Includes bibliographical references (p. [687]-694) and index.

1 An introduction to Mathematica
1.1 Overview of basic operations • i
Numerical and ^mbolic computation ■ Graphics and visualization ■ Working with data • Dynamic
interactivity • Programming
1.2 Getting started • 14
Starting up Mathematica ■ The notebook interface ■ Entering input ■ Mathematical expressions • Syntax of
functions ■ Lists ■ Semicolons ■ Alternative input syntax • Comments • Errors • Getting out of trouble ■ Thefront
end and the kernel
1.3 Getting help • 25
Function information • The Documentation Center
2 The Mathematica language
2.1 Expressions • 29
Types ofexpressions • Atoms ■ Structure of expressions ■ Evaluation of expressions ■ Exercises
2.2 Definitions • 40
Defining variables and functions • Immediate vs. delayed assignments • Term rewriting • Functions with
multiple definitions • Exercises
2.3 Predicates and Boolean operations • 48
Predicates • Relational and logical operators ■ Exercises
2.4 Attributes -53 ; .
Exercises . ..
Lists
3.1 Creating and displaying lists • 58
List structure and ^ntax • List construction ■ Displaying lists ■ Arrays • Exercises
3.2 The structure of lists • 67
Testing a list ■ Measuring lists ■ Exercises
3.3 Operations on lists • 70
Extracting elements ■ Rearranging lists ■ List component assignment • Multiple lists • Exercises
Patterns and rules
4.1 Patterns • 85
Blanks ■ Pattern matching by type • Structured patterns • Sequence pattern matching ■ Conditional pattern
matching ■ Alternatives ■ Repeated patterns ■ Functions that use patterns ■ Exercises
4.2 Transformation rules • 102
Creating and using replacement rules ■ Example: counting coins ■ Example: closed paths ■ Example: finding
maxima ■ Exercises
4.3 Examples and applications • 109
Finding subsequences ■ Sorting a list • Exercises
Functional programming
5.1 Introduction • 116
5.2 Functions for manipulating expressions • 118
Map • Apply • Thread and MapThread • The Listable attribute • Inner and Outer • Select and Pick • Exercises
5.3 Iterating functions • 132
Nest • FixedPoint • NestWhile • Fold ■ Exercises
5.4 Programs as functions • 137
Building up programs • Example: shuffling cards • Compound Junctions • Exercises
5.5 Scoping constructs • 146
Localizing names: Module ■ Localizing values: Block ■ Localizing constants: With ■ Example: matrix
manipulation ■ Exercises
5.6 Pure functions -153
Syntax of pure functions • Using pure Junctions ■ Example: searching for attributes and options • Exercises •
57 Options and messages • 164
Options ■ Messages ■ Exercises
5.8 Examples and applications • 170
Hamming distance • The Josephus problem • Regular graphs/polygons ■ Protein interaction networks ■ Palettes
for projectfiles ■ Operating on arrays • Exercises
6 Procedural programming
6.1 Loops and iteration * 190
Newton's method • Do loops and For loops ■ Example: random permutations • While loops • NestWhile and
NestWhileList • Exercises
6.2 Flow control • 208
Conditional functions • Piecewise-defined Junctions ■ Which and Switch • Argument checking ■ Exercises
6.3 Examples and applications • 219
Classifying points • Sieve of Eratosthenes • Sorting algorithms ■ Exercises
7 Recursion
7.1 Fibonacci numbers • 231
Exercises
7.2 Thinking recursively • 234
Length of a list ■ Recursion with multiple arguments ■ Multiplying pairwise elements • Dealing cards,
recursively • Finding maxima • Higher-order functions • Exercises
7.3 Dynamic programming • 239
Exercises
7.4 Classical examples • 244
Merge sort ■ Run-length encoding • Exercises
8 Numerics
8.1 Numbers in Mathematica -251
Types of numbers • Digits and number bases ■ Random numbers • Exercises
8.2 Numerical computation • 265
Precision and accuracy ■ Representation of approximate numbers • Exact vs. approximate numbers • High
precision vs. machine precision ■ Computations with mixed number types ■ Working with precision and
accuracy • Exercises
8.3 Arrays of numbers • 282
Sparse arrays ■ Packed arrays ■ Exercises
8.4 Examples and applications • 291
Newton's method revisited • Radius ofgyration of a random walk • Statistical tests • Exercises
9 Strings
9.1 Structure and syntax • 310
Character codes ■ Sorting lists of characters ■ Ordered words ■ Exercises
9.2 Operations on strings • 316
Basic string operations • Strings vs. lists • Encoding text • Indexed ^mbols • Anagrams • Exercises
9.3 String patterns • 325
Finding subsequences with strings ■ Alternatives ■ Exercises
9.4 Regular expressions • 332
Word stemming ■ Exercises
9.5 Examples and applications • 343
Random strings ■ Partitioning strings ■ Adler checksum • Search for substrings ■ DNA sequence analysis ■
Displaying DNA sequences ■ Blanagrams • Exercises
10 Graphics and visualization
10.1 Structure of graphics • 365
Graphics primitives ■ Graphics directives ■ Graphics options ■ Combining graphics elements ■ Structure of built-
in graphics functions • Example: Bezier curves • Example: hypocycloids • Exercises
10.2 Efficient structures • 386
Multi-objects • GraphicsComplex • Numeric vs. symbolic expressions • Exercises
10.3 Sound • 396
The sound of mathematics ■ Sound primitives and direaives ■ Exercises
10.4 Examples and applications • 402
Spacefilling plots ■ Plotting lines in space ■ Simple closed paths ■ Points in a polygon ■ Visualizing standard
deviations ■ Root plotting ■ Trend plots ■ Brownian music ■ Exercises
11 Dynamic expressions
II.I Manipulating expressions • 449
Control objects ■ Control wrapper ■ Viewers ■ Animating the hypog'cloid ■ Visualizing logical operators ■
Exercises
11.2 The structure of dynamic expressions • 470
Dynamic ■ DynamicModule ■ Dynamic tips ■ Exercises
11.3 Examples and applications • 481
Creating interfaces for visualizing data ■ File openers • Dynamic random walks • Apollonius' circle • Exercises
12 Optimizing Mathematica programs
12.1 Measuring efficiency • 494
Evaluation time • Memory stoi'age
12.2 Efficient programs • 496
Low-level vs. high-level functions ■ Pattern matching • Reducing size of computation • Symbolic vs. numeric
computation ■ Listabili^ • Pure functions • Packed arrays ■ Exercises
12.3 Parallel processing • 515
Basic examples • Distributing definitions across subkemels • Profiling • Exercises
12.4 Compiling • 523
Compile • Compiling to C • Exercises
13 Applications and packages
13.1 Random walk application • 534
Lattice walks ■ Off-lattice walks ■ RandomWalk ■ Error and usage messages ■ Visualization • Animation •
Exercises
13.2 Overview of packages -555
Working with packages • Package location
13.3 Contexts • 558
13.4 Creating packages • 563
Package framework • Creating and installing the package ■ RandomWalks package • Running the package •
Exercises