The Mathematica Book Online

The Mathematica Book

The Mathematica book, is the classic Mathematica (Wolfram language) manual.

It was a comprehensive Mathematica manual, over one thousand pages. e.g. in 1996, third edition for Mathematica v3, is 1427 pages, that are shipped with every copy of Mathematica. I read it 3 times, cover-to-cover, in different years, in 1990s.

Since 2004, the book is no longer printed. It moved online.

Editions

• 1988 Mathematica: A System for Doing Mathematics by Computer, First Edition.
• 1991 Mathematica: A System for Doing Mathematics by Computer, Second Edition
• 1996 The Mathematica Book, Third Edition
• 1999 The Mathematica Book, Fourth Edition. Buy at amazon
• 2003 The Mathematica Book, Fifth Edition. Buy at amazon

The Mathematica Book Chapters Online

Here i try to collect the book contents together as book Table of Contents. They are known as Tech Notes in the Wolfram Language online documentation.

Lists

Manipulating Lists https://reference.wolfram.com/language/tutorial/ManipulatingLists.html

• Constructing Lists
• Partitioning and Padding Lists
• Manipulating Lists by Their Indices
• Sparse Arrays: Manipulating Lists
• Nested Lists

Lists https://reference.wolfram.com/language/tutorial/Lists.html

• Making Lists of Objects
• Adding, Removing, and Modifying List Elements
• Collecting Objects Together
• Combining Lists
• Making Tables of Values
• Lists as Sets
• Manipulating Elements of Lists
• Rearranging Lists
• Vectors and Matrices
• Grouping and Combining Elements of Lists
• Getting Pieces of Lists
• Ordering in Lists
• Testing and Searching List Elements
• Rearranging Nested Lists

Expressions

Expressions https://reference.wolfram.com/language/tutorial/Expressions.html

• Everything Is an Expression
• Manipulating Expressions like Lists
• The Meaning of Expressions
• Expressions as Trees
• Special Ways to Input Expressions
• Levels in Expressions
• Parts of Expressions

Function

Functional Operations https://reference.wolfram.com/language/tutorial/FunctionalOperations.html

• Function Names as Expressions
• Selecting Parts of Expressions with Functions
• Applying Functions Repeatedly
• Expressions with Heads That Are Not Symbols
• Applying Functions to Lists and Other Expressions
• Working with Operators
• Applying Functions to Parts of Expressions
• Structural Operations
• Pure Functions
• Sequences
• Building Lists from Functions

Patterns

Patterns https://reference.wolfram.com/language/tutorial/Patterns.html

• Introduction to Patterns
• Functions with Variable Numbers of Arguments
• Finding Expressions That Match a Pattern
• Optional and Default Arguments
• Naming Pieces of Patterns
• Setting Up Functions with Optional Arguments
• Specifying Types of Expression in Patterns
• Repeated Patterns
• Putting Constraints on Patterns
• Verbatim Patterns
• Patterns Involving Alternatives
• Patterns for Some Common Types of Expression
• Pattern Sequences
• An Example: Defining Your Own Integration Function
• Flat and Orderless Functions

Patterns and Transformation Rules https://reference.wolfram.com/language/tutorial/PatternsAndTransformationRules.html

• Patterns
• Clearing and Removing Objects
• Assignments
• Transformation Rules
• Types of Values

Transformation Rules and Definitions https://reference.wolfram.com/language/tutorial/TransformationRulesAndDefinitions.html

• Applying Transformation Rules
• Immediate and Delayed Definitions
• Manipulating Sets of Transformation Rules
• Functions That Remember Values They Have Found
• Making Definitions
• Associating Definitions with Different Symbols
• Special Forms of Assignment
• Defining Numerical Values
• Making Definitions for Indexed Objects
• Modifying Built‐in Functions
• Making Definitions for Functions
• Manipulating Value Lists
• The Ordering of Definitions

Evaluation

Evaluation of Expressions https://reference.wolfram.com/language/tutorial/EvaluationOfExpressions.html

• Principles of Evaluation
• Loops and Control Structures
• Reducing Expressions to Their Standard Form
• Collecting Expressions during Evaluation
• Attributes
• Tracing Evaluation
• The Standard Evaluation Procedure
• The Evaluation Stack
• Non‐Standard Evaluation
• Controlling Infinite Evaluation
• Evaluation in Patterns, Rules, and Definitions
• Interrupts and Aborts
• Evaluation in Iteration Functions
• Compiling Wolfram Language Expressions
• Conditionals

Modularity and the Naming of Things

Modularity and the Naming of Things https://reference.wolfram.com/language/tutorial/ModularityAndTheNamingOfThings.html

• Modules and Local Variables
• Contexts and Packages
• Local Constants
• Wolfram Language Packages
• How Modules Work
• Setting Up Wolfram Language Packages
• Variables in Pure Functions and Rules
• Files for Packages
• Dummy Variables in Mathematics
• Automatic Loading of Packages
• Blocks and Local Values
• Manipulating Symbols and Contexts by Name
• Blocks Compared with Modules
• Intercepting the Creation of New Symbols
• Contexts

Strings and Characters

Strings and Characters https://reference.wolfram.com/language/tutorial/StringsAndCharacters.html

• Properties of Strings
• Special Characters in Strings
• Operations on Strings
• Newlines and Tabs in Strings
• Characters in Strings
• Character Codes
• String Patterns
• Raw Character Encodings
• Regular Expressions

Textual Input and Output

Textual Input and Output https://reference.wolfram.com/language/tutorial/TextualInputAndOutput.html

• Forms of Input and Output
• The Syntax of the Wolfram Language
• How Input and Output Work
• Operators without Built‐in Meanings
• The Representation of Textual Forms
• Defining Output Formats
• The Interpretation of Textual Forms
• Low‐Level Input and Output Rules
• Short and Shallow Output
• Generating Unstructured Output
• String‐Oriented Output Formats
• Formatted Output
• Output Formats for Numbers
• Grids, Rows, and Columns in the Wolfram Language
• Tables and Matrices
• Requesting Input
• Styles and Fonts in Output
• Messages
• Representing Textual Forms by Boxes
• International Messages
• String Representation of Boxes
• Documentation Constructs
• Converting between Strings, Boxes, and Expressions

The Structure of Graphics and Sound

The Structure of Graphics and Sound https://reference.wolfram.com/language/tutorial/TheStructureOfGraphicsAndSound.html

• The Structure of Graphics
• Coordinate Systems for Three‐Dimensional Graphics
• Two‐Dimensional Graphics Elements
• Lighting and Surface Properties
• Graphics Directives and Options
• Labeling Three‐Dimensional Graphics
• Coordinate Systems for Two‐Dimensional Graphics
• Efficient Representation of Many Primitives
• Labeling Two‐Dimensional Graphics
• Formats for Text in Graphics
• Insetting Objects in Graphics
• Graphics Primitives for Text
• Density and Contour Plots
• The Representation of Sound
• Three‐Dimensional Graphics Primitives
• Exporting Graphics and Sounds
• Three‐Dimensional Graphics Directives
• Importing Graphics and Sounds

Manipulating Notebooks

Manipulating Notebooks ManipulatingNotebooks

• Cells as Wolfram Language Expressions
• Styles and the Inheritance of Option Settings
• Notebooks as Wolfram Language Expressions
• Options for Cells
• Manipulating Notebooks from the Kernel
• Text and Font Options
• Manipulating the Front End from the Kernel
• Options for Expression Input and Output
• Front End Tokens
• Options for Notebooks
• Executing Notebook Commands Directly in the Front End
• Global Options for the Front End
• The Structure of Cells

Files and Streams

Files and Streams https://reference.wolfram.com/language/tutorial/FilesAndStreams.html

• File Names
• Streams

Files, Streams, and External Operations https://reference.wolfram.com/language/tutorial/FilesStreamsAndExternalOperations.html

• Reading and Writing Wolfram System Files
• Searching Files
• External Programs
• Searching and Reading Strings
• Streams and Low‐Level Input and Output
• Binary Files
• Naming and Finding Files
• Generating C and Fortran Expressions
• Manipulating Files and Directories
• Wolfram Language Scripts
• Reading Textual Data

Introduction to Manipulate

Introduction to Manipulate https://reference.wolfram.com/language/tutorial/IntroductionToManipulate.html

• Manipulate Is as Easy as Table
• Locator
• Symbolic Output and Step Sizes
• 3D Graphics
• Types of Controls
• All Types of Output Are Supported
• Initial Values and Labels
• Saving Definitions of Functions Used inside Manipulate
• Beautifying the Control Area
• Gamepads and Joysticks
• 2D Sliders
• Autorun
• Graphics beyond Plotting
• Bookmarking Combinations of Parameter Values

Introduction to Dynamic https://reference.wolfram.com/language/tutorial/IntroductionToDynamic.html

• The Fundamental Principle of Dynamic
• Dynamic in Options
• Dynamic and Controls
• Dynamic and Infinite Loops
• Dynamic and Other Functions
• A Good Trick to Know
• Localizing Variables in Dynamic Output
• Slow Evaluations inside Dynamic
• The Second Argument of Dynamic
• Further Reading
• Where Should Dynamic Be Placed in an Expression?

Advanced Dynamic Functionality https://reference.wolfram.com/language/tutorial/AdvancedDynamicFunctionality.html

• Module versus DynamicModule
• Synchronous versus Asynchronous Dynamic Evaluations
• Front End Ownership of DynamicModule Variable Values
• ControlActive and SynchronousUpdatingAutomatic
• Automatic Updates of Dynamic Objects
• ImageSizeCache in Dynamic
• Refresh
• One‐Sided Updating of ControlActive
• Nesting Refresh
• DynamicModule Wormholes
• Nesting Dynamic

Views https://reference.wolfram.com/language/tutorial/Views.html

• OpenerView
• Controlling the Currently Displayed Pane
• TabView
• Controlling whether a View Changes Size
• MenuView
• Dynamic Content in Views
• SlideView
• Views versus Controls
• PopupView
• FlipView versus PaneSelector versus Toggler
• FlipView

Wolfram System Internet Connectivity https://reference.wolfram.com/language/tutorial/InternetConnectivity.html

• Introduction
• Troubleshooting Connectivity Problems
• Internet Connectivity Dialog
• Further Information

Other Misc

Mathematical and Other Notation https://reference.wolfram.com/language/tutorial/MathematicalAndOtherNotation

• Mathematical Notation in Notebooks
• Letters and Letter‐like Forms
• Special Characters: Mathematical and Other Notation
• Operators
• Names of Symbols and Mathematical Objects
• Structural Elements and Keyboard Characters

Global Aspects of Wolfram System Sessions https://reference.wolfram.com/language/tutorial/GlobalAspectsOfWolframSystemSessions.html

• The Main Loop
• Memory Management
• Dialogs
• Global System Information
• Date and Time Functions
• Wolfram System Sessions

Operator Input Forms https://reference.wolfram.com/language/tutorial/OperatorInputForms.html

Wolfram Language Protocols

• WSTP and External Program Communication WSTPAndExternalProgramCommunicationOverview

• Wolfram Language LSP (Microsoft Language Server Protocol) https://github.com/kenkangxgwe/lsp-wl

Reference

• The Mathematica Book https://www.stephenwolfram.com/publications/mathematica-book/
• WOLFRAM PRODUCTS DOCUMENTATION HISTORY https://reference.wolfram.com/history/