Mathematical Writing

Franco Vivaldi

This book provides instruction on the art of writing mathematics, which is a vital – and challenging – ability for any mathematics student.

The book’s first part is an informal introduction to fundamental writing ideas, followed by a study of the most important mathematical dictionary entries. The fundamentals of writing are learned step by step, beginning with single words and progressing through phrases, sentences, and paragraphs before moving on to short compositions as the final step. These may stand for the explanation of an idea, the summary of a presentation, or the demonstration of a theorem. Along the way, the learner will pick up skills such as developing a consistent notation, combining words and symbols in a meaningful way, writing elegant formulae, and constructing a definition.

A few components of logic and every conventional method of proving anything are covered in this book, including several variants of induction and existence proofs. The book’s final section provides guidance on various parts of writing a thesis, such as selecting a title, writing an abstract, and building a bibliography, all of which are illustrated by a significant number of real-world cases. Many exercises are provided, and over 150 come with full explanations and solutions to help with independent study.

All mathematics students interested in enhancing the quality of their homework, reports, examinations, and dissertations will find Mathematical Writing to be of great interest.