Experimental Mathematics with Maple

Franco Vivaldi

• Publisher: Chapman and Hall/CRC
• Year: 2018
• Print ISBN: 9781584882336
• eBook ISBN: 9781351990196
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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.

Chapter 1

What is Maple?

Maple is a powerful system for symbolic computation. In this chapter, we intend to give you a flavour of Maple’s capabilities by taking you through a guided tour of some Maple commands. You need a computer with a working copy of Maple software.

Starting and ending a Maple session

The procedure for starting a Maple session depends on the computer and on the details of the software installation. For instance, if you are using a window-based version of the software, you will click on Maple’s icon with the mouse. After starting a Maple session, the system will greet you with a prompt, which may look like this

>

The cursor — the symbol that indicates the place where any typing will end up (typically a bar ‘I’ or an underscore ‘_’) — will be positioned just after the cursor, waiting for input. Whenever Maple displays a prompt, it means that it is ready to accept a new command. One of these commands is quit (or done, or stop), which terminates a Maple session.

> quit

You first type it, then press the RETURN key. In a window environment, you may achieve the same result by clicking on the ‘quit’ button with the mouse. Before falling silent, Maple will display a brief summary of the resources used during the session, which need not concern you now.

A guided tour of Maple

Here are a few...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• 1 What is Maple?
• 2 Integers and rationals
• 3 Sets and functions
• 4 Sequences
• 5 Real and complex numbers
• 6 Structure of expressions
• 7 Polynomials and rational functions
• 8 Finite sums and products
• 9 Elements of programming
• 10 Vector spaces
• 11 Modular arithmetic*
• 12 Some abstract structures*