Mathematical Writing - Vivaldi Franco 2014

Preface

How to use this book

Some Writing Tips

Grammar

Numbers and Symbols

Style

Preparation and Structure

Essential Dictionary I

Sets - Defining Sets

Arithmetic

Sets of Numbers

Writing About Sets

Functions

Some Advanced Terms - Families of Sets

Sums and Products of Sets

Representations of Sets

Essential Dictionary II

Sequences

Sums

Equations and Identities

Expressions - Levels of Description

Describing Expressions

Some Advanced Terms - Sets and Sequences

More on Equations

Mathematical Sentences

Relational Operators

Logical Operators

Predicates

Quantifiers - Quantifiers and Functions

Existence Statements

Negating Logical Expressions

Relations

Describing Functions

Ordering Properties

Symmetries

Boundedness

Neighbourhoods - Neighbourhoods and Sets

Continuity

Other Properties

Describing Sequences

Writing Well

Choosing Words

Choosing Symbols

Improving Formulae

Writing Definitions

Introducing a Concept

Writing a Short Description

Forms of Argument

Anatomy of a Proof

Proof by Cases

Implications - Direct Proof

Proof by Contrapositive

Conjunctions - Loops of Implications

Proof by Contradiction

Counterexamples and Conjectures

Wrong Arguments - Examples Versus Proofs

Wrong Implications

Mishandling Functions

Writing a Good Proof

Induction

The Well-Ordering Principle

The Infinite Descent Method

Peano’s Induction Principle

Strong Induction

Good Manners with Induction Proofs

Existence and Definitions

Proofs of Existence

Unique Existence

Definitions

Recursive Definitions

Wrong Definitions

Writing a Thesis

Theses and Other Publications

Title

Abstract

Citations and Bibliography - Avoiding Plagiarism

TeX and LaTeX

Solutions to Exercises

References