# A Primer of Mathematical Writing

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*Steven G. Krantz*

This book is about writing in the professional mathematical
environment. While the book is nominally about
writing, it's also about how to function in the mathematical
profession. In many ways, this text complements Krantz's previous
bestseller, How to Teach Mathematics. Those who are familiar
with Krantz's writing will recognize his lively, inimitable style.

In this volume, he addresses these nuts-and-bolts issues:

- Syntax, grammar, structure, and style
- Mathematical exposition
- Use of the computer and &tex;
- E-mail etiquette
- All aspects of publishing a journal article

Krantz's frank and straightforward approach makes this book particularly suitable as a textbook. He does not avoid difficult topics. His intent is to demonstrate to the reader how to successfully operate within the profession. He outlines how to write grant proposals that are persuasive and compelling, how to write a letter of recommendation describing the research abilities of a candidate for promotion or tenure, and what a dean is looking for in a letter of recommendation. He further addresses some basic issues such as writing a book proposal to a publisher or applying for a job. Readers will find in reading this text that Krantz has produced a quality work which makes evident the power and significance of writing in the mathematics profession.

#### Reviews & Endorsements

This book is about writing in the professional mathematical environment. While the book is nominally about writing, it's also about how to function in the mathematical profession. Krantz's frank and straightforward approach makes this particularly suitable as a textbook. He does not avoid difficult topics.

-- Zentralblatt für Didaktik der Mathematik

Krantz provides brief but helpful advice on writing a survey article, an
opinion piece, a letter of recommendation, a book review, a referee's
report, a talk, a grant application, a *curriculum vitae*, a job
application, and email. He concludes his book with a chapter called 'The
modern writing environment' which discusses the use of computers, TeX,
spell checkers, etc. Krantz's book is lively, entertaining and provides
many amusing anecdotes … [an] excellent and worthy candidate for a
statistician's library … more useful on your personal bookshelf than in a
shared library, so it can be consulted regularly.

-- Australian and New Zealand Journal of Statistics

Krantz, a prolific and distinguished mathematical author, discourses engagingly (yet seriously) on the art and etiquette of virtually all types of writing an academic mathematician is likely to encounter … Grammatical points, stylistic and typesetting issues, and the correct and effective use of mathematical notation are handled deftly and with good humor … [Hopefully] senior faculty will consider it mandatory reading for graduate students and even upper-division undergraduates. An enjoyable way to learn some fundamentals of good mathematical writing. Highly recommended.

-- CHOICE

Well written in a lively style and will be found useful by anybody who is aware of the power and significance of writing in the mathematical profession.

-- European Mathematical Society Newsletter

[Krantz has] expanded and elaborated the material in Halmos's article [1970] and added discussions of the uses of computer technology in mathematical writing … enjoyable to read … worth having on your bookshelf … written in a very personal style that is meant to engage the reader in a lively conversation … In addition, he has a chapter on how to write a book and sections on other sorts of professional prose such as referee's reports and letters of recommendation. In keeping with his general approach, he also has more to say about the psychological and sociological aspect of mathematical communication …

-- American Mathematical Monthly

[The book] provides a compact set of questions to consider before
undertaking the writing process, questions particularly well suited for
mathematical exposition. In addition to being of value to faculty
interested in thinking about what they write, * A Primer of
Mathematical Writing* would make an excellent gift for a graduate student
or junior colleague.

-- Journal of the American Statistical Association

#### Table of Contents

# Table of Contents

## A Primer of Mathematical Writing

- Cover Cover11 free
- Title i2 free
- Copyright iv5 free
- Table of Contents vii8 free
- Preface xi12 free
- CHAPTER 1: The Basics 118 free
- 1.1 What It Is All About 219
- 1.2 Who Is My Audience? 320
- 1.3 Writing and Thought 421
- 1.4 Say What You Mean; Mean What You Say 522
- 1.5 Proofreading, Reading for Sound, Reading for Sense 1027
- 1.6 Compound Sentences, Passive Voice 1431
- 1.7 Technical Aspects of Writing a Paper 1835
- 1.8 More Specifics of Mathematical Writing 2340
- 1.9 Pretension and Lack of Pretension 3148
- 1.10 We vs. I vs. One 3350
- 1.11 Essential Rules of Grammar, Syntax, and Usage 3451
- 1.12 More Rules of Grammar, Syntax, and Usage 4663

- CHAPTER 2: Topics Specific to the Writing of Mathematics 5976
- CHAPTER 3: Exposition 91108
- CHAPTER 4: Other Types of Writing 103120
- CHAPTER 5: Books 155172
- 5.1 What Constitutes a Good Book? 156173
- 5.2 How to Plan a Book 158175
- 5.3 The Importance of the Preface 160177
- 5.4 The Table of Contents 161178
- 5.5 Technical Aspects: The Bibliography, the Index, Appendices, etc. 162179
- 5.6 How to Manage Your Time When Writing a Book 165182
- 5.7 What to Do with the Book Once It Is Written 168185

- CHAPTER 6: The Modern Writing Environment 181198
- 6.1 Writing on a Computer 182199
- 6.2 Word Processors 187204
- 6.3 Using a Text Editor 189206
- 6.4 Spell-Checkers, Grammar Checkers, and the Like 191208
- 6.5 What Is TEX and Why Should You Use It? 194211
- 6.6 Other Document Preparation Systems 197214
- 6.7 Graphics 198215
- 6.8 The Internet and hypertext 201218
- 6.9 Collaboration by e-Mail; Uploading and Downloading 204221

- CHAPTER 7: Closing Thoughts 207224
- BIBLIOGRAPHY 211228
- INDEX 215232
- Back Cover Back Cover1241