[share_ebook] Discrete Mathematics and its Applications

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The third edition of this textbook has been used at more than 400 schools. Now in its fourth edition, the text retains the many strengths that have marked its success, while incorporating a variety of new features and improvements. The text is designed for use in a sophomore or junior-level introductory course in discrete mathematics, and provides an effective balance of theory and relevant applications. The strength of Dr. Rosen's approach is the thorough coverage of key areas needed for further study in computer science, electrical engineering, and mathematics. Furthermore, this edition's coverage of timely topics and modern day technology better prepares students for future coursework.

• More coverage of probability theory is included in this edition. New topics covered include the variance of a random variable and Chebyshev's inequality. Additional coverage includes a new section on generating functions and coverage of inhomogeneous linear recurrence relations.

• The text contains new coverage of important topics, such as Boolean searches, integer sequences, big-theta notation, Mersenne primes, the halting problem, variance of random variables, nonhomogeneous recurrence relations, generating functions, and the traveling salesman problem.

• Expanded coverage of open problems and new discoveries includes the discovery of new Mersenne primes in 1997 and 1998, the status of the Goldbach conjecture, the variation of the Tower of Hanoi puzzle with four pegs, and the best known algorithms for solving many problems.

• Material relevant to the Internet has been added, such as Boolean searches used by Web search engines, counting IP addresses, and the use of spanning trees in multicasting.

• The text contains an expanded treatment of mathematics logic and reasoning, with more coverage of rules of inference and proofs.

• Strong coverage of key topics involving algorithms, combinatorics, number theory, graph theory, Boolean algebra, and automata theory is included.

• Extensive examples, many taken from computing and communications, highlight important issues in discrete mathematics. The topics and applications featured in these examples are important for further studies and relevant to today's students. For example, numerous exercises and examples illustrate the application of discrete mathematics to the protocols and network architecture of the Internet.

• The text utilizes a clear writing style and accessible presentation without compromising mathematical rigor.

• Biographies of approximately 60 different contributors to discrete mathematics, ranging from ancient to living and active researchers, help students see mathematics as a human endeavor.

• A wide variety of more than 3000 exercises, including computer projects, computational explorations, and writing projects, are integrated throughout the text. Expanded exercise sets are carefully graded by level of difficulty and include both more routine and more challenging exercises. Additional routine exercises have been added to ensure there are both odd-numbered and even-numbered exercises of particular types.

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