Proofs And Logic A Comprehensive Guide To Mathematical Reasoning
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Proofs And Logic A Comprehensive Guide To Mathematical Reasoning
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-15
Proofs And Logic A Comprehensive Guide To Mathematical Reasoning written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-15 with Mathematics categories.
In the realm of mathematics, proofs stand as the gatekeepers of truth, ensuring that mathematical statements are not mere assertions but logical consequences of established axioms and definitions. "Proofs and Logic: A Comprehensive Guide to Mathematical Reasoning" is your gateway to mastering the art of mathematical proof construction. This comprehensive book is meticulously crafted to empower you with the skills and techniques necessary to navigate the intricate world of mathematical arguments. Whether you are a student seeking to excel in your studies, a teacher aiming to inspire your students, or a professional mathematician seeking to expand your knowledge, this book is your essential companion. With crystal-clear explanations, engaging examples, and thought-provoking exercises, this book takes you on a journey through the diverse landscape of proofs. From direct proofs that establish the truth of a statement through a sequence of logical steps to proofs by contradiction that reveal the absurdity of a statement's negation, you will gain a deep understanding of the various methods of proof construction. Beyond the realm of proofs, this book delves into the foundations of logic, set theory, propositional logic, and predicate logic, providing you with a solid grasp of the formal structure of mathematical statements. With this knowledge, you will be able to analyze and evaluate mathematical arguments with precision and rigor. As you progress through this book, you will not only develop a profound appreciation for the beauty and elegance of mathematical proofs but also cultivate a valuable skill set that will serve you well in your academic and professional endeavors. Whether you aspire to pursue a career in mathematics, science, engineering, or any field that values logical reasoning, this book is your indispensable guide. Join us on this intellectual adventure as we unlock the power of logical reasoning and embark on a journey into the fascinating world of mathematical proofs. "Proofs and Logic" is more than just a book; it is an invitation to embark on a transformative learning experience that will reshape your understanding of mathematics and empower you to tackle complex problems with confidence. If you like this book, write a review!
Mathematical Reasoning
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Author : Theodore A. Sundstrom
language : en
Publisher:
Release Date : 2003
Mathematical Reasoning written by Theodore A. Sundstrom and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Proof theory categories.
Focusing on the formal development of mathematics, this book demonstrates how to read and understand, write and construct mathematical proofs. It emphasizes active learning, and uses elementary number theory and congruence arithmetic throughout. Chapter content covers an introduction to writing in mathematics, logical reasoning, constructing proofs, set theory, mathematical induction, functions, equivalence relations, topics in number theory, and topics in set theory. For learners making the transition form calculus to more advanced mathematics.
A Beginner S Guide To Mathematical Logic
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Author : Raymond M. Smullyan
language : en
Publisher: Courier Corporation
Release Date : 2014-07-23
A Beginner S Guide To Mathematical Logic written by Raymond M. Smullyan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-23 with Mathematics categories.
Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. Dover (2014) original publication. See every Dover book in print at www.doverpublications.com
How To Prove It
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Author : Daniel J. Velleman
language : en
Publisher: Cambridge University Press
Release Date : 2006-01-16
How To Prove It written by Daniel J. Velleman 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 2006-01-16 with Mathematics categories.
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Mathematical Logic
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Author : George Tourlakis
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-01
Mathematical Logic written by George Tourlakis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-01 with Mathematics categories.
A comprehensive and user-friendly guide to the use of logic in mathematical reasoning Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning. With its user-friendly approach, this book successfully equips readers with the key concepts and methods for formulating valid mathematical arguments that can be used to uncover truths across diverse areas of study such as mathematics, computer science, and philosophy. The book develops the logical tools for writing proofs by guiding readers through both the established "Hilbert" style of proof writing, as well as the "equational" style that is emerging in computer science and engineering applications. Chapters have been organized into the two topical areas of Boolean logic and predicate logic. Techniques situated outside formal logic are applied to illustrate and demonstrate significant facts regarding the power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems of Post and Gödel). Logic cannot certify all "conditional" truths, such as those that are specific to the Peano arithmetic. Therefore, logic has some serious limitations, as shown through Gödel's incompleteness theorem. Numerous examples and problem sets are provided throughout the text, further facilitating readers' understanding of the capabilities of logic to discover mathematical truths. In addition, an extensive appendix introduces Tarski semantics and proceeds with detailed proofs of completeness and first incompleteness theorems, while also providing a self-contained introduction to the theory of computability. With its thorough scope of coverage and accessible style, Mathematical Logic is an ideal book for courses in mathematics, computer science, and philosophy at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who wish to learn how to use logic in their everyday work.
Discrete Mathematics
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Author : Douglas E. Ensley
language : en
Publisher: John Wiley & Sons
Release Date : 2005-10-07
Discrete Mathematics written by Douglas E. Ensley and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-07 with Mathematics categories.
These active and well-known authors have come together to create a fresh, innovative, and timely approach to Discrete Math. One innovation uses several major threads to help weave core topics into a cohesive whole. Throughout the book the application of mathematical reasoning is emphasized to solve problems while the authors guide the student in thinking about, reading, and writing proofs in a wide variety of contexts. Another important content thread, as the sub-title implies, is the focus on mathematical puzzles, games and magic tricks to engage students.
An Introduction To Mathematical Reasoning
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Author : Peter J. Eccles
language : en
Publisher: Cambridge University Press
Release Date : 1997-12-11
An Introduction To Mathematical Reasoning written by Peter J. Eccles 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 1997-12-11 with Mathematics categories.
ÍNDICE: Part I. Mathematical Statements and Proofs: 1. The language of mathematics; 2. Implications; 3. Proofs; 4. Proof by contradiction; 5. The induction principle; Part II. Sets and Functions: 6. The language of set theory; 7. Quantifiers; 8. Functions; 9. Injections, surjections and bijections; Part III. Numbers and Counting: 10. Counting; 11. Properties of finite sets; 12. Counting functions and subsets; 13. Number systems; 14. Counting infinite sets; Part IV. Arithmetic: 15. The division theorem; 16. The Euclidean algorithm; 17. Consequences of the Euclidean algorithm; 18. Linear diophantine equations; Part V. Modular Arithmetic: 19. Congruences of integers; 20. Linear congruences; 21. Congruence classes and the arithmetic of remainders; 22. Partitions and equivalence relations; Part VI. Prime Numbers: 23. The sequence of prime numbers; 24. Congruence modulo a prime; Solutions to exercises.
Book Of Proof
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Author : Richard H. Hammack
language : en
Publisher:
Release Date : 2013-05
Book Of Proof written by Richard H. Hammack and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05 with Mathematics categories.
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.
An Odyssey Of Ingenious Inquiries
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-05-20
An Odyssey Of Ingenious Inquiries written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-20 with Mathematics categories.
Embark on an intellectual odyssey into the realm of mathematical proofs, where logic and reasoning collide to unveil the hidden truths of mathematics. This comprehensive guide, meticulously crafted for the modern explorer of mathematical thinking, delves into the essence of mathematical reasoning, empowering you to unravel the intricacies of proofs and unlock the secrets of mathematical knowledge. Within these pages, you will embark on a captivating journey through the diverse landscapes of mathematical proofs, encountering fundamental concepts such as sets, functions, and relations. Delve into the fascinating world of number theory, where the mysteries of integers, prime numbers, and modular arithmetic await your discovery. Venture into the realm of real numbers, exploring their properties and uncovering the profound concept of limits and continuity. As you progress, you will encounter the captivating world of complex numbers, unveiling the enigma of imaginary numbers and their wide-ranging applications. This intellectual adventure is not merely a passive exploration; it is an active engagement with the art of mathematical reasoning. You will acquire a diverse arsenal of proof techniques, including direct proofs, indirect proofs, and mathematical induction, gaining the ability to construct rigorous arguments and establish mathematical truths. Along the way, you will delve into the role of axioms and assumptions in mathematical reasoning, understanding their significance in building the foundation of mathematical knowledge. More than just a collection of techniques, this book is an invitation to appreciate the beauty and power of mathematical thinking. As you delve deeper into the world of proofs, you will develop a profound appreciation for the elegance of mathematical arguments, the precision of mathematical language, and the remarkable insights that mathematics can provide into the nature of reality. Whether you are a student seeking to master the art of mathematical reasoning, a professional seeking to expand your mathematical horizons, or simply an intellectually curious individual eager to explore the depths of mathematical thought, this book is your guide to unlocking the secrets of mathematical proofs. If you like this book, write a review on google books!
Boolean Reasoning
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Author : Frank Markham Brown
language : en
Publisher: Courier Corporation
Release Date : 2012-02-10
Boolean Reasoning written by Frank Markham Brown and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-10 with Mathematics categories.
Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.