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Author: Roger Antonsen Publisher: Springer ISBN: 9783030637767 Category : Computers Languages : en Pages : 288
Book Description
Many believe mathematics is only about calculations, formulas, numbers, and strange letters. But mathematics is much more than just crunching numbers or manipulating symbols. Mathematics is about discovering patterns, uncovering hidden structures, finding counterexamples, and thinking logically. Mathematics is a way of thinking. It is an activity that is both highly creative and challenging. This book offers an introduction to mathematical reasoning for beginning university or college students, providing a solid foundation for further study in mathematics, computer science, and related disciplines. Written in a manner that directly conveys the sense of excitement and discovery at the heart of doing science, its 25 short and visually appealing chapters cover the basics of set theory, logic, proof methods, combinatorics, graph theory, and much more. In the book you will, among other things, find answers to: What is a proof? What is a counterexample? What does it mean to say that something follows logically from a set of premises? What does it mean to abstract over something? How can knowledge and information be represented and used in calculations? What is the connection between Morse code and Fibonacci numbers? Why could it take billions of years to solve Hanoi's Tower? Logical Methods is especially appropriate for students encountering such concepts for the very first time. Designed to ease the transition to a university or college level study of mathematics or computer science, it also provides an accessible and fascinating gateway to logical thinking for students of all disciplines.
Author: Roger Antonsen Publisher: Springer ISBN: 9783030637767 Category : Computers Languages : en Pages : 288
Book Description
Many believe mathematics is only about calculations, formulas, numbers, and strange letters. But mathematics is much more than just crunching numbers or manipulating symbols. Mathematics is about discovering patterns, uncovering hidden structures, finding counterexamples, and thinking logically. Mathematics is a way of thinking. It is an activity that is both highly creative and challenging. This book offers an introduction to mathematical reasoning for beginning university or college students, providing a solid foundation for further study in mathematics, computer science, and related disciplines. Written in a manner that directly conveys the sense of excitement and discovery at the heart of doing science, its 25 short and visually appealing chapters cover the basics of set theory, logic, proof methods, combinatorics, graph theory, and much more. In the book you will, among other things, find answers to: What is a proof? What is a counterexample? What does it mean to say that something follows logically from a set of premises? What does it mean to abstract over something? How can knowledge and information be represented and used in calculations? What is the connection between Morse code and Fibonacci numbers? Why could it take billions of years to solve Hanoi's Tower? Logical Methods is especially appropriate for students encountering such concepts for the very first time. Designed to ease the transition to a university or college level study of mathematics or computer science, it also provides an accessible and fascinating gateway to logical thinking for students of all disciplines.
Author: John N. Crossley Publisher: Springer Science & Business Media ISBN: 1461203252 Category : Computers Languages : en Pages : 829
Book Description
The twenty-six papers in this volume reflect the wide and still expanding range of Anil Nerode's work. A conference on Logical Methods was held in honor of Nerode's sixtieth birthday (4 June 1992) at the Mathematical Sciences Institute, Cornell University, 1-3 June 1992. Some of the conference papers are here, but others are from students, co-workers and other colleagues. The intention of the conference was to look forward, and to see the directions currently being pursued, in the development of work by, or with, Nerode. Here is a brief summary of the contents of this book. We give a retrospective view of Nerode's work. A number of specific areas are readily discerned: recursive equivalence types, recursive algebra and model theory, the theory of Turing degrees and r.e. sets, polynomial-time computability and computer science. Nerode began with automata theory and has also taken a keen interest in the history of mathematics. All these areas are represented. The one area missing is Nerode's applied mathematical work relating to the environment. Kozen's paper builds on Nerode's early work on automata. Recursive equivalence types are covered by Dekker and Barback, the latter using directly a fundamental metatheorem of Nerode. Recursive algebra is treated by Ge & Richards (group representations). Recursive model theory is the subject of papers by Hird, Moses, and Khoussainov & Dadajanov, while a combinatorial problem in recursive model theory is discussed in Cherlin & Martin's paper. Cenzer presents a paper on recursive dynamics.
Author: Greg Restall Publisher: MIT Press ISBN: 0262544849 Category : Philosophy Languages : en Pages : 285
Book Description
An accessible introduction to philosophical logic, suitable for undergraduate courses and above. Rigorous yet accessible, Logical Methods introduces logical tools used in philosophy—including proofs, models, modal logics, meta-theory, two-dimensional logics, and quantification—for philosophy students at the undergraduate level and above. The approach developed by Greg Restall and Shawn Standefer is distinct from other texts because it presents proof construction on equal footing with model building and emphasizes connections to other areas of philosophy as the tools are developed. Throughout, the material draws on a broad range of examples to show readers how to develop and master tools of proofs and models for propositional, modal, and predicate logic; to construct and analyze arguments and to find their structure; to build counterexamples; to understand the broad sweep of formal logic’s development in the twentieth and twenty-first centuries; and to grasp key concepts used again and again in philosophy. This text is essential to philosophy curricula, regardless of specialization, and will also find wide use in mathematics and computer science programs. Features: An accessible introduction to proof theory for readers with no background in logic Covers proofs, models, modal logics, meta-theory, two-dimensional logics, quantification, and many other topics Provides tools and techniques of particular interest to philosophers and philosophical logicians Features short summaries of key concepts and skills at the end of each chapter Offers chapter-by-chapter exercises in two categories: basic, designed to reinforce important ideas; and challenge, designed to push students’ understanding and developing skills in new directions
Author: Tukufu Zuberi Publisher: Rowman & Littlefield ISBN: 9780742542815 Category : Social Science Languages : en Pages : 428
Book Description
Examines how the racial lenses of the social sciences and the subscription of social scientists to whites' racial common sense have limited their understanding of racial matters and handicapped their capacity to appreciate the significance of the "race effect" (they call it the "racial stratification effect"). With an assemblage of leading scholars, White Logic, White Methods explores the possibilities and necessary dethroning of current social research practices, and demands a complete overhaul of current methods, towards a multicultural and pluralist approach to what we know, think, and question. Readers in various social sciences will find useful the chapters in the collection, but all will agree that the introductory and concluding chapters to the volume (Towards a Definition of White Logic and White Methods, and Telling the Real Tale of the Hunt: Towards a Race Conscious Sociology of Racial Stratification) are likely to become classics in the field of racial and ethnic relations.
Author: Robert J. Girod Publisher: CRC Press ISBN: 1482243148 Category : Computers Languages : en Pages : 274
Book Description
This book describes how to use logic, reasoning, critical thinking, and the scientific method to conduct and improve criminal and civil investigations. The author discusses how investigators and attorneys can avoid assumptions and false premises and instead make valid deductions, inductions, and inferences. He explains how tools such as interview and interrogation can be used to detect deception and profile unknown individuals and suspects. The book is aimed at improving not only the conduct of investigations, but also the logical use of cognitive, analytical, documentation, and presentation tools to win cases.
Author: Min Ding Publisher: Routledge ISBN: 1000060128 Category : Business & Economics Languages : en Pages : 205
Book Description
Using a new, systematic framework, this illuminating book turns ideation into a task anybody with sound logic and a determination to learn can do, and do well, by separating the process from the outcome. In a competitive marketplace, all firms must constantly innovate to create sustained shareholder value. The main roadblock in innovation is ideation: the identification of value-creating ideas, often seen as the work of innately creative people. This first-of-its-kind textbook demonstrates that anyone can ideate through specific logical processes that require no creativity when used, but generate valuable and creative outcomes. To help students master and apply these methods, the book is filled with innovation examples across many sectors that can be explained and recreated using a specific LCT method. The book also includes exercises that enable readers to practice applying each method to solve real life innovation challenges. Upper-level undergraduate and postgraduate students of innovation, creativity, and new product development will appreciate the demystification of ideation into a problem that can be solved by applying a series of rigorous, defined methods that can be followed without ambiguity.
Author: Willard Van Orman Quine Publisher: Harvard University Press ISBN: 9780674571761 Category : Philosophy Languages : en Pages : 348
Book Description
This widely used textbook of modern formal logic now offers a number of new features. Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate-functor logic and the affinities between higher set theory and the elementary logic of terms, W. V. Quine's new edition will serve admirably for both classroom and independent use.
Author: J. Michael Dunn Publisher: OUP Oxford ISBN: 0191589225 Category : Languages : en Pages : 490
Book Description
This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily for logisticians in mathematics, philosophy, computer science and linguistics with an interest in algebraic logic, but is also accessible to those from a non-logistics background. It is suitable for researchers, graduates and advanced undergraduates who have an introductory knowledge of algebraic logic providing more advanced concepts, as well as more theoretical aspects. The main theme is that standard algebraic results (representations) translate into standard logical results (completeness). Other themes involve identification of a class of algebras appropriate for classical and non-classical logic studies, including: gaggles, distributoids, partial- gaggles, and tonoids. An imporatant sub title is that logic is fundamentally information based, with its main elements being propositions, that can be understood as sets of information states. Logics are considered in various senses e.g. systems of theorems, consequence relations and, symmetric consequence relations.
Author: John L. Bell Publisher: Broadview Press ISBN: 1551112973 Category : Philosophy Languages : en Pages : 313
Book Description
Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some classical first-order logic and would like to learn about other logics important to their philosophical work.
Author: Vijay Chandru Publisher: John Wiley & Sons ISBN: 1118031415 Category : Mathematics Languages : en Pages : 386
Book Description
Merging logic and mathematics in deductive inference-an innovative, cutting-edge approach. Optimization methods for logical inference? Absolutely, say Vijay Chandru and John Hooker, two major contributors to this rapidly expanding field. And even though "solving logical inference problems with optimization methods may seem a bit like eating sauerkraut with chopsticks. . . it is the mathematical structure of a problem that determines whether an optimization model can help solve it, not the context in which the problem occurs." Presenting powerful, proven optimization techniques for logic inference problems, Chandru and Hooker show how optimization models can be used not only to solve problems in artificial intelligence and mathematical programming, but also have tremendous application in complex systems in general. They survey most of the recent research from the past decade in logic/optimization interfaces, incorporate some of their own results, and emphasize the types of logic most receptive to optimization methods-propositional logic, first order predicate logic, probabilistic and related logics, logics that combine evidence such as Dempster-Shafer theory, rule systems with confidence factors, and constraint logic programming systems. Requiring no background in logic and clearly explaining all topics from the ground up, Optimization Methods for Logical Inference is an invaluable guide for scientists and students in diverse fields, including operations research, computer science, artificial intelligence, decision support systems, and engineering.
Author: Roger Antonsen
Author: Roger Antonsen
Author: John N. Crossley
Author: Greg Restall
Author: Tukufu Zuberi
Author: Robert J. Girod
Author: Min Ding
Author: Willard Van Orman Quine
Author: J. Michael Dunn
Author: John L. Bell
Author: Vijay Chandru