Mathematical Writing

Franco Vivaldi

This book emphasizes the craft of mathematical writing, a crucial but challenging ability for any student of the subject.

The book starts off with a casual introduction to fundamental writing rules and a review of the key mathematics lexicon. Writing skills are acquired progressively, starting with the smallest units—words, phrases, sentences, and paragraphs—and working up to longer compositions. These might be a concept’s introduction, a presentation’s abstract, or a theorem’s proof. Along the way, the learner will learn how to create a clear notation, efficiently combine words and symbols, construct tidy formulas, and organize a definition.

All common proving techniques, including multiple iterations of induction and existence proofs, are presented, along with some of the logic’s basic building blocks. The book ends with recommendations for specific areas of thesis writing (choosing a title, creating an abstract, and building a bibliography) supported by numerous examples from real-world situations. Over 150 of the many exercises feature comprehensive solutions, making self-study easier.

All mathematics students who desire to improve the quality of their assignments, reports, exams, and dissertations will be interested in Mathematical Writing.