How to Write Mathematics: Proofs, Papers, and Problem Sets for Students

Stop losing marks you've already earned.

You may understand the mathematics and still hand in a proof your grader cannot follow. How to Write Mathematics closes that gap. It shows students how to turn scratch work into clear proofs, full-credit problem-set solutions, and readable papers and theses.

Inside, you'll learn how to:

• unpack definitions, hypotheses, conclusions, and quantifiers;
• choose and structure direct proofs, contradiction, contrapositive, induction, cases, existence, and uniqueness;
• replace vague phrases like "clearly" with the detail a reader actually needs;
• revise weak proofs through five complete before-and-after makeovers;
• write problem-set and exam solutions that preserve partial credit;
• build mathematical papers, abstracts, notation, figures, and references;
• catch common errors with practical submission checklists.

Written for undergraduates taking their first proof course, with useful guidance for engineering, physics, and early graduate students, this is a practical handbook for writing mathematics your reader can verify.