Maple Experiments in Discrete Mathematics

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.
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Maple Experiments in Discrete MathematicsMaple Experiments inDiscrete MathematicsJam es L . H e i nPortland State UniversityMarch 2009Copyright © 2 0 0 9 by J a me s L . Hein. All rights re served.ContentsPreface .........................................................................................................40 Introduction to Maple ...............................................................................5 0 .1 Getting Started ...........................................................................5 0 .2 Some Programming Tools ...........................................................61 Elementary Notions and Notations ..........................................................8 1 .1 Logic Operations .........................................................................8 1 .2 Set Operations.i.Set operations .................................................9 1 .3 Lis t Operations ...........................................................................11 1 .4 String Operations........................................................................12 1 .5 Graph Constructions ...................................................................13 1 .6 Spanning Trees ...........................................................................152 Facts About Functions.............................................................................17 2 .1 Sequences ....................................................................................17 2 .2 The Map Function .......................................................................18 2 .3 Function Composi tions ...............................................................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 ...............................................................273 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 34 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 .....................................................................................465 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 M arkov Chains ............................................................................63 5 .8 Efficiency and Accumulating Parameters ..................................63 5 .9 Solving Recurrences ....................................................................65 5.10 Generating Functions ................................. ...