## About this book

### Introduction

This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student.

The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition.

Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150 of them have complete solutions, to facilitate self-study.

*Mathematical Writing* will be of interest to all mathematics students who want to raise the quality of their coursework, reports, exams, and dissertations.

### Keywords

Elementary Logic Mathematical Notation Mathematical Symbols Mathematical Thesis Mathematical Writing Proof Techniques

#### Authors and affiliations

- 1.School of Mathematical SciencesQueen Mary University of LondonLondonUnited Kingdom

#### About the authors

Franco Vivaldi is a mathematician at the University of London; his research lies at the interface between dynamical systems and number theory.

### Bibliographic information