Numbers And Proofs
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Numbers And Proofs
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Author : Reg Allenby
language : en
Publisher: Elsevier
Release Date : 1997-09-26
Numbers And Proofs written by Reg Allenby and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-26 with Mathematics categories.
'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all students of mathematics. Each proof is preceded by a discussion which is intended to show the reader the kind of thoughts they might have before any attempt proof is made. Established proofs which the student is in a better position to follow then follow.Presented in the author's entertaining and informal style, and written to reflect the changing profile of students entering universities, this book will prove essential reading for all seeking an introduction to the notion of proof as well as giving a definitive guide to the more common forms. Stressing the importance of backing up "truths" found through experimentation, with logically sound and watertight arguments, it provides an ideal bridge to more complex undergraduate maths.
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 Illustrated Theory Of Numbers
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Author : Martin H. Weissman
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-15
An Illustrated Theory Of Numbers written by Martin H. Weissman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-15 with Education categories.
News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.
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.
Proofs And Fundamentals
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Author : Ethan D. Bloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Proofs And Fundamentals written by Ethan D. Bloch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
In an effort to make advanced mathematics accessible to a wide variety of students, and to give even the most mathematically inclined students a solid basis upon which to build their continuing study of mathematics, there has been a tendency in recent years to introduce students to the for mulation and writing of rigorous mathematical proofs, and to teach topics such as sets, functions, relations and countability, in a "transition" course, rather than in traditional courses such as linear algebra. A transition course functions as a bridge between computational courses such as Calculus, and more theoretical courses such as linear algebra and abstract algebra. This text contains core topics that I believe any transition course should cover, as well as some optional material intended to give the instructor some flexibility in designing a course. The presentation is straightforward and focuses on the essentials, without being too elementary, too exces sively pedagogical, and too full to distractions. Some of features of this text are the following: (1) Symbolic logic and the use of logical notation are kept to a minimum. We discuss only what is absolutely necessary - as is the case in most advanced mathematics courses that are not focused on logic per se.
An Introduction To Proofs With Set Theory
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Author : Daniel Ashlock
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
An Introduction To Proofs With Set Theory written by Daniel Ashlock and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Mathematics categories.
This text is intended as an introduction to mathematical proofs for students. It is distilled from the lecture notes for a course focused on set theory subject matter as a means of teaching proofs. Chapter 1 contains an introduction and provides a brief summary of some background material students may be unfamiliar with. Chapters 2 and 3 introduce the basics of logic for students not yet familiar with these topics. Included is material on Boolean logic, propositions and predicates, logical operations, truth tables, tautologies and contradictions, rules of inference and logical arguments. Chapter 4 introduces mathematical proofs, including proof conventions, direct proofs, proof-by-contradiction, and proof-by-contraposition. Chapter 5 introduces the basics of naive set theory, including Venn diagrams and operations on sets. Chapter 6 introduces mathematical induction and recurrence relations. Chapter 7 introduces set-theoretic functions and covers injective, surjective, and bijective functions, as well as permutations. Chapter 8 covers the fundamental properties of the integers including primes, unique factorization, and Euclid's algorithm. Chapter 9 is an introduction to combinatorics; topics included are combinatorial proofs, binomial and multinomial coefficients, the Inclusion-Exclusion principle, and counting the number of surjective functions between finite sets. Chapter 10 introduces relations and covers equivalence relations and partial orders. Chapter 11 covers number bases, number systems, and operations. Chapter 12 covers cardinality, including basic results on countable and uncountable infinities, and introduces cardinal numbers. Chapter 13 expands on partial orders and introduces ordinal numbers. Chapter 14 examines the paradoxes of naive set theory and introduces and discusses axiomatic set theory. This chapter also includes Cantor's Paradox, Russel's Paradox, a discussion of axiomatic theories, an exposition on Zermelo‒Fraenkel Set Theory with the Axiom of Choice, and a brief explanation of Gödel's Incompleteness Theorems.
Introduction To Mathematical Proofs
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Author : Charles Roberts
language : en
Publisher: CRC Press
Release Date : 2009-06-24
Introduction To Mathematical Proofs written by Charles Roberts and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-24 with Mathematics categories.
Shows How to Read & Write Mathematical ProofsIdeal Foundation for More Advanced Mathematics CoursesIntroduction 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 n
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!
Introduction To Mathematical Structures And Proofs
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Author : Larry J. Gerstein
language : en
Publisher: Springer
Release Date : 2013-03-14
Introduction To Mathematical Structures And Proofs written by Larry J. Gerstein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Medical categories.
This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the . rudiments of logic, set theory, equivalence relations, and other basic mathematiCal raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried tHe students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a n
Proofs And Algorithms
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Author : Gilles Dowek
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-11
Proofs And Algorithms written by Gilles Dowek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-11 with Computers categories.
Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.