Discrete Mathematics With Ducks
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| Author | : Oscar Levin |
| Publisher | : Createspace Independent Publishing Platform |
| Total Pages | : 342 |
| Release | : 2016-08-16 |
| Genre | : |
| ISBN | : 9781534970748 |
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.
| Author | : Sarah-Marie Belcastro |
| Publisher | : A K PETERS |
| Total Pages | : |
| Release | : 2017-08-02 |
| Genre | : |
| ISBN | : 9781138435858 |
Student Handbook for Discrete Mathematics with Ducks is a Student Reference, Review, Supplemental Learning, and Example Handbook (SRRSLEH) that mirrors the content of the author�s popular textbook Discrete Mathematics with Ducks (DMwD). This handbook provides a review of key material, illustrative examples, and new problems with accompanying solutions that are helpful even for those using a traditional discrete mathematics textbook. Every chapter in SRRSLEH matches the corresponding chapter of DMwD. Chapters in SRRSLEH contain the following: A list of the notation introduced in the corresponding chapter A list of definitions that students need to know from the corresponding chapter Theorems/facts of note appearing in the corresponding chapter A list of proof techniques introduced, with templates and/or examples given for each one A selection of examples from DMwD, written out formally and briefly rather than colloquially as in DMwD A quick refresher for any discrete math student, this handbook enables students to find information easily and reminds them of the terms and results they should know during their course. Read reviews of DMwD.
| Author | : Martin Aigner |
| Publisher | : American Mathematical Society |
| Total Pages | : 402 |
| Release | : 2023-01-24 |
| Genre | : Mathematics |
| ISBN | : 1470470632 |
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 and solutions 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 of mathematics 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 the MAA for expository writing, and his book Proofs from the BOOK with Günter M. Ziegler has been an international success with translations into 12 languages.
| Author | : Ken Levasseur |
| Publisher | : Lulu.com |
| Total Pages | : 574 |
| Release | : 2012-02-25 |
| Genre | : Computers |
| ISBN | : 1105559297 |
''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).''--
| Author | : Eric Gossett |
| Publisher | : John Wiley & Sons |
| Total Pages | : 932 |
| Release | : 2009-06-22 |
| Genre | : Mathematics |
| ISBN | : 0470457937 |
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.
| Author | : Susanna Epp |
| Publisher | : |
| Total Pages | : 984 |
| Release | : 2019 |
| Genre | : |
| ISBN | : 9780357114087 |
DISCRETE MATHEMATICS WITH APPLICATIONS, 5th Edition, Metric Edition explains complex, abstract concepts with clarity and precision and provides a strong foundation for computer science and upper-level mathematics courses of the computer age. Author Susanna Epp 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 today's science and technology.
| Author | : Jean Gallier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 473 |
| Release | : 2011-02-01 |
| Genre | : Mathematics |
| ISBN | : 1441980474 |
This books gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal proofs are given. With this logical framework firmly in place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book is more standard. It deals with functions and relations, directed and undirected graphs, and an introduction to combinatorics. There is a section on public key cryptography and RSA, with complete proofs of Fermat's little theorem and the correctness of the RSA scheme, as well as explicit algorithms to perform modular arithmetic. The last chapter provides more graph theory. Eulerian and Hamiltonian cycles are discussed. Then, we study flows and tensions and state and prove the max flow min-cut theorem. We also discuss matchings, covering, bipartite graphs.
| Author | : Norman Biggs |
| Publisher | : Oxford University Press |
| Total Pages | : 444 |
| Release | : 2002-12-19 |
| Genre | : Computers |
| ISBN | : 9780198507178 |
Discrete mathematics is a compulsory subject for undergraduate computer scientists. This new edition includes new chapters on statements and proof, logical framework, natural numbers and the integers and updated exercises from the previous edition.
| Author | : László Lovász |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2006-05-10 |
| Genre | : Mathematics |
| ISBN | : 0387217770 |
Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.
| Author | : Owen D. Byer |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 402 |
| Release | : 2018-11-13 |
| Genre | : Mathematics |
| ISBN | : 1470446960 |
Journey into Discrete Mathematics is designed for use in a first course in mathematical abstraction for early-career undergraduate mathematics majors. The important ideas of discrete mathematics are included—logic, sets, proof writing, relations, counting, number theory, and graph theory—in a manner that promotes development of a mathematical mindset and prepares students for further study. While the treatment is designed to prepare the student reader for the mathematics major, the book remains attractive and appealing to students of computer science and other problem-solving disciplines. The exposition is exquisite and engaging and features detailed descriptions of the thought processes that one might follow to attack the problems of mathematics. The problems are appealing and vary widely in depth and difficulty. Careful design of the book helps the student reader learn to think like a mathematician through the exposition and the problems provided. Several of the core topics, including counting, number theory, and graph theory, are visited twice: once in an introductory manner and then again in a later chapter with more advanced concepts and with a deeper perspective. Owen D. Byer and Deirdre L. Smeltzer are both Professors of Mathematics at Eastern Mennonite University. Kenneth L. Wantz is Professor of Mathematics at Regent University. Collectively the authors have specialized expertise and research publications ranging widely over discrete mathematics and have over fifty semesters of combined experience in teaching this subject.
