Experimental Mathematics with Maple

Experimental Mathematics with Maple

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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(R) 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.show more

Product details

  • Paperback | 240 pages
  • 154 x 230 x 16mm | 379.99g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 2002.
  • 25 black & white illustrations, 8 black & white tables
  • 1584882336
  • 9781584882336
  • 2,431,735

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 Spacesshow more