Discrete Algorithmic Mathematics Third Edition by Stephen B. Maurer and Anthony Ralston: A Review
Discrete Algorithmic Mathematics is a well-known and highly regarded textbook for undergraduate discrete mathematics courses. The third edition, published in 2005 by A K Peters/CRC Press, is a thorough revision of the previous editions, with new or extended discussions of order notation, generating functions, chaos, aspects of statistics, and computational biology. The book is written in a lively, clear style that talks to the reader, and is unique for its emphasis on algorithmics and the inductive and recursive paradigms as central mathematical themes. It also includes a broad variety of applications, not just to mathematics and computer science, but to natural and social science as well.
The book covers topics such as logic, sets, relations, functions, induction, recursion, combinatorics, graph theory, number theory, cryptography, algebraic structures, Boolean algebra, automata theory, languages, and computability. Each chapter contains definitions, theorems, proofs, examples, exercises, historical notes, and references. The book also provides a manual of selected solutions for sale to students (see sidebar), and a complete solution manual for free to instructors who have adopted the book as a required text.
Discrete Algorithmic Mathematics is an ideal textbook for students who want to learn discrete mathematics with an emphasis on algorithms and problem-solving. It is also a valuable reference for researchers and practitioners who use discrete mathematics in their work. The book is suitable for a one-semester course or a two-semester sequence, depending on the instructor's preference and the level of the students.
If you are interested in learning more about Discrete Algorithmic Mathematics Third Edition by Stephen B. Maurer and Anthony Ralston, you can visit the publisher's website[^1^], read a preview on Google Books[^2^], or check out the book's page on Taylor & Francis[^3^]. You can also order the book online from various sellers such as Amazon.com[^2^], Barnes & Noble[^2^], Books-A-Million[^1^], or IndieBound[^1^].
In this section, we will review some of the main features and topics of Discrete Algorithmic Mathematics Third Edition by Stephen B. Maurer and Anthony Ralston.
Features of the Book
Discrete Algorithmic Mathematics has several features that make it a distinctive and effective textbook for discrete mathematics. Some of these features are:
The book is organized around the themes of algorithmics, induction, and recursion, which are essential tools for discrete mathematics and computer science. The book shows how these themes are interconnected and how they can be used to solve various problems.
The book uses a conversational style that engages the reader and explains the concepts and techniques in a clear and intuitive way. The book also uses humor, anecdotes, and historical notes to make the material more interesting and memorable.
The book provides a wide range of applications of discrete mathematics to various fields of science and technology, such as cryptography, coding theory, graph algorithms, computational geometry, computational biology, chaos theory, statistics, and social choice theory. The book also discusses some open problems and challenges in discrete mathematics and computer science.
The book contains many examples and exercises that illustrate the concepts and techniques and test the reader's understanding and skills. The exercises range from simple to challenging, and some of them are marked with stars to indicate their difficulty level. The book also provides hints and solutions for some of the exercises.
The book includes references to other sources of information and further reading for each chapter. The book also provides a comprehensive index and a glossary of terms.
Topics of the Book
Discrete Algorithmic Mathematics covers a broad spectrum of topics in discrete mathematics and computer science. Some of the topics are:
Logic: The book introduces the basic concepts and methods of logic, such as propositions, truth values, truth tables, logical connectives, logical equivalence, implication, tautologies, contradictions, validity, soundness, arguments, proofs, quantifiers, predicates, sets, set operations, Venn diagrams, Russell's paradox, Boolean functions, Boolean expressions, Karnaugh maps, logic circuits, logic gates, De Morgan's laws.
Relations: The book discusses the properties and types of relations, such as reflexivity, symmetry, transitivity, antisymmetry, equivalence relations, equivalence classes, partitions, partial orders, total orders, linear orders, aa16f39245