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انتشارات: Pearson Education

اثر: Ralph P. Grimaldi

تعداد صفحه: 1005

حجم: 12.5MB

جلد کتاب

توضیحات کتاب (خلاصه پیشگفتار):

The technological advances of the last four decades have resulted in many changes in the undergraduate curriculum. These changes have fostered the development of many single-semester and multiple-semester courses where some of the following are introduced:

1. Discrete methods that stress the finite nature inherent in many problems and structures;

2. Combinatorics — the algebra of enumeration, or counting, with its fascinating interrelations with so many finite structures;

3. Graph theory with its applications and interrelations with areas such as data structures and methods of optimization; and

4. Finite algebraic structures that arise in conjunction with disciplines such as coding theory, methods of enumeration, gating networks, and combinatorial designs.

A primary reason for studying the material in any or all of these four major topics is the abundance of applications one finds in the study of computer science — especially in the areas of data structures, the theory of computer languages, and the analysis of algorithms. In addition, there are also applications in engineering and the physical and life sciences, as well as in statistics and the social sciences.

The major purpose of this new edition is to continue to provide an introductory survey in both discrete and combinatorial mathematics. The coverage is intended for the beginning student, so there are a great number of examples with detailed explanations. In addition, wherever proofs are given, they too are presented with sufficient detail (with the novice in mind).

The text strives to accomplish the following objectives:

1. To introduce the student at the sophomore-junior level, if not earlier, to the topics and techniques of discrete methods and combinatorial reasoning. Problems in counting, or enumeration, require a careful analysis of structure (for example, whether or not order and repetition are relevant) and logical possibilities. There may even be a question of existence for some situations.

2. To introduce a wide variety of applications. In this regard, whenever data structures (from computer science) or structures from abstract algebra are required, only the basic theory needed for the application is developed. Furthermore, the solutions of some applications lend themselves to iterative procedures that lead to specific algorithms. The algorithmic approach to the solution of problems is fundamental in discrete mathematics, and this approach reinforces the close ties between this discipline and the area of computer science.

3. To develop the mathematical maturity of the student through the study of an area that is so different from the traditional coverage in calculus and differential equations. Here, for example, there is the opportunity to establish results by counting a certain collection of objects in more than one way. This provides what are called combinatorial identities; With regard to theorems and their proofs, in many instances an attempt has been made to motivate theorems from observations on specific examples.

4. To present an adequate survey of topics for the computer science student who will be taking more advanced courses in areas such as data structures, the theory of computer languages, and the analysis of algorithms. The coverage here on groups, rings, fields, and Boolean algebras will also provide an applied introduction for mathematics majors who wish to continue their study of abstract algebra.

The prerequisites for using this book are primarily a sound background in high school mathematics and an interest in attacking and solving a variety of problems. No particular programming ability is assumed.

دانلود


راهنمای مدرس (حل تمرینات کتاب):

Instructor's Manual-Discrete And Combinatorial Mathematics An Applied Introduction-5th Edition-By Ralph P. Grimaldi-2004

انتشارات: Pearson Education

اثر: Ralph P. Grimaldi

تعداد صفحه: 465

 

حجم: 40.2MB

آیکن نشانگر نوع فایل در سایت CEBدانلود

 

حجم: 6.23MB

آیکن نشانگر نوع فایل در سایت CEBدانلود

 


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