## Experimental Mathematics with MapleAs 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. |

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### Contents

What is Maple? | 1 |

Sets and functions | 39 |

Sequences | 59 |

Real and complex numbers | 89 |

Polynomials and rational functions | 127 |

Finite sums and products | 147 |

Elements of programming | 163 |

Vector spaces | 185 |

Modular arithmetic | 201 |

Some abstract structures | 213 |

### Common terms and phrases

algebraic arbitrary arithmetical operations assigned behaviour binomial binomial coefficient Boolean called chapter characteristic function co-domain coefficients complex numbers Compute Consider the following Construct a function construct a user-defined coprime corresponding data type decimal digits defined definition denominator denoted display divides division do-structure domain elements equal equation evalb evalf evaluation eventually periodic Example Exercises Exercise exponentiation expression sequence factorial function factors false finite given greatest common divisor indeterminate inequality instance irem isprime logical expression loop Maple Maple function matrix modular arithmetic modulo multiplication natural numbers nonzero obtain operands option parentheses Pascal's triangle plot polynomials positive integer prime number procedure Pythagorean triple quotient radix point rational function rational number real number recursive sequence relatively prime remainder represented scalar smallest square standard library function statement subset subtraction summation sums and products surjective symbol theorem trapdoor function true user-defined function vector space Verify zero