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The Nuts And Bolts Of Proofs


The Nuts And Bolts Of Proofs
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The Nuts And Bolts Of Proofs


The Nuts And Bolts Of Proofs
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Author : Antonella Cupillari
language : en
Publisher: Academic Press
Release Date : 2001

The Nuts And Bolts Of Proofs written by Antonella Cupillari and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.


This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course. This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers are provided, enabling students to practice on their own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments. * Successfully class-tested over a number of years * Index for easy reference * Extensive list of definitions and concepts * Updated biblography



The Nuts And Bolts Of Proofs


The Nuts And Bolts Of Proofs
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Author : Antonella Cupillari
language : en
Publisher: Academic Press
Release Date : 2012-01-05

The Nuts And Bolts Of Proofs written by Antonella Cupillari and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-05 with Mathematics categories.


Annotation The Nuts and Bolts of Proofs instructs students on the primary basic logic of mathematical proofs, showing how proofs of mathematical statements work. The text provides basic core techniques of how to read and write proofs through examples. The basic mechanics of proofs are provided for a methodical approach in gaining an understanding of the fundamentals to help students reach different results. A variety of fundamental proofs demonstrate the basic steps in the construction of a proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems.Jumps right in with the needed vocabulary-gets students thinking like mathematicians from the beginningOffers a large variety of examples and problems with solutions for students to work through on their ownIncludes a collection of exercises without solutions to help instructors prepare assignmentsContains an extensive list of basic mathematical definitions and concepts needed in abstract mathematics.



The Nuts And Bolts Of Proofs


The Nuts And Bolts Of Proofs
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Author : Antonella Cupillari
language : en
Publisher:
Release Date : 2005

The Nuts And Bolts Of Proofs written by Antonella Cupillari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.




Advanced Calculus


Advanced Calculus
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Author : Thomas P. Dence
language : en
Publisher: Academic Press
Release Date : 2009-12-02

Advanced Calculus written by Thomas P. Dence and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-02 with Mathematics categories.


Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis – providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. It covers exponential function, and the development of trigonometric functions from the integral. The text is designed for a one-semester advanced calculus course for advanced undergraduates or graduate students. - Appropriate rigor for a one-semester advanced calculus course - Presents modern materials and nontraditional ways of stating and proving some results - Includes precise historical notes throughout the bookoutstanding feature is the collection of exercises in each chapter - Provides coverage of exponential function, and the development of trigonometric functions from the integral



Understanding Mathematical Proof


Understanding Mathematical Proof
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Author : John Taylor
language : en
Publisher: CRC Press
Release Date : 2016-04-19

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 2016-04-19 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 techn



Proofs And Refutations


Proofs And Refutations
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Author : Imre Lakatos
language : en
Publisher: Cambridge University Press
Release Date : 1976

Proofs And Refutations written by Imre Lakatos 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 1976 with Mathematics categories.


Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.



How To Read And Do Proofs


How To Read And Do Proofs
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Author : Daniel Solow
language : en
Publisher: John Wiley & Sons
Release Date : 2013-07-29

How To Read And Do Proofs written by Daniel Solow 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 2013-07-29 with Mathematics categories.


This text makes a great supplement and provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to categorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the problem.



Debugging By Thinking


Debugging By Thinking
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Author : Robert C. Metzger
language : en
Publisher: Digital Press
Release Date : 2004

Debugging By Thinking written by Robert C. Metzger and has been published by Digital Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.


Debugging by Thinking: A Multi-Disciplinary Approach is the first book to apply the wisdom of six disciplines-logic, mathematics, psychology, safety analysis, computer science, and engineering-to the problem of debugging. It uses the methods of literary detectives such as Sherlock Holmes, the techniques of mathematical problem solving, the results of research into the cognitive psychology of human error, the root cause analyses of safety experts, the compiler analyses of computer science, and the processes of modern engineering to define a systematic approach to identifying and correcting software errors. * Language Independent Methods: Examples are given in Java and C++ * Complete source code shows actual bugs, rather than contrived examples * Examples are accessible with no more knowledge than a course in Data Structures and Algorithms requires * A "thought process diary" shows how the author actually resolved the problems as they occurred



Elements Of The Theory Of Numbers


Elements Of The Theory Of Numbers
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Author : Joseph B. Dence
language : en
Publisher: Academic Press
Release Date : 1999-01-20

Elements Of The Theory Of Numbers written by Joseph B. Dence and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-20 with Mathematics categories.


Elements of the Theory of Numbers teaches students how to develop, implement, and test numerical methods for standard mathematical problems. The authors have created a two-pronged pedagogical approach that integrates analysis and algebra with classical number theory. Making greater use of the language and concepts in algebra and analysis than is traditionally encountered in introductory courses, this pedagogical approach helps to instill in the minds of the students the idea of the unity of mathematics. Elements of the Theory of Numbers is a superb summary of classical material as well as allowing the reader to take a look at the exciting role of analysis and algebra in number theory. * In-depth coverage of classical number theory * Thorough discussion of the theory of groups and rings * Includes application of Taylor polynomials * Contains more advanced material than other texts * Illustrates the results of a theorem with an example * Excellent presentation of the standard computational exercises * Nearly 1000 problems--many are proof-oriented, several others require the writing of computer programs to complete the computations * Clear and well-motivated presentation * Provides historical references noting distinguished number theory luminaries such as Euclid, de Fermat, Hilbert, Brun, and Lehmer, to name a few * Annotated bibliographies appear at the end of all of the chapters



Introduction To Mathematical Logic


Introduction To Mathematical Logic
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Author : Jayant Ramaswamy
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Introduction To Mathematical Logic written by Jayant Ramaswamy and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.


"Introduction to Mathematical Logic" is tailored for undergraduate students seeking a comprehensive introduction to this essential field of mathematics. We provide an accessible yet rigorous exploration of the principles, methods, and applications of mathematical logic. From the foundations of propositional and predicate logic to advanced topics like Gödel's incompleteness theorems and computability theory, we cover a broad range of concepts central to the study of logic. Through clear explanations, illustrative examples, and carefully crafted exercises, students will develop a deep understanding of logical reasoning, formal proof techniques, and the structure of mathematical arguments. Moreover, we emphasize the interdisciplinary nature of mathematical logic, showcasing its relevance in mathematics, philosophy, computer science, and beyond. Real-world applications of logical reasoning are woven throughout the text, demonstrating how logical principles underpin various fields of study, from algorithm design and formal verification to philosophical analysis and linguistic theory. Whether you're a mathematics major, a philosophy student, or pursuing studies in computer science, this book equips you with the tools and insights necessary to navigate the complexities of mathematical logic with confidence. With its blend of theory and application, this text serves as an invaluable resource for undergraduate students embarking on their journey into the realm of mathematical logic.