Table of Contents
                        for
         SHORT GUIDE TO WRITING MATHEMATICS
                        by
                 Stephen B Maurer


   Preface...iv.

  Part I. Basic Forms of Mathematical Writing and Communicating...1.

   Chapter 1    Overview...2.
     Section 1.1    Writing in Mathematics?...2.
       Section 1.1.A    Why You Need It...2.
       Section 1.1.B    Why There Is Something to Learn...3.
       Section 1.1.C    Is this book for you?...4.
     Section 1.2    Thinking Like a Mathematician...5.
     Section 1.3    The Plan of This Book...7.
       Section 1.3.A    More on the Web...8.

   Chapter 2    Traditional Math Writing -- Notes, Homework, and Tests...9.
     Section 2.1    Introduction...9.
     Section 2.2    Taking Notes...9.
       Section 2.2.A    Expand Your Notes...11.
       Section 2.2.B    Detailed Examples...11.
       Section 2.2.C    Final Advice on Taking Notes...17.
     Section 2.3    Tests and Homework: General Advice...18.
       Section 2.3.A    The Purpose of Tests and Homework...18.
       Section 2.3.B    Are computations enough on tests and homework?...18.
       Section 2.3.C    If You're Stuck...19.
       Section 2.3.D    Wrong Solutions and Multiple Solutions...19.
       Section 2.3.E    Scratchwork...20.
       Section 2.3.F    How Much Simplification Should You Do?...21.
       Section 2.3.G    Keep your work...21.
     Section 2.4    Examples of Homework and Test Solutions...22.
       Section 2.4.A    Saying What you Would Do...29.
       Section 2.4.B    Existence Problems...30.
     Section 2.5    Grading Abbreviations...31.

   Chapter 3    Papers and Reports...33.
     Section 3.1    Introduction...33.
     Section 3.2    General Advice on Writing Papers...34.
       Section 3.2.A    Should you write on a computer?...34.
       Section 3.2.B    Start Early...34.
       Section 3.2.C    How to Make Yourself Start...35.
       Section 3.2.D    Know Your Audience...35.
       Section 3.2.E    Set a Clear Objective...37.
       Section 3.2.F    Make the Material Your Own...38.
       Section 3.2.G    Write a Strong Beginning...39.
       Section 3.2.H    Sectioning...40.
       Section 3.2.I    Conclusion Section...40.
       Section 3.2.J    What Not to Write...40.
     Section 3.3    Longer Papers...41.
       Section 3.3.A    Organizing Information...41.
       Section 3.3.B    Special Long-Paper Formats...41.
       Section 3.3.C    Keeping up Steam while Writing...42.
     Section 3.4    Group Work...42.
     Section 3.5    Expository and Research Papers...44.
       Section 3.5.A    What Is Research?...44.
       Section 3.5.B    How to Find What You Need to Know...45.
       Section 3.5.C    Research Papers...47.
       Section 3.5.D    Exposition...48.
     Section 3.6    Lab Reports...48.
     Section 3.7    Modeling Papers...50.
     Section 3.8    Writing for Managers and Other Lay People...53.
       Section 3.8.A    Writing in and writing about mathematics...53.
       Section 3.8.B    How to write for a lay audience...53.
     Section 3.9    Sample Introductions...56.
     Section 3.10    Sample Papers...60.
       Section 3.10.A    General comments...66.
       Section 3.10.B    Line-by-line comments on the papers...68.

   Chapter 4    Hypertext and Other Emerging Communication Formats...71.
     Section 4.1    What Is Electronic Networked Writing?...71.
       Section 4.1.A    Is Nonlinearity Good?...73.
     Section 4.2    Limitations in Posting Mathematics...73.
     Section 4.3    Learning to Do Hypermedia...76.
     Section 4.4    Some Illustrative Mathematics Web Sites...78.

   Chapter 5    Oral Reports...79.
     Section 5.1    Introduction...79.
     Section 5.2    The Keys to a Good Talk...79.
     Section 5.3    Preparing Your Talk...81.
     Section 5.4    Using Presentation Tools...82.
       Section 5.4.A    General Advice for Talk Technology...83.
       Section 5.4.B    Transparencies...83.
       Section 5.4.C    Computers as Presentation Aids...84.
     Section 5.5    Sample Presentations...85.

   Chapter 6    Revision...89.
     Section 6.1    Introduction...89.
     Section 6.2    Techniques That Work...89.
     Section 6.3    Ask Yourself Questions...90.
       Section 6.3.A    My own questions...90.
       Section 6.3.B    Countryman's Questions...92.
       Section 6.3.C    Gopen and Smith's Questions...92.
       Section 6.3.D    Questions teachers ask while grading...93.
     Section 6.4    Revising by Computer and Hand...93.
     Section 6.5    Examples of Revision...94.
       Section 6.5.A    Use Symbols...94.
       Section 6.5.B    Clarify, Shorten, Move...95.
       Section 6.5.C    Delete Entirely...96.
     Section 6.6    How Many Revisions?...96.


  Part II. Nuts and Bolts of Writing in Professional Mathematical Style...98.

   Chapter 7    Reasoning...99.
     Section 7.1    Global Issues...99.
       Section 7.1.A    Reasoning is Sequential and Must Get Somewhere...99.
       Section 7.1.B    Give One Complete Argument...100.
       Section 7.1.C    Particular to General or Vice Versa?...102.
       Section 7.1.D    Levels of Verification...103.
       Section 7.1.E    Consistent Level of Detail...104.
     Section 7.2    Local Issues...104.
       Section 7.2.A    Paragraphs...104.
       Section 7.2.B    Sentences...105.
     Section 7.3    Logic Concepts...108.
       Section 7.3.A    Converses and Other Implications...108.
       Section 7.3.B    Quantifiers...109.
       Section 7.3.C    Negation...111.
       Section 7.3.D    Logic Notation...111.
     Section 7.4    Proofs...112.
       Section 7.4.A    Proof Placement...116.
     Section 7.5    Computational Arguments...116.

   Chapter 8    Definitions...119.
     Section 8.1    Introduction...119.
     Section 8.2    Why Have Definitions?...120.
     Section 8.3    Local and Global Definitions...123.
       Section 8.3.A    Local and global in computer programs...124.
     Section 8.4    What to Define...124.
     Section 8.5    How to Write Definitions...125.
       Section 8.5.A    Choice of letters...126.
       Section 8.5.B    Formula definitions...127.
       Section 8.5.C    Parallel definitions...127.
       Section 8.5.D    Acronyms...128.
       Section 8.5.E    Type styles for definitions in this book...128.
     Section 8.6    Where to Put Definitions...128.
       Section 8.6.A    Definitions in Long Papers...129.
     Section 8.7    Dangers to Avoid...130.

   Chapter 9    Alphabetical Compendium of Special Aspects of Writing Mathematics...131.
     Section 9.1    Introduction...131.
     Section 9.2    Algorithms...131.
     Section 9.3    Credit and References...133.
       Section 9.3.A    Credit for Specific Items...134.
       Section 9.3.B    Format for References...136.
     Section 9.4    Displays...137.
       Section 9.4.A    Multiline Displays...138.
       Section 9.4.B    Explaining your displays...140.
     Section 9.5    Examples...141.
     Section 9.6    Exercises (in your writing)...141.
     Section 9.7    Expressions and Statements...142.
       Section 9.7.A    Rules for Creating Expressions...144.
       Section 9.7.B    Common confusions and their resolutions...146.
       Section 9.7.C    More about Delimiters...148.
       Section 9.7.D    Mathematical expressions in computer languages...149.
     Section 9.8    Figures...150.
       Section 9.8.A    Placing Figures...150.
     Section 9.9    Footnotes...151.
     Section 9.10    Highlighting...152.
     Section 9.11    Humor...153.
     Section 9.12    Lists...153.
     Section 9.13    The Look of the Page...154.
     Section 9.14    Numbering...158.
       Section 9.14.A    Display Numbering...159.
     Section 9.15    Say What You Mean...159.
     Section 9.16    Style...162.
       Section 9.16.A    Style Common to Math and Other Writing...162.
       Section 9.16.B    Issues Special to Mathematics...165.
       Section 9.16.C    Differences from General Writing Style...168.
     Section 9.17    Symbols and Fonts...170.
       Section 9.17.A    Fonts...172.
       Section 9.17.B    Why so many fonts?...173.
       Section 9.17.C    Multisymbol names...174.
     Section 9.18    Tables...175.
     Section 9.19    Theorems...177.
       Section 9.19.A    The Theorem Statement...178.
     Section 9.20    Voice and Gender...179.
       Section 9.20.A    He or She?...181.
     Section 9.21    Words or Symbols?...182.
     Section 9.22    Writing Tools: Computers and Hands...183.
       Section 9.22.A    General Pros and Cons of Writing with Computers...184.
       Section 9.22.B    General and Mathematical Word Processors...185.
       Section 9.22.C    Writing Mathematical Symbols and Expressions...187.
       Section 9.22.D    Creating Figures...189.

   Chapter 10    A Glossary of Mathematical Terms...190.
   Appendix: Symbol Tables...215.
   References...220.
   Index...223.