Author: Nancy Crisler,Gary Froelich

Publisher: Macmillan

ISBN: 071670000X

Category: Mathematics

Page: 622

View: 458

Author: Nancy Crisler,Gary Froelich

Publisher: Macmillan

ISBN: 071670000X

Category: Mathematics

Page: 622

View: 458

Listen here for author Nancy Crisler's introduction to Discrete Mathematics Through Applications. Written specifically for high school courses, Discrete Mathematics Through Applications is designed to help you put the established NCTM Standards for Discrete Math to work in your classroom, in a way that promotes active learning, critical thinking, and fully-engaged student participation. With this text, students will see the connections among mathematical topics and real-life events and situations, while sharpening their problem solving, mathematical reasoning and communication skills. The new edition adds new topics and significantly revised exercise sets and enhanced supplements.

Author: Nancy Crisler,Patience Fisher,Gary Froelich

Publisher: Macmillan

ISBN: 9780716736523

Category: Mathematics

Page: 552

View: 4716

Written specifically for the high school discrete math course, Discrete Mathematics Through Applications lets the recently revised NCTM Standards be its guide. The book focuses on the connections among mathematical topics and real-life events and situations, emphasizing problem solving, mathematical reasoning and communication.

Author: Nancy Crisler,Gary Froelich

Publisher: Macmillan Higher Education

ISBN: 1429281251

Category: Mathematics

Page: N.A

View: 8664

Listen here for author Nancy Crisler's introduction to Discrete Mathematics Through Applications. Written specifically for high school courses, Discrete Mathematics Through Applications is designed to help you put the established NCTM Standards for Discrete Math to work in your classroom, in a way that promotes active learning, critical thinking, and fully-engaged student participation. With this text, students will see the connections among mathematical topics and real-life events and situations, while sharpening their problem solving, mathematical reasoning and communication skills. The new edition adds new topics and significantly revised exercise sets and enhanced supplements.

Author: Susanna S. Epp

Publisher: Cengage Learning

ISBN: 0495391328

Category: Mathematics

Page: 984

View: 8619

Susanna Epp's DISCRETE MATHEMATICS WITH APPLICATIONS, FOURTH EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Author: H. F. Mattson

Publisher: Wiley

ISBN: 9780471606727

Category: Computers

Page: 672

View: 4914

Applauded by reviewers for its inviting, conversational style and outstanding coverage of logic and inductions, it introduces students to the topics and language of discrete mathematics and prepares them for future work in mathematics and/or computer science. Mattson develops students' mathematical thinking and overall maturity through careful presentation and development of proofs, numerous detailed examples and corresponding exercises and applications that allow students to make concrete use of the theory presented. Exercises are varied, ranging from simple problems to challenging extensions of the topics introduced.

Author: Kenneth Rosen

Publisher: McGraw-Hill Higher Education

ISBN: 007741893X

Category: Education

Page: N.A

View: 7455

Author: Thomas Koshy

Publisher: Elsevier

ISBN: 9780080477343

Category: Mathematics

Page: 1042

View: 8748

This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation. * Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations * Weaves numerous applications into the text * Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects * Includes chapter summaries of important vocabulary, formulas, and properties, plus the chapter review exercises * Features interesting anecdotes and biographies of 60 mathematicians and computer scientists * Instructor's Manual available for adopters * Student Solutions Manual available separately for purchase (ISBN: 0124211828)

Author: Martin Erickson

Publisher: CRC Press

ISBN: 1439816174

Category: Computers

Page: 280

View: 3349

Methods Used to Solve Discrete Math Problems Interesting examples highlight the interdisciplinary nature of this area Pearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics. Each chapter begins with a mathematical teaser to engage readers and includes a particularly surprising, stunning, elegant, or unusual result. The author covers the upward extension of Pascal’s triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuin’s sequence, and Rook and Queen paths and the equivalent Nim and Wythoff’s Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonacci-like sequence of composite numbers, Shannon’s theorems of information theory, higher-dimensional tic-tac-toe, animal achievement and avoidance games, and an algorithm for solving Sudoku puzzles and polycube packing problems. Exercises ranging from easy to challenging are found in each chapter while hints and solutions are provided in an appendix. With over twenty-five years of teaching experience, the author takes an organic approach that explores concrete problems, introduces theory, and adds generalizations as needed. He delivers an absorbing treatment of the basic principles of discrete mathematics.

Author: Cordelia Hall,John O'Donnell

Publisher: Springer Science & Business Media

ISBN: 1447136578

Category: Mathematics

Page: 339

View: 8009

Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools such as proof checkers. These connections are emphasised throughout the book. Software tools (see Appendix A) enable the computer to serve as a calculator, but instead of just doing arithmetic and trigonometric functions, it will be used to calculate with sets, relations, functions, predicates and inferences. There are also special software tools, for example a proof checker for logical proofs using natural deduction.

Author: Jonathan L. Gross

Publisher: CRC Press

ISBN: 1584887443

Category: Mathematics

Page: 664

View: 3072

Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course. After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces. Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences.

Author: Gordon J. Pace

Publisher: Springer Science & Business Media

ISBN: 3642298397

Category: Computers

Page: 296

View: 6952

Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circuit, a computer program or a new programming language, you need mathematics to be able to reason about the design -- its correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science. The common approach to presenting mathematical concepts and operators is to define them in terms of properties they satisfy, and then based on these definitions develop ways of computing the result of applying the operators and prove them correct. This book is mainly written for computer science students, so here the author takes a different approach: he starts by defining ways of calculating the results of applying the operators and then proves that they satisfy various properties. After justifying his underlying approach the author offers detailed chapters covering propositional logic, predicate calculus, sets, relations, discrete structures, structured types, numbers, and reasoning about programs. The book contains chapter and section summaries, detailed proofs and many end-of-section exercises -- key to the learning process. The book is suitable for undergraduate and graduate students, and although the treatment focuses on areas with frequent applications in computer science, the book is also suitable for students of mathematics and engineering.

Author: Kuldeep Singh

Publisher: Macmillan International Higher Education

ISBN: 0230345980

Category: Mathematics

Page: 944

View: 8869

This text teaches maths in a step-by-step fashion – ideal for students on first-year engineering and pre-degree courses. - Hundreds of examples and exercises, the majority set in an applied engineering context so that you immediately see the purpose of what you are learning - Introductory chapter revises indices, fractions, decimals, percentages and ratios - Fully worked solutions to every problem on the companion website at www.palgrave.com/engineering/singh plus searchable glossary, e-index, extra exercises, extra content and more!

Author: David J. Hunter

Publisher: Jones & Bartlett Publishers

ISBN: 1284106535

Category: Mathematics

Page: 548

View: 8734

Written for the one-term course, the Third Edition of Essentials of Discrete Mathematics is designed to serve computer science majors as well as students from a wide range of disciplines. The material is organized around five types of thinking: logical, relational, recursive, quantitative, and analytical. This presentation results in a coherent outline that steadily builds upon mathematical sophistication. Graphs are introduced early and referred to throughout the text, providing a richer context for examples and applications. tudents will encounter algorithms near the end of the text, after they have acquired the skills and experience needed to analyze them. The final chapter contains in-depth case studies from a variety of fields, including biology, sociology, linguistics, economics, and music.

Author: Kenneth H. Rosen

Publisher: CRC Press

ISBN: 135164405X

Category: Mathematics

Page: 1612

View: 6873

Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.

*Proofs, Structures and Applications, Third Edition*

Author: Rowan Garnier,John Taylor

Publisher: Taylor & Francis

ISBN: 1439812810

Category: Mathematics

Page: 843

View: 742

Taking an approach to the subject that is suitable for a broad readership, Discrete Mathematics: Proofs, Structures, and Applications, Third Edition provides a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. The approach is comprehensive yet maintains an easy-to-follow progression from the basic mathematical ideas to the more sophisticated concepts examined later in the book. This edition preserves the philosophy of its predecessors while updating and revising some of the content. New to the Third Edition In the expanded first chapter, the text includes a new section on the formal proof of the validity of arguments in propositional logic before moving on to predicate logic. This edition also contains a new chapter on elementary number theory and congruences. This chapter explores groups that arise in modular arithmetic and RSA encryption, a widely used public key encryption scheme that enables practical and secure means of encrypting data. This third edition also offers a detailed solutions manual for qualifying instructors. Exploring the relationship between mathematics and computer science, this text continues to provide a secure grounding in the theory of discrete mathematics and to augment the theoretical foundation with salient applications. It is designed to help readers develop the rigorous logical thinking required to adapt to the demands of the ever-evolving discipline of computer science.

Author: Martin Aigner

Publisher: American Mathematical Soc.

ISBN: 9780821886151

Category: Mathematics

Page: 388

View: 9084

The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints andsolutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level. Praise for the German edition ... This book is a well-written introduction to discrete mathematics and is highly recommended to every student ofmathematics and computer science as well as to teachers of these topics. --Konrad Engel for MathSciNet Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of theMAA for expository writing, and his book Proofs from the BOOK with Gunter M. Ziegler has been an international success with translations into 12 languages.

Author: Kenneth Rosen

Publisher: McGraw-Hill Higher Education

ISBN: 007741893X

Category: Education

Page: N.A

View: 8283

Author: Richard Johnsonbaugh

Publisher: Simon & Schuster Books For Young Readers

ISBN: 9780023607219

Category: Mathematics

Page: 800

View: 6640

This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem- solving techniques. This edition has the techniques of proofs woven into the text as a running theme and each chapter has the problem-solving corner. The text provides complete coverage of: Logic and Proofs; Algorithms; Counting Methods and the Pigeonhole Principle; Recurrence Relations; Graph Theory; Trees; Network Models; Boolean Algebra and Combinatorial Circuits; Automata, Grammars, and Languages; Computational Geometry. For individuals interested in mastering introductory discrete mathematics.