Mathematical Proofs
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An Introduction To Mathematical Proofs
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Author : Nicholas A. Loehr
language : en
Publisher: CRC Press
Release Date : 2019-11-20
An Introduction To Mathematical Proofs written by Nicholas A. Loehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-20 with Mathematics categories.
An Introduction to Mathematical Proofs presents fundamental material on logic, proof methods, set theory, number theory, relations, functions, cardinality, and the real number system. The text uses a methodical, detailed, and highly structured approach to proof techniques and related topics. No prerequisites are needed beyond high-school algebra. New material is presented in small chunks that are easy for beginners to digest. The author offers a friendly style without sacrificing mathematical rigor. Ideas are developed through motivating examples, precise definitions, carefully stated theorems, clear proofs, and a continual review of preceding topics. Features Study aids including section summaries and over 1100 exercises Careful coverage of individual proof-writing skills Proof annotations and structural outlines clarify tricky steps in proofs Thorough treatment of multiple quantifiers and their role in proofs Unified explanation of recursive definitions and induction proofs, with applications to greatest common divisors and prime factorizations About the Author: Nicholas A. Loehr is an associate professor of mathematics at Virginia Technical University. He has taught at College of William and Mary, United States Naval Academy, and University of Pennsylvania. He has won many teaching awards at three different schools. He has published over 50 journal articles. He also authored three other books for CRC Press, including Combinatorics, Second Edition, and Advanced Linear Algebra.
The Meaning Of Proofs
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Author : Gabriele Lolli
language : en
Publisher: MIT Press
Release Date : 2022-09-27
The Meaning Of Proofs written by Gabriele Lolli and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-27 with Mathematics categories.
Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story. In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.
Theoremus
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Author : Lito Perez Cruz
language : en
Publisher: Springer Nature
Release Date : 2021-05-24
Theoremus written by Lito Perez Cruz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-24 with Computers categories.
A compact and easily accessible book, it guides the reader in unravelling the apparent mysteries found in doing mathematical proofs. Simply written, it introduces the art and science of proving mathematical theorems and propositions and equips students with the skill required to tackle the task of proving mathematical assertions. Theoremus - A Student's Guide to Mathematical Proofs is divided into two parts. Part 1 provides a grounding in the notion of mathematical assertions, arguments and fallacies and Part 2, presents lessons learned in action by applying them into the study of logic itself. The book supplies plenty of examples and figures, gives some historical background on personalities that gave rise to the topic and provides reflective problems to try and solve. The author aims to provide the reader with the confidence to take a deep dive into some more advanced work in mathematics or logic.
The Nuts And Bolts Of Proofs
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Author : Antonella Cupillari
language : en
Publisher: Elsevier
Release Date : 2023-01-05
The Nuts And Bolts Of Proofs written by Antonella Cupillari and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-05 with Mathematics categories.
The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs, Fifth Edition provides basic logic of mathematical proofs and how they work. The book offers techniques for both reading and writing proofs, discusses techniques in proving if/then statements by contrapositive and proofing by contradiction, includes the negation statement, and/or, examines various theorems, such as the if and only-if, equivalence theorems, existence theorems, and the uniqueness theorems. In addition, the use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are also covered. The book also provides mathematical topics for practicing proof techniques. Included here are the Cartesian products, indexed families, functions, and relations. The last chapter of the book provides review exercises on various topics. Undergraduate students in engineering and physical science will find this book accessible as well as invaluable. Jumps right in with the needed vocabulary to get students thinking like mathematicians from the beginning Offers a large variety of examples and problems with solutions for students to work through on their own Includes a collection of exercises without solutions to help instructors prepare assignments Contains an extensive list of basic mathematical definitions and concepts needed in abstract mathematics
Proofs From The Book
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Author : Martin Aigner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Proofs From The Book written by Martin Aigner 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 2013-06-29 with Mathematics categories.
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Logic Sets And The Techniques Of Mathematical Proofs
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Author : Brahima Mbodje Ph. D.
language : en
Publisher: AuthorHouse
Release Date : 2011-06
Logic Sets And The Techniques Of Mathematical Proofs written by Brahima Mbodje Ph. D. and has been published by AuthorHouse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06 with Education categories.
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.
Understanding Mathematical Proof
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Author : John Taylor
language : en
Publisher: CRC Press
Release Date : 2014-03-21
Understanding Mathematical Proof written by John Taylor and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-21 with Mathematics categories.
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 techniques that mathematicians adopt to prove their results, and offers advice and strategies for constructing proofs. It will improve students’ ability to understand proofs and construct correct proofs of their own. The first chapter of the text introduces the kind of reasoning that mathematicians use when writing their proofs and gives some example proofs to set the scene. The book then describes basic logic to enable an understanding of the structure of both individual mathematical statements and whole mathematical proofs. It also explains the notions of sets and functions and dissects several proofs with a view to exposing some of the underlying features common to most mathematical proofs. The remainder of the book delves further into different types of proof, including direct proof, proof using contrapositive, proof by contradiction, and mathematical induction. The authors also discuss existence and uniqueness proofs and the role of counter examples.
A Logical Introduction To Proof
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Author : Daniel Cunningham
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-19
A Logical Introduction To Proof written by Daniel Cunningham 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 2012-09-19 with Mathematics categories.
The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.
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
Write Your Own Proofs
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Author : Amy Babich
language : en
Publisher: Courier Dover Publications
Release Date : 2019-08-14
Write Your Own Proofs written by Amy Babich and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-14 with Mathematics categories.
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.