Topics In Discrete Mathematics
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Discrete Mathematics
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Author : Oscar Levin
language : en
Publisher:
Release Date : 2016-08-16
Discrete Mathematics written by Oscar Levin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-16 with categories.
This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions. Update: as of July 2017, this 2nd edition has been updated, correcting numerous typos and a few mathematical errors. Pagination is almost identical to the earlier printing of the 2nd edition. For a list of changes, see the book's website: http: //discretetext.oscarlevin.com
Introduction To Discrete Mathematics Via Logic And Proof
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Author : Calvin Jongsma
language : en
Publisher: Springer Nature
Release Date : 2019-11-08
Introduction To Discrete Mathematics Via Logic And Proof written by Calvin Jongsma and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-08 with Mathematics categories.
This textbook introduces discrete mathematics by emphasizing the importance of reading and writing proofs. Because it begins by carefully establishing a familiarity with mathematical logic and proof, this approach suits not only a discrete mathematics course, but can also function as a transition to proof. Its unique, deductive perspective on mathematical logic provides students with the tools to more deeply understand mathematical methodology—an approach that the author has successfully classroom tested for decades. Chapters are helpfully organized so that, as they escalate in complexity, their underlying connections are easily identifiable. Mathematical logic and proofs are first introduced before moving onto more complex topics in discrete mathematics. Some of these topics include: Mathematical and structural induction Set theory Combinatorics Functions, relations, and ordered sets Boolean algebra and Boolean functions Graph theory Introduction to Discrete Mathematics via Logic and Proof will suit intermediate undergraduates majoring in mathematics, computer science, engineering, and related subjects with no formal prerequisites beyond a background in secondary mathematics.
Classical Topics In Discrete Geometry
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Author : Károly Bezdek
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-23
Classical Topics In Discrete Geometry written by Károly Bezdek 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 2010-06-23 with Mathematics categories.
Geometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many important developments of mathematics in the past, as well as in present times. While focusing on modern mathematics, one has to emphasize the increasing role of discrete mathematics, or equivalently, the broad movement to establish discrete analogues of major components of mathematics. In this way, the works of a number of outstanding mathema- cians including H. S. M. Coxeter (Canada), C. A. Rogers (United Kingdom), and L. Fejes-T oth (Hungary) led to the new and fast developing eld called discrete geometry. One can brie y describe this branch of geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. This, as a classical core part, also includes the theory of polytopes and tilings in addition to the theory of packing and covering. D- crete geometry is driven by problems often featuring a very clear visual and applied character. The solutions use a variety of methods of modern mat- matics, including convex and combinatorial geometry, coding theory, calculus of variations, di erential geometry, group theory, and topology, as well as geometric analysis and number theory.
Fundamentals Of Discrete Math For Computer Science
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Author : Tom Jenkyns
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-16
Fundamentals Of Discrete Math For Computer Science written by Tom Jenkyns 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 2012-10-16 with Computers categories.
This textbook provides an engaging and motivational introduction to traditional topics in discrete mathematics, in a manner specifically designed to appeal to computer science students. The text empowers students to think critically, to be effective problem solvers, to integrate theory and practice, and to recognize the importance of abstraction. Clearly structured and interactive in nature, the book presents detailed walkthroughs of several algorithms, stimulating a conversation with the reader through informal commentary and provocative questions. Features: no university-level background in mathematics required; ideally structured for classroom-use and self-study, with modular chapters following ACM curriculum recommendations; describes mathematical processes in an algorithmic manner; contains examples and exercises throughout the text, and highlights the most important concepts in each section; selects examples that demonstrate a practical use for the concept in question.
A Beginner S Guide To Discrete Mathematics
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Author : W. D. Wallis
language : en
Publisher: Springer Science & Business Media
Release Date : 2003
A Beginner S Guide To Discrete Mathematics written by W. D. Wallis 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 2003 with Computers categories.
This introduction to discrete mathematics is aimed primarily at undergraduates in mathematics and computer science at the freshmen and sophomore levels. The text has a distinctly applied orientation and begins with a survey of number systems and elementary set theory. Included are discussions of scientific notation and the representation of numbers in computers. Lists are presented as an example of data structures. An introduction to counting includes the Binomial Theorem and mathematical induction, which serves as a starting point for a brief study of recursion. The basics of probability theory are then covered.Graph study is discussed, including Euler and Hamilton cycles and trees. This is a vehicle for some easy proofs, as well as serving as another example of a data structure. Matrices and vectors are then defined. The book concludes with an introduction to cryptography, including the RSA cryptosystem, together with the necessary elementary number theory, e.g., Euclidean algorithm, Fermat's Little Theorem.Good examples occur throughout. At the end of every section there are two problem sets of equal difficulty. However, solutions are only given to the first set. References and index conclude the work.A math course at the college level is required to handle this text. College algebra would be the most helpful.
Topics In Finite And Discrete Mathematics
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Author : Sheldon M. Ross
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-31
Topics In Finite And Discrete Mathematics written by Sheldon M. Ross and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-31 with Mathematics categories.
A text for engineering students with many examples not normally found in finite mathematics courses.
Problems And Exercises In Discrete Mathematics
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Author : G.P. Gavrilov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Problems And Exercises In Discrete Mathematics written by G.P. Gavrilov 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 2013-03-09 with Mathematics categories.
Many years of practical experience in teaching discrete mathematics form the basis of this text book. Part I contains problems on such topics as Boolean algebra, k-valued logics, graphs and networks, elements of coding theory, automata theory, algorithms theory, combinatorics, Boolean minimization and logical design. The exercises are preceded by ample theoretical background material. For further study the reader is referred to the extensive bibliography. Part II follows the same structure as Part I, and gives helpful hints and solutions. Audience:This book will be of great value to undergraduate students of discrete mathematics, whereas the more difficult exercises, which comprise about one-third of the material, will also appeal to postgraduates and researchers.
Discrete Mathematics For Computer Science
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Author : John Schlipf
language : en
Publisher:
Release Date : 2020-09-22
Discrete Mathematics For Computer Science written by John Schlipf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-22 with categories.
Discrete Mathematics for Computer Science by Gary Haggard , John Schlipf , Sue Whitesides A major aim of this book is to help you develop mathematical maturity-elusive as thisobjective may be. We interpret this as preparing you to understand how to do proofs ofresults about discrete structures that represent concepts you deal with in computer science.A correct proof can be viewed as a set of reasoned steps that persuade another student,the course grader, or the instructor about the truth of the assertion. Writing proofs is hardwork even for the most experienced person, but it is a skill that needs to be developedthrough practice. We can only encourage you to be patient with the process. Keep tryingout your proofs on other students, graders, and instructors to gain the confidence that willhelp you in using proofs as a natural part of your ability to solve problems and understandnew material. The six chapters referred to contain the fundamental topics. Thesechapters are used to guide students in learning how to express mathematically precise ideasin the language of mathematics.The two chapters dealing with graph theory and combinatorics are also core materialfor a discrete structures course, but this material always seems more intuitive to studentsthan the formalism of the first four chapters. Topics from the first four chapters are freelyused in these later chapters. The chapter on discrete probability builds on the chapter oncombinatorics. The chapter on the analysis of algorithms uses notions from the core chap-ters but can be presented at an informal level to motivate the topic without spending a lot oftime with the details of the chapter. Finally, the chapter on recurrence relations primarilyuses the early material on induction and an intuitive understanding of the chapter on theanalysis of algorithms. The material in Chapters 1 through 4 deals with sets, logic, relations, and functions.This material should be mastered by all students. A course can cover this material at differ-ent levels and paces depending on the program and the background of the students whenthey take the course. Chapter 6 introduces graph theory, with an emphasis on examplesthat are encountered in computer science. Undirected graphs, trees, and directed graphsare studied. Chapter 7 deals with counting and combinatorics, with topics ranging from theaddition and multiplication principles to permutations and combinations of distinguishableor indistinguishable sets of elements to combinatorial identities.Enrichment topics such as relational databases, languages and regular sets, uncom-putability, finite probability, and recurrence relations all provide insights regarding howdiscrete structures describe the important notions studied and used in computer science.Obviously, these additional topics cannot be dealt with along with the all the core materialin a one-semester course, but the topics provide attractive alternatives for a variety of pro-grams. This text can also be used as a reference in courses. The many problems provideample opportunity for students to deal with the material presented.
How To Think Like A Mathematician
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Author : Kevin Houston
language : en
Publisher: Cambridge University Press
Release Date : 2009-02-12
How To Think Like A Mathematician written by Kevin Houston and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-12 with Mathematics categories.
Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.
Connections In Discrete Mathematics
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Author : Steve Butler
language : en
Publisher: Cambridge University Press
Release Date : 2018-06-14
Connections In Discrete Mathematics written by Steve Butler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-14 with Mathematics categories.
Many of the best researchers and writers in discrete mathematics come together in a volume inspired by Ron Graham.