An Introduction To Mathematical Proofs

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An Introduction to Mathematical Proofs

Nicholas A. Loehr
An Introduction to Mathematical Proofs Book PDF

Author : Nicholas A. Loehr
Publisher : CRC Press
Page : 483 pages
File Size : 52,5 Mb
Release : 2019-11-20
Category : Mathematics
ISBN : 9781000709803

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An Introduction to Mathematical Proofs by Nicholas A. Loehr Pdf

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.

Proofs from THE BOOK

Martin Aigner,Günter M. Ziegler
Proofs from THE BOOK Book PDF

Author : Martin Aigner,Günter M. Ziegler
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 46,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662223437

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Proofs from THE BOOK by Martin Aigner,Günter M. Ziegler Pdf

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.

Introduction · to Mathematical Structures and · Proofs

Larry Gerstein
Introduction to Mathematical Structures and Proofs Book PDF

Author : Larry Gerstein
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 51,5 Mb
Release : 2013-11-21
Category : Science
ISBN : 9781468467086

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Introduction · to Mathematical Structures and · Proofs by Larry Gerstein Pdf

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 nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.

Introduction to Proof in Abstract Mathematics

Andrew Wohlgemuth
Introduction to Proof in Abstract Mathematics Book PDF

Author : Andrew Wohlgemuth
Publisher : Courier Corporation
Page : 385 pages
File Size : 48,5 Mb
Release : 2014-06-10
Category : Mathematics
ISBN : 9780486141688

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Introduction to Proof in Abstract Mathematics by Andrew Wohlgemuth Pdf

The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.

Introduction to Mathematical Proofs, Second Edition

Charles Roberts
Introduction to Mathematical Proofs Second Edition Book PDF

Author : Charles Roberts
Publisher : Chapman and Hall/CRC
Page : 0 pages
File Size : 47,8 Mb
Release : 2014-12-17
Category : Mathematics
ISBN : 1482246872

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Introduction to Mathematical Proofs, Second Edition by Charles Roberts Pdf

Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs. Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs. This new edition includes more than 125 new exercises in sections titled More Challenging Exercises. Also, numerous examples illustrate in detail how to write proofs and show how to solve problems. These examples can serve as models for students to emulate when solving exercises. Several biographical sketches and historical comments have been included to enrich and enliven the text. Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It prepares them to succeed in more advanced mathematics courses, such as abstract algebra and analysis.

The Nuts and Bolts of Proofs

Antonella Cupillari
The Nuts and Bolts of Proofs Book PDF

Author : Antonella Cupillari
Publisher : Academic Press
Page : 297 pages
File Size : 41,9 Mb
Release : 2011-11-25
Category : Mathematics
ISBN : 9780123822185

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The Nuts and Bolts of Proofs by Antonella Cupillari Pdf

The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs provides basic logic of mathematical proofs and shows how mathematical proofs work. It offers techniques for both reading and writing proofs. The second chapter of the book discusses the techniques in proving if/then statements by contrapositive and proofing by contradiction. It also includes the negation statement, and/or. It examines various theorems, such as the if and only-if, or equivalence theorems, the existence theorems, and the uniqueness theorems. In addition, use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are covered in this chapter. 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 invaluable. Jumps right in with the needed vocabulary—gets 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

Understanding Mathematical Proof

John Taylor,Rowan Garnier
Understanding Mathematical Proof Book PDF

Author : John Taylor,Rowan Garnier
Publisher : CRC Press
Page : 414 pages
File Size : 50,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781466514911

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Understanding Mathematical Proof by John Taylor,Rowan Garnier Pdf

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

How to Prove It

Daniel J. Velleman
How to Prove It Book PDF

Author : Daniel J. Velleman
Publisher : Cambridge University Press
Page : 401 pages
File Size : 50,8 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9780521861243

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How to Prove It by Daniel J. Velleman Pdf

This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.

An Introduction to Writing Mathematical Proofs

Thomas Bieske
An Introduction to Writing Mathematical Proofs Book PDF

Author : Thomas Bieske
Publisher : Unknown
Page : 202 pages
File Size : 44,8 Mb
Release : 2020-11-08
Category : Electronic
ISBN : 9798561230653

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An Introduction to Writing Mathematical Proofs by Thomas Bieske Pdf

This textbook is designed to help students transition from calculus-type courses that focus on computation to upper-level mathematics courses that focus on proof-writing. Using the familiar topics of real numbers, high school geometry, and calculus, students are introduced to the methods of proof-writing and pre-proof strategy planning. A supplemental workbook for instructors is available upon request from the author. The workbook includes chapter vocabulary lists, creative writing exercises, group projects, and classroom discussions.

Journey into Mathematics

Joseph J. Rotman
Journey into Mathematics Book PDF

Author : Joseph J. Rotman
Publisher : Courier Corporation
Page : 386 pages
File Size : 55,6 Mb
Release : 2013-01-18
Category : Mathematics
ISBN : 9780486151687

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Journey into Mathematics by Joseph J. Rotman Pdf

Students learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely reading about mathematics is no substitute for doing mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and illustrates the intrinsic beauty and interest of mathematics. Journey into Mathematics offers a coherent story, with intriguing historical and etymological asides. The three-part treatment begins with the mechanics of writing proofs, including some very elementary mathematics--induction, binomial coefficients, and polygonal areas--that allow students to focus on the proofs without the distraction of absorbing unfamiliar ideas at the same time. Once they have acquired some geometric experience with the simpler classical notion of limit, they proceed to considerations of the area and circumference of circles. The text concludes with examinations of complex numbers and their application, via De Moivre's theorem, to real numbers.

A Transition to Proof

Neil R. Nicholson
A Transition to Proof Book PDF

Author : Neil R. Nicholson
Publisher : CRC Press
Page : 323 pages
File Size : 50,7 Mb
Release : 2019-03-21
Category : Mathematics
ISBN : 9780429535475

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A Transition to Proof by Neil R. Nicholson Pdf

A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology

An Introduction to Mathematical Reasoning

Peter J. Eccles
An Introduction to Mathematical Reasoning Book PDF

Author : Peter J. Eccles
Publisher : Cambridge University Press
Page : 366 pages
File Size : 40,6 Mb
Release : 1997-12-11
Category : Mathematics
ISBN : 0521597188

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An Introduction to Mathematical Reasoning by Peter J. Eccles Pdf

The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. Over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

An Introduction to Proof through Real Analysis

Daniel J. Madden,Jason A. Aubrey
An Introduction to Proof through Real Analysis Book PDF

Author : Daniel J. Madden,Jason A. Aubrey
Publisher : John Wiley & Sons
Page : 450 pages
File Size : 45,8 Mb
Release : 2017-09-12
Category : Education
ISBN : 9781119314721

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An Introduction to Proof through Real Analysis by Daniel J. Madden,Jason A. Aubrey Pdf

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.

Mathematical Reasoning

Theodore A. Sundstrom
Mathematical Reasoning Book PDF

Author : Theodore A. Sundstrom
Publisher : Prentice Hall
Page : 0 pages
File Size : 52,5 Mb
Release : 2007
Category : Logic, Symbolic and mathematical
ISBN : 0131877186

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Mathematical Reasoning by Theodore A. Sundstrom Pdf

Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom

Mathematical Proofs

Gary Chartrand,Albert D. Polimeni,Ping Zhang
Mathematical Proofs Book PDF

Author : Gary Chartrand,Albert D. Polimeni,Ping Zhang
Publisher : Pearson Educacion
Page : 400 pages
File Size : 51,7 Mb
Release : 2013
Category : Logic, Symbolic and mathematical
ISBN : 0321782518

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Mathematical Proofs by Gary Chartrand,Albert D. Polimeni,Ping Zhang Pdf

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.