Mathematical reasoning¶

Five ranked references. Rank 1 is the default spine, not a requirement to read all five.

1 | How to Prove It: A Structured Approach¶

Daniel J. Velleman | Primary spine | Undergraduate

The cleanest transition from calculation to proof: logic, quantifiers, sets, functions, relations, induction, proof construction.

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2 | Book of Proof¶

Richard Hammack | Open primary / practice | Undergraduate

Excellent proof apprenticeship with abundant exercises; unusually strong legal free option.

Amazon search | Full open text

3 | Mathematical Proofs: A Transition to Advanced Mathematics¶

Gary Chartrand, Albert D. Polimeni, Ping Zhang | Depth | Undergraduate

Broad proof toolkit with a conventional course structure; useful for systematic drill.

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4 | How to Read and Do Proofs¶

Daniel Solow | Technique | Undergraduate

Compact and methodical; good for learning proof moves and debugging failed arguments.

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5 | Proofs: A Long-Form Mathematics Textbook¶

Jay Cummings | Alternate voice | Undergraduate

Conversational but rigorous; strong for independent learners who need motivation plus many examples.

Amazon search | No legal full text located

Strongest legal free/open path¶

• Book of Proof: Full open text: open