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Programming with Mathematica 4th edition by Paul Wellin ISBN 1107009464 9781107009462

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Programming with Mathematica 4th Revised edition Edition Paul Wellin Digital Instant Download

Author(s): Paul Wellin
ISBN(s): 9781107009462, 1107009464
Edition: 4th Revised edition
File Details: PDF, 11.27 MB
Year: 2013
Language: english
SKU: EB-10312766 Category: Tag:

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Product details: 

ISBN 10: 1107009464

ISBN 13: 9781107009462

Author: Paul Wellin

Starting from first principles, this book covers all of the foundational material needed to develop a clear understanding of the Mathematica language, with a practical emphasis on solving problems. Concrete examples throughout the text demonstrate how Mathematica can be used to solve problems in science, engineering, economics/finance, computational linguistics, geoscience, bioinformatics, and a range of other fields. The book will appeal to students, researchers and programmers wishing to further their understanding of Mathematica. Designed to suit users of any ability, it assumes no formal knowledge of programming so it is ideal for self-study. Over 290 exercises are provided to challenge the reader’s understanding of the material covered and these provide ample opportunity to practice using the language. Mathematica notebooks containing examples, programs and solutions to exercises are available from www.cambridge.org/wellin.

Table of contents: 

1 An introduction to Mathematica
1.1 Overview of basic operations
Numerical and symbolic computation
Graphics and visualization
Working with data
Dynamic interactivity
Programming
1.2 Getting started
Starting up Mathematica
The notebook interface
Entering input
Mathematical expressions
Syntax of functions
Lists
Semicolons
Alternative input syntax
Comments
Errors
Getting out of trouble
The front end and the kernel
1.3 Getting help
Function information
The Documentation Center
2 The Mathematica language
2.1 Expressions
Types of expressions
Atoms
Structure of expressions
Evaluation of expressions
Exercises
2.2 Definitions
Defining variables and functions
Immediate vs. delayed assignments
Term rewriting
Functions with multiple definitions
Exercises
2.3 Predicates and Boolean operations
Predicates
Relational and logical operators
Exercises
2.4 Attributes
Exercises
3 Lists
3.1 Creating and displaying lists
List structure and syntax
List construction
Displaying lists
Arrays
Exercises
3.2 The structure of lists
Testing a list
Measuring lists
Exercises
3.3 Operations on lists
Extracting elements
Rearranging lists
List component assignment
Multiple lists
Exercises
4 Patterns and rules
4.1 Patterns
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
Creating and using replacement rules
Example: counting coins
Example: closed paths
Example: finding maxima
Exercises
4.3 Examples and applications
Finding subsequences
Sorting a list
Exercises
5 Functional programming
5.1 Introduction
5.2 Functions for manipulating expressions
Map
Apply
Thread and MapThread
The Listable attribute
Inner and Outer
Select and Pick
Exercises
5.3 Iterating functions
Nest
FixedPoint
NestWhile
Fold
Exercises
5.4 Programs as functions
Building up programs
Example: shuffling cards
Compound functions
Exercises
5.5 Scoping constructs
Localizing names: Module
Localizing values: Block
Localizing constants: With
Example: matrix manipulation
Exercises
5.6 Pure functions
Syntax of pure functions
Using pure functions
Example: searching for attributes and options
Exercises ·
5.7 Options and messages
Options
Messages
Exercises
5.8 Examples and applications
Hamming distance
The Josephus problem
Regular graphs/polygons
Protein interaction networks
Palettes for project files
Operating on arrays
Exercises
6 Procedural programming
6.1 Loops and iteration
Newton’s method
Do loops and For loops
Example: random permutations
While loops
NestWhile and NestWhileList
Exercises
6.2 Flow control
Conditional functions
Piecewise-defined functions
Which and Switch
Argument checking
Exercises
6.3 Examples and applications
Classifying points
Sieve of Eratosthenes
Sorting algorithms
Exercises
7 Recursion
7.1 Fibonacci numbers
Exercises
7.2 Thinking recursively
Length of a list
Recursion with multiple arguments
Multiplying pairwise elements
Dealing cards, recursively
Finding maxima
Higher-order functions
Exercises
7.3 Dynamic programming
Exercises
7.4 Classical examples
Merge sort
Run-length encoding
Exercises
8 Numerics
8.1 Numbers in Mathematica
Types of numbers
Digits and number bases
Random numbers
Exercises
8.2 Numerical computation
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
Sparse arrays
Packed arrays
Exercises
8.4 Examples and applications
Newton’s method revisited
Radius of gyration of a random walk
Statistical tests
Exercises
9 Strings
9.1 Structure and syntax
Character codes
Sorting lists of characters
Ordered words
Exercises
9.2 Operations on strings
Basic string operations
Strings vs. lists
Encoding text
Indexed symbols
Anagrams
Exercises
9.3 String patterns
Finding subsequences with strings
Alternatives
Exercises
9.4 Regular expressions
Word stemming
Exercises
9.5 Examples and applications
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
Graphics primitives
Graphics directives
Graphics options
Combining graphics elements
Structure of builtin graphics functions
Example: Bézier curves
Example: hypocycloids
Exercises
10.2 Efficient structures
Multi-objects
GraphicsComplex
Numeric vs. symbolic expressions
Exercises
10.3 Sound
The sound of mathematics
Sound primitives and directives
Exercises
10.4 Examples and applications
Space filling 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
11.1 Manipulating expressions
Control objects
Control wrapper
Viewers
Animating the hypocycloid
Visualizing logical operators
Exercises
11.2 The structure of dynamic expressions
Dynamic
DynamicModule
Dynamic tips
Exercises
11.3 Examples and applications
Creating interfaces for visualizing data
File openers
Dynamic random walks
Apollonius’ circle
Exercises
12 Optimizing Mathematica programs
12.1 Measuring efficiency
Evaluation time
Memory storage
12.2 Efficient programs
Low-level vs. high-level functions
Pattern matching
Reducing size of computation
Symbolic vs. numeric computation
Listability
Pure functions
Packed arrays
Exercises
12.3 Parallel processing
Basic examples
Distributing definitions across subkernels
Profiling
Exercises
12.4 Compiling
Compile
Compiling to C
Exercises
13 Applications and packages
13.1 Random walk application
Lattice walks
Off-lattice walks
RandomWalk
Error and usage messages
Visualization
Animation
Exercises
13.2 Overview of packages
Working with packages
Package location
13.3 Contexts
13.4 Creating packages
Package framework
Creating and installing the package
RandomWalks package
Running the package

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