Discrete And Algebraic Structures
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Fundamental Structures of Algebra and Discrete Mathematics
Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.
Discrete and Algebraic Structures
This textbook presents the topics typically covered in a standard course on discrete structures. It is aimed at students of computer science and mathematics (teaching degree and Bachelor's/Master's) and is designed to accompany lectures, for self-study, and for exam preparation. Through explanatory introductions to definitions, numerous examples, counterexamples, diagrams, cross-references, and outlooks, the authors manage to present the wide range of topics concisely and comprehensibly. Numerous exercises facilitate the deepening of the material. Due to its compact presentation of all important discrete and algebraic structures and its extensive index, the book also serves as a reference for mathematicians, computer scientists, and natural scientists. Contents: From propositional and predicate logic to sets and combinatorics, numbers, relations and mappings, graphs, to the rich spectrum of algebraic structures, and a brief introduction to category theory. Additional chapters include rings and modules as well as matroids. This book is a translation of the second German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so the book may read stylistically differently from a conventional translation.
Applied Discrete Structures
''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''--