Inhaltsangabe1 Preliminaries.- 1.1 Introduction.- 1.2 Using Mathematica.- 1.2.1 Getting Into and Out of Mathematica.- 1.2.2 Getting Help.- 1.2.3 The Syntax of Inputs.- 1.2.4 Errors.- 1.3 The Mathematica Language.- 1.3.1 Internal Forms of Expressions.- 1.3.2 Predicates and Boolean Operations.- 1.3.3 Evaluation of Expressions.- 1.3.4 Attributes.- 1.4 The Mathematica Interface.- 1.4.1 The Notebook Front End.- 1.4.2 The Command Line Interface.- 2 A Brief Overview of Mathematica.- 2.1 Numerical and Symbolic Computations.- 2.2 Functions.- 2.2.1 Functions of Number Theory.- 2.2.2 Functions of Linear Algebra.- 2.2.3 Random Number Generators.- 2.2.4 Packages.- 2.3 Graphics.- 2.3.1 Two-Dimensional Plots.- 2.3.2 Parametric Plots.- 2.3.3 Three-Dimensional Plots.- 2.4 Representation of Data.- 2.5 Programming.- 2.5.1 Example-Harmonic Numbers.- 2.5.2 Example-Perfect Numbers.- 3 List Manipulation.- 3.1 Introduction.- 3.2 Creating and Measuring Lists.- 3.2.1 List Construction.- 3.2.2 Dimensions of Lists.- 3.3 Working With the Elements of a List.- 3.3.1 Positions in a List.- 3.3.2 Extracting Elements and Rearranging Lists.- 3.4 Working with Several Lists.- 3.5 Higher-Order Functions.- 3.6 Applying Functions to Lists Repeatedly.- 3.7 Strings and Characters.- 4 Functions.- 4.1 Introduction.- 4.2 Programs as Functions.- 4.2.1 Nesting Function Calls.- 4.2.2 Value Names.- 4.3 User-Defined Functions.- 4.4 Auxiliary Functions.- 4.4.1 Compound Functions.- 4.4.2 Localizing Names.- 4.5 Anonymous Functions.- 4.6 One-Liners.- 4.6.1 The Josephus Problem.- 4.6.2 Pocket Change.- 5 Evaluation of Expressions.- 5.1 Introduction.- 5.2 Creating Rewrite Rules.- 5.2.1 The Global Rule Base.- 5.3 Expressions.- 5.3.1 Atoms.- 5.4 Patterns.- 5.4.1 Blanks.- 5.4.2 Expression Pattern-Matching.- 5.4.3 Sequence Pattern-Matching.- 5.4.4 Conditional Pattern-Matching.- 5.4.5 Alternatives.- 5.5 Term Rewriting.- 5.6 Transformation Rules.- 6 Conditional Function Definitions.- 6.1 Introduction.- 6.2 Conditional Functions.- 6.3 Example-Classifying Points.- 7 Recursion.- 7.1 Fibonacci Numbers.- 7.2 List Functions.- 7.3 Thinking Recursively.- 7.4 Recursion and Symbolic Computations.- 7.5 Gaussian Elimination.- 7.6 Trees.- 7.6.1 Binary Trees.- 7.6.2 Huffman Encoding.- 7.7 Dynamic Programming.- 7.8 Higher-Order Functions and Recursion.- 7.9 Debugging.- 7.9.1 Tracing Evaluation.- 7.9.2 Printing Variables.- 7.9.3 Common Errors.- 8 Iteration.- 8.1 Newtons Method.- 8.1.1 Do Loops.- 8.1.2 While Loops.- 8.2 Vectors and Matrices.- 8.2.1 List Component Assignment.- 8.2.2 Finding prime numbers.- 8.3 Passing Arrays to Functions.- 8.4 Gaussian Elimination Revisited.- 9 Numerics.- 9.1 Types of Numbers.- 9.1.1 Integers and Rationals.- 9.1.2 Real Numbers.- 9.1.3 Complex Numbers.- 9.1.4 Computing with Different Number Types.- 9.1.5 Digits and Number Bases.- 9.2 Random Numbers.- 9.3 Precision and Accuracy.- 9.3.1 Roundoff Errors.- 9.4 Numerical Computations.- 9.4.1 Newton's Method Revisited.- 9.4.2 Gaussian Elimination Revisited Again.- 10 Graphics Programming.- 10.1 Graphics Primitives.- 10.1.1 Two-Dimensional Graphics Primitives.- 10.1.2 Three-Dimensional Graphics Primitives.- 10.2 Graphics Directives and Options.- 10.3 Built-in Graphics Functions.- 10.3.1 The Structure of Built-in Graphics.- 10.3.2 Graphics Anomalies.- 10.3.3 Options for Built-in Graphics Functions.- 10.4 Graphics Programming.- 10.4.1 Simple Closed Paths.- 10.4.2 Drawing Trees.- 10.5 Sound.- 10.5.1 The Sound of Mathematics.- 10.5.2 White Music, Brownian Music, and Fractal Noise.- 11 Applications.- 11.1 The Random Walk.- 11.1.1 Introduction.- 11.1.2 The One-Dimensional Random Walk.- 11.1.3 The Two-Dimensional Lattice Walk.- 11.1.4 Visualizing The Two-Dimensional Lattice Walk.- 11.1.5 Numerical Analysis Of The Two-Dimensional Lattice Walk.- 11.2 The Game of Life.- 11.3 Implementing Languages.- 12 Contexts and Packages.- 12.1 Introduction.- 12.2 Using Packages.- 12.2.1 Loading Packages.- 12.2.2 Finding Out What s in a Package.- 12.3 Contexts.- 12.4

Inhaltsangabe1 Preliminaries.- 1.1 Introduction.- 1.2 Using Mathematica.- 1.2.1 Getting Into and Out of Mathematica.- 1.2.2 Getting Help.- 1.2.3 The Syntax of Inputs.- 1.2.4 Errors.- 1.3 The Mathematica Language.- 1.3.1 Internal Forms of Expressions.- 1.3.2 Predicates and Boolean Operations.- 1.3.3 Evaluation of Expressions.- 1.3.4 Attributes.- 1.4 The Mathematica Interface.- 1.4.1 The Notebook Front End.- 1.4.2 The Command Line Interface.- 2 A Brief Overview of Mathematica.- 2.1 Numerical and Symbolic Computations.- 2.2 Functions.- 2.2.1 Functions of Number Theory.- 2.2.2 Functions of Linear Algebra.- 2.2.3 Random Number Generators.- 2.2.4 Packages.- 2.3 Graphics.- 2.3.1 Two-Dimensional Plots.- 2.3.2 Parametric Plots.- 2.3.3 Three-Dimensional Plots.- 2.4 Representation of Data.- 2.5 Programming.- 2.5.1 Example-Harmonic Numbers.- 2.5.2 Example-Perfect Numbers.- 3 List Manipulation.- 3.1 Introduction.- 3.2 Creating and Measuring Lists.- 3.2.1 List Construction.- 3.2.2 Dimensions of Lists.- 3.3 Working With the Elements of a List.- 3.3.1 Positions in a List.- 3.3.2 Extracting Elements and Rearranging Lists.- 3.4 Working with Several Lists.- 3.5 Higher-Order Functions.- 3.6 Applying Functions to Lists Repeatedly.- 3.7 Strings and Characters.- 4 Functions.- 4.1 Introduction.- 4.2 Programs as Functions.- 4.2.1 Nesting Function Calls.- 4.2.2 Value Names.- 4.3 User-Defined Functions.- 4.4 Auxiliary Functions.- 4.4.1 Compound Functions.- 4.4.2 Localizing Names.- 4.5 Anonymous Functions.- 4.6 One-Liners.- 4.6.1 The Josephus Problem.- 4.6.2 Pocket Change.- 5 Evaluation of Expressions.- 5.1 Introduction.- 5.2 Creating Rewrite Rules.- 5.2.1 The Global Rule Base.- 5.3 Expressions.- 5.3.1 Atoms.- 5.4 Patterns.- 5.4.1 Blanks.- 5.4.2 Expression Pattern-Matching.- 5.4.3 Sequence Pattern-Matching.- 5.4.4 Conditional Pattern-Matching.- 5.4.5 Alternatives.- 5.5 Term Rewriting.- 5.6 Transformation Rules.- 6 Conditional Function Definitions.- 6.1 Introduction.- 6.2 Conditional Functions.- 6.3 Example-Classifying Points.- 7 Recursion.- 7.1 Fibonacci Numbers.- 7.2 List Functions.- 7.3 Thinking Recursively.- 7.4 Recursion and Symbolic Computations.- 7.5 Gaussian Elimination.- 7.6 Trees.- 7.6.1 Binary Trees.- 7.6.2 Huffman Encoding.- 7.7 Dynamic Programming.- 7.8 Higher-Order Functions and Recursion.- 7.9 Debugging.- 7.9.1 Tracing Evaluation.- 7.9.2 Printing Variables.- 7.9.3 Common Errors.- 8 Iteration.- 8.1 Newtons Method.- 8.1.1 Do Loops.- 8.1.2 While Loops.- 8.2 Vectors and Matrices.- 8.2.1 List Component Assignment.- 8.2.2 Finding prime numbers.- 8.3 Passing Arrays to Functions.- 8.4 Gaussian Elimination Revisited.- 9 Numerics.- 9.1 Types of Numbers.- 9.1.1 Integers and Rationals.- 9.1.2 Real Numbers.- 9.1.3 Complex Numbers.- 9.1.4 Computing with Different Number Types.- 9.1.5 Digits and Number Bases.- 9.2 Random Numbers.- 9.3 Precision and Accuracy.- 9.3.1 Roundoff Errors.- 9.4 Numerical Computations.- 9.4.1 Newton's Method Revisited.- 9.4.2 Gaussian Elimination Revisited Again.- 10 Graphics Programming.- 10.1 Graphics Primitives.- 10.1.1 Two-Dimensional Graphics Primitives.- 10.1.2 Three-Dimensional Graphics Primitives.- 10.2 Graphics Directives and Options.- 10.3 Built-in Graphics Functions.- 10.3.1 The Structure of Built-in Graphics.- 10.3.2 Graphics Anomalies.- 10.3.3 Options for Built-in Graphics Functions.- 10.4 Graphics Programming.- 10.4.1 Simple Closed Paths.- 10.4.2 Drawing Trees.- 10.5 Sound.- 10.5.1 The Sound of Mathematics.- 10.5.2 White Music, Brownian Music, and Fractal Noise.- 11 Applications.- 11.1 The Random Walk.- 11.1.1 Introduction.- 11.1.2 The One-Dimensional Random Walk.- 11.1.3 The Two-Dimensional Lattice Walk.- 11.1.4 Visualizing The Two-Dimensional Lattice Walk.- 11.1.5 Numerical Analysis Of The Two-Dimensional Lattice Walk.- 11.2 The Game of Life.- 11.3 Implementing Languages.- 12 Contexts and Packages.- 12.1 Introduction.- 12.2 Using Packages.- 12.2.1 Loading Packages.- 12.2.2 Finding Out What s in a Package.- 12.3 Contexts.- 12.4

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