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Author: Willem Labuschagne Publisher: Unisa Press ISBN: 9780869818107 Category : Computer science Languages : en Pages : 320

Book Description
What mathematical skills do you need to understand computers and the problems they can solve? This book introduces the basic ideas of set theory, logic and combinatorics. Intended for those who work alone and whose experiences of mathematics have in the past perhaps been somewhat intimidating, the book adopts an informal tone and chats to the reader as a well-informed friend might. In addition to its treatment of mathematical topics, it draws the attention of the reader to general patterns of thought, some of which constitute useful problem-solving skills that may be used in other domains.

Author: Willem Labuschagne Publisher: Unisa Press ISBN: 9780869818107 Category : Computer science Languages : en Pages : 320

Book Description
What mathematical skills do you need to understand computers and the problems they can solve? This book introduces the basic ideas of set theory, logic and combinatorics. Intended for those who work alone and whose experiences of mathematics have in the past perhaps been somewhat intimidating, the book adopts an informal tone and chats to the reader as a well-informed friend might. In addition to its treatment of mathematical topics, it draws the attention of the reader to general patterns of thought, some of which constitute useful problem-solving skills that may be used in other domains.

Author: Christopher C. Leary Publisher: Lulu.com ISBN: 1942341075 Category : Education Languages : en Pages : 382

Book Description
At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.

Author: Gary Chartrand Publisher: Waveland Press ISBN: 1478608323 Category : Mathematics Languages : en Pages : 671

Book Description
Chartrand and Zhangs Discrete Mathematics presents a clearly written, student-friendly introduction to discrete mathematics. The authors draw from their background as researchers and educators to offer lucid discussions and descriptions fundamental to the subject of discrete mathematics. Unique among discrete mathematics textbooks for its treatment of proof techniques and graph theory, topics discussed also include logic, relations and functions (especially equivalence relations and bijective functions), algorithms and analysis of algorithms, introduction to number theory, combinatorics (counting, the Pascal triangle, and the binomial theorem), discrete probability, partially ordered sets, lattices and Boolean algebras, cryptography, and finite-state machines. This highly versatile text provides mathematical background used in a wide variety of disciplines, including mathematics and mathematics education, computer science, biology, chemistry, engineering, communications, and business. Some of the major features and strengths of this textbook Numerous, carefully explained examples and applications facilitate learning. More than 1,600 exercises, ranging from elementary to challenging, are included with hints/answers to all odd-numbered exercises. Descriptions of proof techniques are accessible and lively. Students benefit from the historical discussions throughout the textbook.

Author: Willem Conradie Publisher: John Wiley & Sons ISBN: 1119000092 Category : Mathematics Languages : en Pages : 456

Book Description
A concise yet rigorous introduction to logic and discrete mathematics. This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical logic as well as practical applications through the easy to understand and use deductive systems of Semantic Tableaux and Resolution. The chapters on set theory, number theory, combinatorics and graph theory combine the necessary minimum of theory with numerous examples and selected applications. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in the accompanying solutions manual. Key Features: Suitable for a variety of courses for students in both Mathematics and Computer Science. Extensive, in-depth coverage of classical logic, combined with a solid exposition of a selection of the most important fields of discrete mathematics Concise, clear and uncluttered presentation with numerous examples. Covers some applications including cryptographic systems, discrete probability and network algorithms. Logic and Discrete Mathematics: A Concise Introduction is aimed mainly at undergraduate courses for students in mathematics and computer science, but the book will also be a valuable resource for graduate modules and for self-study.

Author: Elliott Mendelson Publisher: CRC Press ISBN: 9780412808302 Category : Mathematics Languages : en Pages : 464

Book Description
The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.

Author: sarah-marie belcastro Publisher: CRC Press ISBN: 1351683691 Category : Mathematics Languages : en Pages : 658

Book Description
Discrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels. The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they’ve learned. As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems. The author’s lively and friendly writing style is appealing to both instructors and students alike and encourages readers to learn. The book’s light-hearted approach to the subject is a guiding principle and helps students learn mathematical abstraction. Features: The book’s Try This! sections encourage students to construct components of discussed concepts, theorems, and proofs Provided sets of discovery problems and illustrative examples reinforce learning Bonus sections can be used by instructors as part of their regular curriculum, for projects, or for further study

Author: Jayant Ganguly Publisher: ISBN: 9788188849222 Category : Languages : en Pages : 873

Book Description
A Treatise on Discrete Mathematical Structures has been designed to build a foundation of the type of mathematical thinking that is required to be built at the basic level. The approach chosen is comprehensive while maintaining an easy to follow progression from the basic mathematical concepts covered by high school algebra to the more sophisticated concepts. The rigorous treatment of theory is augmented by numerous examples (SP : Solved Problem). This is then reinforced by exercises (EP : Exercise Problem) at the end of each chapter. Further, for the exercise problems whose serial number is in bold face letter, a hint or solution is provided in the corresponding answer section. Although this treatise aims at the learners of computer science, it can very well be used by anyone who requires an understanding of discrete mathematical concepts. Features The presentation style of each chapter resembles that as done in a classroom. The book is intended for anybody interested in the subject. Prerequisite requirement is mostly high school mathematics. Each chapter begins with an outline of the topics covered in the book. Contains a large number of examples with steps over-simplified. Each chapter ends with a chapter summary under the heading RECAP. A large number of practice problems are included with sufficient hints. Many new results from recently published papers are incorporated. A number of exhaustive appendices are included for those interested. A problem bank is included containing problems from Mathematical Tripods examination. The book is user friendly and Diffi cult situations are illustrated with diagrams. Some interesting non mathematical but related topics are discussed in brief. Contents Set Theory Relations Functions Mathematical Induction Recursive Definitions probability and Counting Elementary Concepts Fundamentals of Logic Groups coding Theory- An Introduction Elementary Number Theory Rings Graph Theory Basic Formulas Matrices and Determinants and Some Results Series and their Summing Techniques-An Introduction Stable Graphs-A Note Problem Bank List of Symbols.