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A Student’s Guide to the Study, Practice, and Tools of Modern Mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica® and Maple™ to MATLAB® and R. Along with a color insert, the text includes exercises and challenges to stimulate creativity and improve problem solving abilities. | Maple Experiments in Discrete Mathematics James L. Hein Portland State University March 2009 Copyright 2009 by James L. Hein. All rights reserved. Contents Preface.4 0 Introduction to Maple.5 0.1 Getting Started.5 0.2 Some Programming Tools.6 1 Elementary Notions and Notations.8 1.1 Logic Operations.8 1.2 Set Operations.i.Set operations.9 1.3 List Operations.11 1.4 String Operations.12 1.5 Graph Constructions.13 1.6 Spanning Trees .15 2 Facts About Functions.17 2.1 Sequences.17 2.2 The Map Function.18 2.3 Function Compositions .20 2.4 If-Then-Else Definitions for Functions .21 2.5 Evaluating Expressions.23 2.6 Comparing Functions.24 2.7 Type Checking .26 2.8 Properties of Functions .27 3 Construction Techniques.29 3.1 Examples of Recursively Defined Functions .29 3.2 Strings and Palindromes .31 3.3 A Recursively Defined Sorting Function .32 3.4 Binary Trees.33 3.5 Type Checking for Inductively Defined Sets .34 3.6 Inductively Defined Sets .35 3.7 Subsets and Power Sets .36 2 Contents 3 4 Binary Relations.39 4.1 Composing Two Binary Relations.39 4.2 Constructing Closures of Binary Relations.40 4.3 Testing for Closures.42 4.4 Warshall Floyd Algorithms.43 4.5 Orderings.46 5 Analysis Techniques.48 5.1 Finite Sums.48 5.2 Permutations .50 5.3 Combinations .51 5.4 Error Detection and Correction.52 5.5 The Birthday Paradox.57 5.6 It Pays to Switch .58 5.7 Markov Chains.63 5.8 Efficiency and Accumulating Parameters .63 5.9 Solving Recurrences .65 5.10 Generating Functions.68 5.11 The Factorial and GAMMA Functions.70 5.12 Orders of Growth.72 Answers to Selected Experiments .75 .
