Experimental Mathematics with Maple: 1st Edition (Paperback) book cover

Experimental Mathematics with Maple

1st Edition

By Franco Vivaldi

Chapman and Hall/CRC

240 pages | 25 B/W Illus.

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Paperback: 9781584882336
pub: 2001-02-20
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Description

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.

Table of Contents

WHAT IS MAPLE?

INTEGERS AND RATIONALS

Integers

Arithmetical Expressions

Some Maple

Divisibility

Rationals

Primes

Standard Library Functions

SETS AND FUNCTIONS

Sets

Sets with Maple

Functions

User-Defined Functions

SEQUENCES

Basics

Sequences with Maple

Plotting the Elements of a Sequence

Periodic and Eventually Periodic Sequences

Some Non-Periodic Sequences

Basic Counting Sequences

Sequences Defined Recursively

REAL AND COMPLEX NUMBERS

Digits of Rationals

Real Numbers

Random and Pseudo-Random Digits

Complex Numbers

Standard Library Functions

STRUCTURE OF EXPRESSIONS

Analysis of an Expression

More on Substitutions

Functions Acting on Operands of Expressions

POLYNOMIALS AND RATIONAL FUNCTIONS

Polynomials

Polynomial Arithmetic

Rational Functions

Manipulating Polynomials and Rational Functions

Partial Fractions Decomposition

FINITE SUMS AND PRODUCTS

Basics

Sums and Products with Maple

Symbolic Evaluation of Sums and Products

Double Sums and Products

Sums and Products as Recursive Sequences

ELEMENTS OF PROGRAMMING

Iteration

Study of an Eventually Periodic Sequence

Conditional Execution

Procedures

VECTOR SPACES

Cartesian Product of Sets

Vector Spaces

Vectors with Maple

Matrices

Matrices with Maple

MODULAR ARITHMETIC

A Modular System

Arithmetic of Equivalence Classes

Some Arithmetical Constructions in Fp

SOME ABSTRACT STRUCTURES

The Axioms of Arithmetic

Metric Spaces

Rings and Fields

Vector Spaces

About the Series

Chapman Hall/CRC Mathematics Series

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT021000
MATHEMATICS / Number Systems
MAT036000
MATHEMATICS / Combinatorics