Writing Proofs In Analysis
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Writing Proofs In Analysis
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Author : Jonathan M. Kane
language : en
Publisher: Springer
Release Date : 2018-05-30
Writing Proofs In Analysis written by Jonathan M. Kane and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-30 with Mathematics categories.
This is a textbook on proof writing in the area of analysis, balancing a survey of the core concepts of mathematical proof with a tight, rigorous examination of the specific tools needed for an understanding of analysis. Instead of the standard "transition" approach to teaching proofs, wherein students are taught fundamentals of logic, given some common proof strategies such as mathematical induction, and presented with a series of well-written proofs to mimic, this textbook teaches what a student needs to be thinking about when trying to construct a proof. Covering the fundamentals of analysis sufficient for a typical beginning Real Analysis course, it never loses sight of the fact that its primary focus is about proof writing skills. This book aims to give the student precise training in the writing of proofs by explaining exactly what elements make up a correct proof, how one goes about constructing an acceptable proof, and, by learning to recognize a correct proof, how to avoid writing incorrect proofs. To this end, all proofs presented in this text are preceded by detailed explanations describing the thought process one goes through when constructing the proof. Over 150 example proofs, templates, and axioms are presented alongside full-color diagrams to elucidate the topics at hand.
Writing Proofs In Analysis
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Author : Jonathan M. Kane
language : en
Publisher: Springer
Release Date : 2016-06-06
Writing Proofs In Analysis written by Jonathan M. Kane and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-06 with Mathematics categories.
This is a textbook on proof writing in the area of analysis, balancing a survey of the core concepts of mathematical proof with a tight, rigorous examination of the specific tools needed for an understanding of analysis. Instead of the standard "transition" approach to teaching proofs, wherein students are taught fundamentals of logic, given some common proof strategies such as mathematical induction, and presented with a series of well-written proofs to mimic, this textbook teaches what a student needs to be thinking about when trying to construct a proof. Covering the fundamentals of analysis sufficient for a typical beginning Real Analysis course, it never loses sight of the fact that its primary focus is about proof writing skills. This book aims to give the student precise training in the writing of proofs by explaining exactly what elements make up a correct proof, how one goes about constructing an acceptable proof, and, by learning to recognize a correct proof, how to avoid writing incorrect proofs. To this end, all proofs presented in this text are preceded by detailed explanations describing the thought process one goes through when constructing the proof. Over 150 example proofs, templates, and axioms are presented alongside full-color diagrams to elucidate the topics at hand.
Introduction To Analysis
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Author : Maxwell Rosenlicht
language : en
Publisher: Courier Corporation
Release Date : 2012-05-04
Introduction To Analysis written by Maxwell Rosenlicht and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Mathematics categories.
Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.
An Introduction To Proof Through Real Analysis
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Author : Daniel J. Madden
language : en
Publisher: John Wiley & Sons
Release Date : 2017-09-12
An Introduction To Proof Through Real Analysis written by Daniel J. Madden 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 2017-09-12 with Education categories.
An engaging and accessible introduction to mathematical proof incorporating ideas from real analysis A mathematical proof is an inferential argument for a mathematical statement. Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics. The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own. An Introduction to Proof through Real Analysis is based on course material developed and refined over thirty years by Professor Daniel J. Madden and was designed to function as a complete text for both first proofs and first analysis courses. Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity. The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems. • Concentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects • Departs from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation • Written in an engaging narrative style to tell the story of proof and its meaning, function, and construction • Uses a particular mathematical idea as the focus of each type of proof presented • Developed from material that has been class-tested and fine-tuned over thirty years in university introductory courses An Introduction to Proof through Real Analysis is the ideal introductory text to proofs for second and third-year undergraduate mathematics students, especially those who have completed a calculus sequence, students learning real analysis for the first time, and those learning proofs for the first time. Daniel J. Madden, PhD, is an Associate Professor of Mathematics at The University of Arizona, Tucson, Arizona, USA. He has taught a junior level course introducing students to the idea of a rigorous proof based on real analysis almost every semester since 1990. Dr. Madden is the winner of the 2015 Southwest Section of the Mathematical Association of America Distinguished Teacher Award. Jason A. Aubrey, PhD, is Assistant Professor of Mathematics and Director, Mathematics Center of the University of Arizona.
A Concise Approach To Mathematical Analysis
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Author : Mangatiana A. Robdera
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27
A Concise Approach To Mathematical Analysis written by Mangatiana A. Robdera 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 2011-06-27 with Mathematics categories.
A Concise Approach to Mathematical Analysis introduces the undergraduate student to the more abstract concepts of advanced calculus. The main aim of the book is to smooth the transition from the problem-solving approach of standard calculus to the more rigorous approach of proof-writing and a deeper understanding of mathematical analysis. The first half of the textbook deals with the basic foundation of analysis on the real line; the second half introduces more abstract notions in mathematical analysis. Each topic begins with a brief introduction followed by detailed examples. A selection of exercises, ranging from the routine to the more challenging, then gives students the opportunity to practise writing proofs. The book is designed to be accessible to students with appropriate backgrounds from standard calculus courses but with limited or no previous experience in rigorous proofs. It is written primarily for advanced students of mathematics - in the 3rd or 4th year of their degree - who wish to specialise in pure and applied mathematics, but it will also prove useful to students of physics, engineering and computer science who also use advanced mathematical techniques.
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.
A First Course In Real Analysis
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Author : Sterling K. Berberian
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-10
A First Course In Real Analysis written by Sterling K. Berberian 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 2012-09-10 with Mathematics categories.
Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along theway, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.
A Basic Course In Real Analysis
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Author : Ajit Kumar
language : en
Publisher: CRC Press
Release Date : 2014-01-10
A Basic Course In Real Analysis written by Ajit Kumar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-10 with Mathematics categories.
Based on the authors' combined 35 years of experience in teaching, A Basic Course in Real Analysis introduces students to the aspects of real analysis in a friendly way. The authors offer insights into the way a typical mathematician works observing patterns, conducting experiments by means of looking at or creating examples, trying to understand t
Mathematical Proofs
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Author : Gary Chartrand
language : en
Publisher: Pearson
Release Date : 2013
Mathematical Proofs written by Gary Chartrand and has been published by Pearson this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Proof theory categories.
This book prepares students for the more abstract mathematics courses that follow calculus. The author introduces students to proof techniques, analyzing proofs, and writing proofs of their own. It also 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.
Reading Writing And Proving
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Author : Ulrich Daepp
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Reading Writing And Proving written by Ulrich Daepp 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 2006-04-18 with Mathematics categories.
This book, based on Pólya's method of problem solving, aids students in their transition to higher-level mathematics. It begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends by providing projects for independent study. Students will follow Pólya's four step process: learn to understand the problem; devise a plan to solve the problem; carry out that plan; and look back and check what the results told them.