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I have to teach the "bridge" course for junior level math and math ed majors on proofs and logic, and need to find a book. I do not like books that are mathematically vacuous.

I.e. I want one that teaches how to prove things and then actually proves something of mathematical interest, like some modular arithmetic, and hopefully also some elementary analysis (every continuous function on a closed bounded interval is bounded?). A book that spends 100 or 200 pages still puffing about sets, logic, and injective vs. surjective functions turns me off.

I have another difficult requirement: the book should not set the poor student back 100 or 120 dollars, as several otherwise reasonable ones do (e.g. Bond and Keane). To me it is a crime that a fluffy book like that should cost more than Spivak's great calculus book.

At the moment I am tempted to use a small, relatively inexpensive ($36), and intellectually lightweight book by Velleman, for the logic, but combined with the very substantial and cheap ($15) classic: What is Mathematics?" by Courant and Robbins for the actual mathematical content.

I learned the propositional calculus myself in high school out of allendoerfer and oakley's excellent Principles of Mathematics. This also included complex numbers (invaluable), groups rings and fields (just the definitions, almost worthless), analytic geometry, probability, and calculus.

Unfortunately this is out of print. And one is always afraid that a book written in the 50's may be unreadably difficult for todays average student, since it tends to assume a decent high school education, now all too rare.

I taught the course successfully in the 70's out of Robert Stoll's book, something like Sets, Functions and Logic (which in spite of the title did prove the Bolzano Weiewrstrass theorem.) It too is apparently out of print.

Any suggestions?

I.e. I want one that teaches how to prove things and then actually proves something of mathematical interest, like some modular arithmetic, and hopefully also some elementary analysis (every continuous function on a closed bounded interval is bounded?). A book that spends 100 or 200 pages still puffing about sets, logic, and injective vs. surjective functions turns me off.

I have another difficult requirement: the book should not set the poor student back 100 or 120 dollars, as several otherwise reasonable ones do (e.g. Bond and Keane). To me it is a crime that a fluffy book like that should cost more than Spivak's great calculus book.

At the moment I am tempted to use a small, relatively inexpensive ($36), and intellectually lightweight book by Velleman, for the logic, but combined with the very substantial and cheap ($15) classic: What is Mathematics?" by Courant and Robbins for the actual mathematical content.

I learned the propositional calculus myself in high school out of allendoerfer and oakley's excellent Principles of Mathematics. This also included complex numbers (invaluable), groups rings and fields (just the definitions, almost worthless), analytic geometry, probability, and calculus.

Unfortunately this is out of print. And one is always afraid that a book written in the 50's may be unreadably difficult for todays average student, since it tends to assume a decent high school education, now all too rare.

I taught the course successfully in the 70's out of Robert Stoll's book, something like Sets, Functions and Logic (which in spite of the title did prove the Bolzano Weiewrstrass theorem.) It too is apparently out of print.

Any suggestions?

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