Experimental Mathematics with Maple

While discrete mathematics rapidly becomes a standard requirement in undergraduate mathematics programs, algebraic computing is now the computational tool of choice. This book merges these two trends. It introduces the foundations of discrete mathematics and assuming no previous knowledge of computing, gradually develops basic computational skills using MAPLE. The author's approach is to expose readers to a large number of concrete computational examples, encouraging them to isolate the general from the particular, to synthesize computational results, formulate conjectures, and attempt rigorous proofs. MAPLE worksheets and solutions to selected exercises are available on the Internet.

As discrete mathematics rapidly becomes a required element of undergraduate mathematics programs, algebraic software systems replace compiled languages and are now most often the computational tool of choice. Newcomers to university level mathematics, therefore, must not only grasp the fundamentals of discrete mathematics, they must also learn to use an algebraic manipulator and develop skills in abstract reasoning.Experimental Mathematics with MAPLE uniquely responds to these needs. Following an emerging trend in research, it places abstraction and axiomatization at the end of a learning process that begins with computer experimentation. It introduces the foundations of discrete mathematics and, assuming no previous knowledge of computing, gradually develops basic computational skills using the latest version of the powerful MAPLE® software. The author's approach is to expose readers to a large number of concrete computational examples and encourage them to isolate the general from the particular, to synthesize computational results, formulate conjectures, and attempt rigorous proofs. Using this approach, Experimental Mathematics with MAPLE enables readers to build a foundation in discrete mathematics, gain valuable experience with algebraic computing, and develop a familiarity with basic abstract concepts, notation, and jargon. Its engaging style, numerous exercises and examples, and Internet posting of selected solutions and MAPLE worksheets make this text ideal for use both in the classroom and for self-study.

WHAT IS MAPLE?INTEGERS AND RATIONALSIntegersArithmetical ExpressionsSome MapleDivisibilityRationalsPrimesStandard Library FunctionsSETS AND FUNCTIONSSetsSets with MapleFunctionsUser-Defined FunctionsSEQUENCESBasicsSequences with MaplePlotting the Elements of a SequencePeriodic and Eventually Periodic SequencesSome Non-Periodic SequencesBasic Counting SequencesSequences Defined RecursivelyREAL AND COMPLEX NUMBERSDigits of RationalsReal NumbersRandom and Pseudo-Random DigitsComplex NumbersStandard Library FunctionsSTRUCTURE OF EXPRESSIONSAnalysis of an ExpressionMore on SubstitutionsFunctions Acting on Operands of ExpressionsPOLYNOMIALS AND RATIONAL FUNCTIONSPolynomialsPolynomial ArithmeticRational FunctionsManipulating Polynomials and Rational FunctionsPartial Fractions DecompositionFINITE SUMS AND PRODUCTSBasicsSums and Products with MapleSymbolic Evaluation of Sums and ProductsDouble Sums and ProductsSums and Products as Recursive SequencesELEMENTS OF PROGRAMMINGIterationStudy of an Eventually Periodic SequenceConditional ExecutionProceduresVECTOR SPACESCartesian Product of SetsVector SpacesVectors with MapleMatricesMatrices with MapleMODULAR ARITHMETICA Modular SystemArithmetic of Equivalence ClassesSome Arithmetical Constructions in FpSOME ABSTRACT STRUCTURESThe Axioms of ArithmeticMetric SpacesRings and FieldsVector Spaces

Franco Vivaldi is Professor of Applied Mathematics at Queen Mary University of London. His research interests include maps over arithmetical sets (finite fields, p-adic and algebraic numbers), piecewise isometries, space discretization and round-off errors.