Discrete Mathematics And The Art Of Proof
DOWNLOAD
Download Discrete Mathematics And The Art Of Proof PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Discrete Mathematics And The Art Of Proof book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Discrete Mathematics And The Art Of Proof
DOWNLOAD
Author : David Reimer
language : en
Publisher:
Release Date : 2004-08-28
Discrete Mathematics And The Art Of Proof written by David Reimer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-28 with Mathematics categories.
The Art Of Proving Binomial Identities
DOWNLOAD
Author : Michael Z. Spivey
language : en
Publisher: CRC Press
Release Date : 2019-05-10
The Art Of Proving Binomial Identities written by Michael Z. Spivey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-10 with Mathematics categories.
The book has two goals: (1) Provide a unified treatment of the binomial coefficients, and (2) Bring together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients). The binomial coefficients arise in a variety of areas of mathematics: combinatorics, of course, but also basic algebra (binomial theorem), infinite series (Newton’s binomial series), differentiation (Leibniz’s generalized product rule), special functions (the beta and gamma functions), probability, statistics, number theory, finite difference calculus, algorithm analysis, and even statistical mechanics.
The Art Of Proof
DOWNLOAD
Author : Matthias Beck
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-17
The Art Of Proof written by Matthias Beck and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-17 with Mathematics categories.
The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.
Proofs That Really Count
DOWNLOAD
Author : Arthur T. Benjamin
language : en
Publisher: American Mathematical Society
Release Date : 2022-09-21
Proofs That Really Count written by Arthur T. Benjamin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-21 with Mathematics categories.
Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.
Proof And The Art Of Mathematics
DOWNLOAD
Author : Joel David Hamkins
language : en
Publisher: MIT Press
Release Date : 2021-02-23
Proof And The Art Of Mathematics written by Joel David Hamkins and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-23 with Mathematics categories.
How to write mathematical proofs, shown in fully-worked out examples. This is a companion volume Joel Hamkins's Proof and the Art of Mathematics, providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs. The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.
Discrete Mathematics With Proof
DOWNLOAD
Author : Eric Gossett
language : en
Publisher: John Wiley & Sons
Release Date : 2009-06-22
Discrete Mathematics With Proof written by Eric Gossett and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-22 with Mathematics categories.
A Trusted Guide to Discrete Mathematics with Proof?Now in a Newly Revised Edition Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include: An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofs New sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distribution Important examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databases Numerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theorem Extensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercises Combinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics.
Essential Discrete Mathematics For Computer Scientists
DOWNLOAD
Author : Harry Lewis
language : en
Publisher: Princeton University Press
Release Date : 2019-03-19
Essential Discrete Mathematics For Computer Scientists written by Harry Lewis and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-19 with Mathematics categories.
A more intuitive approach to the mathematical foundation of computer science Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. This textbook covers the discrete mathematics that every computer science student needs to learn. Guiding students quickly through thirty-one short chapters that discuss one major topic each, this flexible book can be tailored to fit the syllabi for a variety of courses. Proven in the classroom, Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof. It is fully illustrated in color, and each chapter includes a concise summary as well as a set of exercises. The text requires only precalculus, and where calculus is needed, a quick summary of the basic facts is provided. Essential Discrete Mathematics for Computer Science is the ideal introductory textbook for standard undergraduate courses, and is also suitable for high school courses, distance education for adult learners, and self-study. The essential introduction to discrete mathematics Features thirty-one short chapters, each suitable for a single class lesson Includes more than 300 exercises Almost every formula and theorem proved in full Breadth of content makes the book adaptable to a variety of courses Each chapter includes a concise summary Solutions manual available to instructors
Discrete Mathematics
DOWNLOAD
Author : Rowan Garnier
language : en
Publisher: CRC Press
Release Date : 2009-11-09
Discrete Mathematics written by Rowan Garnier and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-09 with Mathematics categories.
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.
Discrete Mathematics Proof Techniques And Mathematical Structures
DOWNLOAD
Author : Robert Clark Penner
language : en
Publisher: World Scientific Publishing Company
Release Date : 1999-10-19
Discrete Mathematics Proof Techniques And Mathematical Structures written by Robert Clark Penner and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-19 with Mathematics categories.
This book offers an introduction to mathematical proofs and to the fundamentals of modern mathematics. No real prerequisites are needed other than a suitable level of mathematical maturity. The text is divided into two parts, the first of which constitutes the core of a one-semester course covering proofs, predicate calculus, set theory, elementary number theory, relations, and functions, and the second of which applies this material to a more advanced study of selected topics in pure mathematics, applied mathematics, and computer science, specifically cardinality, combinatorics, finite-state automata, and graphs. In both parts, deeper and more interesting material is treated in optional sections, and the text has been kept flexible by allowing many different possible courses or emphases based upon different paths through the volume.
Proof And The Art Of Mathematics
DOWNLOAD
Author : Joel David Hamkins
language : en
Publisher: MIT Press
Release Date : 2021-02-23
Proof And The Art Of Mathematics written by Joel David Hamkins and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-23 with Mathematics categories.
How to write mathematical proofs, shown in fully-worked out examples. This is a companion volume Joel Hamkins's Proof and the Art of Mathematics, providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs. The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.