Logic Sets And The Techniques Of Mathematical Proofs

Logic  Sets and the Techniques of Mathematical Proofs PDF
Author: Brahima Mbodje Ph. D.
Publisher: AuthorHouse
ISBN: 1463429673
Size: 75.58 MB
Format: PDF, Docs
Category : Education
Languages : en
Pages : 356
View: 6051

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As its title indicates, this book is about logic, sets and mathematical proofs. It is a careful, patient and rigorous introduction for readers with very limited mathematical maturity. It teaches the reader not only how to read a mathematical proof, but also how to write one. To achieve this, we carefully lay out all the various proof methods encountered in mathematical discourse, give their logical justifications, and apply them to the study of topics [such as real numbers, relations, functions, sequences, fine sets, infinite sets, countable sets, uncountable sets and transfinite numbers] whose mastery is important for anyone contemplating advanced studies in mathematics. The book is completely self-contained; since the prerequisites for reading it are only a sound background in high school algebra. Though this book is meant to be a companion specifically for senior high school pupils and college undergraduate students, it will also be of immense value to anyone interested in acquiring the tools and way of thinking of the mathematician.

Mathematical Proofs

Mathematical Proofs PDF
Author: Gary Chartrand
Publisher: Addison-Wesley Longman
ISBN:
Size: 75.65 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 365
View: 2553

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Mathematical Proofs: A Transition to Advanced Mathematics, 2/e, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets. KEY TOPICS: Communicating Mathematics, Sets, Logic, Direct Proof and Proof by Contrapositive, More on Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory. MARKET: For all readers interested in advanced mathematics and logic.

Proof And The Art Of Mathematics

Proof and the Art of Mathematics PDF
Author: Joel David Hamkins
Publisher:
ISBN: 0262539799
Size: 78.25 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 232
View: 5813

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"A textbook for students who are learning how to write a mathematical proof, a validation of the truth of a mathematical statement"--

Attributing Knowledge

Attributing Knowledge PDF
Author: Jody Azzouni
Publisher: Oxford University Press, USA
ISBN: 0197508812
Size: 14.41 MB
Format: PDF, ePub, Mobi
Category : Language Arts & Disciplines
Languages : en
Pages : 480
View: 4722

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"The word "know" is revealed as vague, applicable to fallible agents, factive and criterion transcendent. It is invariant in its meaning across contexts and invariant relative to different agents. Only purely epistemic properties affect its correct application-not the interests of agents or those who attribute the word to agents. These properties enable "know" to be applied correctly-as it routinely is-to cognitive agents ranging from sophisticated human knowers, who engage in substantial metacognition, to various animals, who know much less and do much less, if any, metacognition, to nonconscious mechanical devices such as drones, robots, and the like. These properties of the word "know" suffice to explain the usage phenomena that contextualists and subject-sensitive invariantists invoke to place pressure on an understanding of the word that treats its application as involving no interests of agents, or others. It is also shown the factivity and the fallibilist-compatibility of the word "know" explains Moorean paradoxes, the preface paradox, and the lottery paradox. A fallibility-sensitive failure of knowledge-closure is given along with a similar failure of rational-belief closure. The latter explains why rational agents can nevertheless believe A and B, where A and B contradict one another. A substantial discussion of various kinds of metacognition is given-as well as a discussion of the metacognition literature in cognitive ethology. An appendix offers a new resolution of the hangman paradox, one that turns neither on a failure of knowledge closure nor on a failure of KK"--

Computational Models Of Argument

Computational Models of Argument PDF
Author: S. Modgil
Publisher: IOS Press
ISBN: 1614999066
Size: 29.39 MB
Format: PDF, ePub, Docs
Category : Computers
Languages : en
Pages : 496
View: 2269

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In its classical form, the study of argumentation focuses on human-oriented uses of argument, such as whether an argument is legitimate or flawed, engagement in debate, or the rhetorical aspects of argumentation. In recent decades, however, the study of logic and computational models of argumentation has emerged as a growing sub-area of AI. This book presents the Seventh International Conference on Computational Models of Argument (COMMA’18), held in Warsaw, Poland, from 12 to 14 September 2018. Since its inception in 2006, the conference and its related activities have developed alongside the steady growth of interest in computational argumentation worldwide, and the selection of 25 full papers and 17 short papers, out of a total of 70 submissions, and 15 demonstration abstracts included here reflect the broad multidisciplinary nature of argumentation and the increasing body of work which establishes the relevance of computational models to various disciplines and real world applications. Subjects covered include: algorithm development; innovative applications; argument mining, argumentation-based models of dialogue; abstract argument frameworks; and structured argumentation. Representing an overview of current developments in the field, this book will appeal to all those with an interest in computational models of argument.

An Introduction To Mathematical Reasoning

An Introduction to Mathematical Reasoning PDF
Author: Peter J. Eccles
Publisher: Cambridge University Press
ISBN: 1139632566
Size: 19.30 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 364
View: 4945

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This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

Handbook Of Mathematical Induction

Handbook of Mathematical Induction PDF
Author: David S. Gunderson
Publisher: CRC Press
ISBN: 1420093657
Size: 63.41 MB
Format: PDF, Docs
Category : Computers
Languages : en
Pages : 921
View: 1380

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Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics.In the first part of the book, the author discuss

Write Your Own Proofs

Write Your Own Proofs PDF
Author: Amy Babich
Publisher: Courier Dover Publications
ISBN: 0486832813
Size: 30.82 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 256
View: 4311

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Written by a pair of math teachers and based on their classroom notes and experiences, this introductory treatment of theory, proof techniques, and related concepts is designed for undergraduate courses. No knowledge of calculus is assumed, making it a useful text for students at many levels. The focus is on teaching students to prove theorems and write mathematical proofs so that others can read them. Since proving theorems takes lots of practice, this text is designed to provide plenty of exercises. The authors break the theorems into pieces and walk readers through examples, encouraging them to use mathematical notation and write proofs themselves. Topics include propositional logic, set notation, basic set theory proofs, relations, functions, induction, countability, and some combinatorics, including a small amount of probability. The text is ideal for courses in discrete mathematics or logic and set theory, and its accessibility makes the book equally suitable for classes in mathematics for liberal arts students or courses geared toward proof writing in mathematics.

Mathematical Proofs Pearson New International Edition

Mathematical Proofs  Pearson New International Edition PDF
Author: Gary Chartrand
Publisher: Pearson Higher Ed
ISBN: 1292052341
Size: 44.40 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 424
View: 5928

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Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.

Understanding Mathematical Proof

Understanding Mathematical Proof PDF
Author: John Taylor
Publisher: CRC Press
ISBN: 1466514914
Size: 51.68 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 414
View: 2974

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The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs.Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techn

Introduction To Mathematical Proofs

Introduction to Mathematical Proofs PDF
Author: Charles Roberts
Publisher: CRC Press
ISBN: 9781420069563
Size: 13.90 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 433
View: 4915

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Shows How to Read & Write Mathematical Proofs Ideal Foundation for More Advanced Mathematics Courses Introduction to Mathematical Proofs: A Transition facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize theorem proving. It helps students develop the skills necessary to write clear, correct, and concise proofs. Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs. Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It will prepare them to succeed in more advanced mathematics courses, such as abstract algebra and geometry.

Introduction To Abstract Mathematics

Introduction to Abstract Mathematics PDF
Author: John F. Lucas
Publisher: Rowman & Littlefield
ISBN: 9780912675732
Size: 36.64 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 382
View: 4515

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This is a book about mathematics and mathematical thinking. It is intended for the serious learner who is interested in studying some deductive strategies in the context of a variety of elementary mathematical situations. No background beyond single-variable calculus is presumed.

100 Mathematical Proof

100  Mathematical Proof PDF
Author: Rowan Garnier
Publisher: John Wiley & Son Limited
ISBN:
Size: 44.75 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 317
View: 2008

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"Proof" has been and remains one of the concepts which characterises mathematics. Covering basic propositional and predicate logic as well as discussing axiom systems and formal proofs, the book seeks to explain what mathematicians understand by proofs and how they are communicated. The authors explore the principle techniques of direct and indirect proof including induction, existence and uniqueness proofs, proof by contradiction, constructive and non-constructive proofs, etc. Many examples from analysis and modern algebra are included. The exceptionally clear style and presentation ensures that the book will be useful and enjoyable to those studying and interested in the notion of mathematical "proof."