1 Introduction
    1.1 Mathematics and its Notation
    1.2 Origins and Goals
        1.2.1 The History of MathML
        1.2.2 Limitations of HTML
        1.2.3 Requirements for Mathematics Markup
        1.2.4 Design Goals of MathML
    1.3 The Role of MathML on the Web
        1.3.1 Layered Design of Mathematical Web Services
        1.3.2 Relation to Other Web Technology
2 MathML Fundamentals
    2.1 MathML Overview
        2.1.1 Taxonomy of MathML Elements
        2.1.2 Presentation Markup
        2.1.3 Content Markup
        2.1.4 Mixing Presentation and Content
    2.2 MathML in a Document
    2.3 Some MathML Examples
        2.3.1 Presentation Examples
        2.3.2 Content Examples
        2.3.3 Mixed Markup Examples
    2.4 MathML Syntax and Grammar
        2.4.1 MathML Syntax and Grammar
        2.4.2 An XML Syntax Primer
        2.4.3 Children versus Arguments
        2.4.4 MathML Attribute Values
        2.4.5 Attributes Shared by all MathML Elements
        2.4.6 Collapsing Whitespace in Input
3 Presentation Markup
    3.1 Introduction
        3.1.1 What Presentation Elements Represent
        3.1.2 Terminology Used In This Chapter
        3.1.3 Required Arguments
        3.1.4 Elements with Special Behaviors
        3.1.5 Bidirectional Layout
        3.1.6 Summary of Presentation Elements
    3.2 Token Elements
        3.2.1 MathML characters in token elements
        3.2.2 Mathematics style attributes common to token elements
        3.2.3 Identifier (mi)
        3.2.4 Number (mn)
        3.2.5 Operator, Fence, Separator or Accent (mo)
        3.2.6 Text (mtext)
        3.2.7 Space (mspace)
        3.2.8 String Literal (ms)
        3.2.9 Accessing glyphs for characters from MathML (mglyph)
    3.3 General Layout Schemata
        3.3.1 Horizontally Group Sub-Expressions (mrow)
        3.3.2 Fractions (mfrac)
        3.3.3 Radicals (msqrt, mroot)
        3.3.4 Style Change (mstyle)
        3.3.5 Error Message (merror)
        3.3.6 Adjust Space Around Content (mpadded)
        3.3.7 Making Sub-Expressions Invisible (mphantom)
        3.3.8 Expression Inside Pair of Fences (mfenced)
        3.3.9 Enclose Expression Inside Notation (menclose)
    3.4 Script and Limit Schemata
        3.4.1 Subscript (msub)
        3.4.2 Superscript (msup)
        3.4.3 Subscript-superscript Pair (msubsup)
        3.4.4 Underscript (munder)
        3.4.5 Overscript (mover)
        3.4.6 Underscript-overscript Pair (munderover)
        3.4.7 Prescripts and Tensor Indices (mmultiscripts)
    3.5 Tables and Matrices
        3.5.1 Table or Matrix (mtable)
        3.5.2 Row in Table or Matrix (mtr)
        3.5.3 Labeled Row in Table or Matrix (mlabeledtr)
        3.5.4 Entry in Table or Matrix (mtd)
        3.5.5 Alignment Markers
    3.6 Enlivening Expressions
        3.6.1 Bind Action to Sub-Expression (maction)
4 Content Markup
    4.1 Introduction
        4.1.1 The Intent of Content Markup
        4.1.2 The Scope of Content Markup
        4.1.3 Basic Concepts of Content Markup
    4.2 Content Element Usage Guide
        4.2.1 Overview of Syntax and Usage
        4.2.2 Containers
        4.2.3 Functions, Operators and Qualifiers
        4.2.4 Relations
        4.2.5 Conditions
        4.2.6 Syntax and Semantics
        4.2.7 Semantic Mappings
        4.2.8 Constants and Symbols
        4.2.9 MathML element types
    4.3 Content Element Attributes
        4.3.1 Content Element Attribute Values
        4.3.2 Attributes Modifying Content Markup Semantics
        4.3.3 Attributes Modifying Content Markup Rendering
    4.4 The Content Markup Elements
        4.4.1 Token Elements
        4.4.2 Basic Content Elements
        4.4.3 Arithmetic, Algebra and Logic
        4.4.4 Relations
        4.4.5 Calculus and Vector Calculus
        4.4.6 Theory of Sets
        4.4.7 Sequences and Series
        4.4.8 Elementary classical functions
        4.4.9 Statistics
        4.4.10 Linear Algebra
        4.4.11 Semantic Mapping Elements
        4.4.12 Constant and Symbol Elements
5 Combining Presentation and Content Markup
    5.1 Why Two Different Kinds of Markup?
    5.2 Mixed Markup
        5.2.1 Reasons to Mix Markup
        5.2.2 Combinations that are prohibited
        5.2.3 Presentation Markup Contained in Content Markup
        5.2.4 Content Markup Contained in Presentation Markup
    5.3 Parallel Markup
        5.3.1 Top-level Parallel Markup
        5.3.2 Fine-grained Parallel Markup
        5.3.3 Parallel Markup via Cross-References: id and xref
        5.3.4 Annotation Cross-References using XLink: id and href
    5.4 Tools, Style Sheets and Macros for Combined Markup
        5.4.1 Notational Style Sheets
        5.4.2 Content-Faithful Transformations
        5.4.3 Style Sheets for Extensions
6 Characters, Entities and Fonts
    6.1 Introduction
    6.2 MathML Characters
        6.2.1 Unicode Character Data
        6.2.2 Special Characters Not in Unicode
        6.2.3 Mathematical Alphanumeric Symbols Characters
        6.2.4 Non-Marking Characters
    6.3 Character Symbol Listings
        6.3.1 Special Constants
        6.3.2 Character Tables (ASCII format)
        6.3.3 Tables arranged by Unicode block
        6.3.4 Negated Mathematical Characters
        6.3.5 Variant Mathematical Characters
        6.3.6 Mathematical Alphanumeric Symbols
        6.3.7 MathML Character Names
    6.4 Differences from Characters in MathML 1
        6.4.1 Coverage
        6.4.2 Fewer Non-marking Characters
        6.4.3 ISO Tables
        6.4.4 Status of Character Encodings
7 The MathML Interface
    7.1 Embedding MathML in other Documents
        7.1.1 MathML and Namespaces
        7.1.2 The Top-Level math Element
        7.1.3 Invoking MathML Processors
        7.1.4 Mixing and Linking MathML and HTML
        7.1.5 MathML and Graphical Markup
        7.1.6 Using CSS with MathML
    7.2 Conformance
        7.2.1 MathML Conformance
        7.2.2 Handling of Errors
        7.2.3 Attributes for unspecified data
    7.3 Future Extensions
        7.3.1 Macros and Style Sheets
        7.3.2 XML Extensions to MathML
8 Document Object Model for MathML
    8.1 Introduction
        8.1.1 hasFeature String
        8.1.2 MathML DOM Extensions

Appendices

A Parsing MathML
    A.1 Use of MathML as Well-Formed XML
    A.2 Using the MathML DTD
        A.2.1 DOCTYPE declaration for MathML
        A.2.2 DTD Parameters
        A.2.3 MathML as a DTD Module
        A.2.4 SGML
        A.2.5 The MathML DTD
    A.3 Using the MathML XML Schema
        A.3.1 Associating the MathML schema with MathML fragments
        A.3.2 Character entity references
B Content Markup Validation Grammar
C Content Element Definitions
    C.1 About Content Markup Elements
        C.1.1 The Default Definitions
        C.1.2 The Structure of an MMLdefinition.
    C.2 Definitions of MathML Content Elements
        C.2.1 Token Elements
        C.2.2 Basic Content Elements
        C.2.3 Arithmetic Algebra and Logic
        C.2.4 Relations
        C.2.5 Calculus and Vector Calculus
        C.2.6 Theory of Sets
        C.2.7 Sequences and Series
        C.2.8 Elementary Classical Functions
        C.2.9 Statistics
        C.2.10 Linear Algebra
        C.2.11 Constants and Symbol Elements
D Document Object Model for MathML
    D.1 IDL Interfaces
        D.1.1 Miscellaneous Object Definitions
        D.1.2 Generic MathML Elements
        D.1.3 Presentation Elements
        D.1.4 Content Elements
    D.2 MathML DOM Tables
        D.2.1 Chart of MathML DOM Inheritance
        D.2.2 Table of Elements and MathML DOM Representations
E MathML Document Object Model Bindings (Non-Normative)
    E.1 MathML Document Object Model IDL Binding
    E.2 MathML Document Object Model Java Binding
    E.3 MathML Document Object Model ECMAScript Binding
F Operator Dictionary (Non-Normative)
    F.1 Format of operator dictionary entries
    F.2 Indexing of operator dictionary
    F.3 Choice of entity names
    F.4 Notes on lspace and rspace attributes
    F.5 Operator dictionary entries
G Sample CSS Style Sheet for MathML (Non-Normative)
H Glossary (Non-Normative)
I Working Group Membership and Acknowledgments (Non-Normative)
    I.1 The Math Working Group Membership
    I.2 Acknowledgments
J Changes (Non-Normative)
    J.1 Changes between MathML 2.0 and MathML 2.0 Second Edition
    J.2 Changes between MathML 1.01 and MathML 2.0
K References (Non-Normative)
L Index (Non-Normative)
    L.1 MathML Elements
    L.2 MathML Attributes