to be popular and it's shorter than most.
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 | Introduction to Mathematical Structures and Proofs by Larry J. Gerstein
Buy new: $63.19 / Used from: $4.98 |
 | Thinking Mathematically by J. Mason
Buy new: $11.56 / Used from: $8.75 May be more a problem solving text than a proof text, but proof is discussed.
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 | Proofs from THE BOOK by Martin Aigner
Buy used from: $19.48 Nice to have a collection of proofs selected by and for mathematicians.
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 | Math Proofs Demystified by Stan Gibilisco
Buy new: $15.56 / Used from: $4.12 More a self-help book than a textbook.
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 | One Equals Zero and Other Mathematical Surprises: Paradoxes, Fallacies, Mind Booglers by Nitsa Movshovitz-Hadar
Buy new: $15.95 / Used from: $7.88 You're doing it wrong.
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