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.
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
Biography
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.
