Proofs from THE BOOK

Proofs from THE BOOK
Available:
Author: Martin Aigner,Günter M. Ziegler
Pages: 199
ISBN: 9783662223437
Release: 2013-06-29
Editor: Springer Science & Business Media

DESCRIPTION OF THE BOOK:

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.

Understanding Mathematical Proof

Understanding Mathematical Proof
Available:
Author: John Taylor,Rowan Garnier
Pages: 414
ISBN: 9781466514911
Release: 2016-04-19
Editor: CRC Press

DESCRIPTION OF THE BOOK:

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

Introduction to Mathematical Proofs

Introduction to Mathematical Proofs
Available:
Author: Charles Roberts
Pages: 414
ISBN: 9781482246889
Release: 2014-12-17
Editor: CRC Press

DESCRIPTION OF THE BOOK:

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.

Mathematical Proofs

Mathematical Proofs
Available:
Author: Gary Chartrand,Albert D. Polimeni,Ping Zhang
Pages: 400
ISBN: 0321782518
Release: 2013
Editor: Pearson Educacion

DESCRIPTION OF THE BOOK:

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.

Book of Proof

Book of Proof
Available:
Author: Richard H. Hammack
Pages: 314
ISBN: 0989472116
Release: 2016-01-01
Editor: Unknown

DESCRIPTION OF THE BOOK:

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.

How to Read and Do Proofs

How to Read and Do Proofs
Available:
Author: Daniel Solow
Pages: 48
ISBN: 0471558990
Release: 1991-12-05
Editor: Wiley

DESCRIPTION OF THE BOOK:

This straightforward guide describes the main methods used to prove mathematical theorems. Shows how and when to use each technique such as the contrapositive, induction and proof by contradiction. Each method is illustrated by step-by-step examples. The Second Edition features new chapters on nested quantifiers and proof by cases, and the number of exercises has been doubled with answers to odd-numbered exercises provided. This text will be useful as a supplement in mathematics and logic courses. Prerequisite is high-school algebra.

Mathematical Reasoning

Mathematical Reasoning
Available:
Author: Ted Sundstrom
Pages: 608
ISBN: 1500143413
Release: 2014-06-11
Editor: Unknown

DESCRIPTION OF THE BOOK:

Mathematical Reasoning: Writing and Proof is a text for the ?rst college mathematics course that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students: Develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting; develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, and counterexamples; develop the ability to read and understand written mathematical proofs; develop talents for creative thinking and problem solving; improve their quality of communication in mathematics. This includes improving writing techniques, reading comprehension, and oral communication in mathematics; better understand the nature of mathematics and its language. Another important goal of this text is to provide students with material that will be needed for their further study of mathematics. Important features of the book include: Emphasis on writing in mathematics; instruction in the process of constructing proofs; emphasis on active learning.There are no changes in content between Version 2.0 and previous versions of the book. The only change is that the appendix with answers and hints for selected exercises now contains solutions and hints for more exercises.

Mathematical Proofs

Mathematical Proofs
Available:
Author: Gary Chartrand,Albert D. Polimeni,Ping Zhang
Pages: 418
ISBN: 1292040645
Release: 2013-11-01
Editor: Unknown

DESCRIPTION OF THE BOOK:

Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book 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. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.

Math Proofs Demystified

Math Proofs Demystified
Available:
Author: Stan Gibilisco
Pages: 290
ISBN: 9780071469920
Release: 2005-05-13
Editor: McGraw Hill Professional

DESCRIPTION OF THE BOOK:

Almost every student has to study some sort of mathematical proofs, whether it be in geometry, trigonometry, or with higher-level topics. In addition, mathematical theorems have become an interesting course for many students outside of the mathematical arena, purely for the reasoning and logic that is needed to complete them. Therefore, it is not uncommon to have philosophy and law students grappling with proofs. This book is the perfect resource for demystifying the techniques and principles that govern the mathematical proof area, and is done with the standard “Demystified” level, questions and answers, and accessibility.

The Nuts and Bolts of Proofs

The Nuts and Bolts of Proofs
Available:
Author: Antonella Cupillari
Pages: 283
ISBN: 9780123822178
Release: 2012
Editor: Academic Press

DESCRIPTION OF THE BOOK:

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. New chapter on proof by contradiction New updated proofs A full range of accessible proofs Symbols indicating level of difficulty help students understand whether a problem is based on calculus or linear algebra Basic terminology list with definitions at the beginning of the text

Proof and the Art of Mathematics

Proof and the Art of Mathematics
Available:
Author: Joel David Hamkins
Pages: 132
ISBN: 9780262362566
Release: 2021-02-23
Editor: MIT Press

DESCRIPTION OF THE BOOK:

How to write mathematical proofs, shown in fully-worked out examples. This is a companion volume Joel Hamkins's Proof and the Art of Mathematics, providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs. The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.

Proofs and Refutations

Proofs and Refutations
Available:
Author: Imre Lakatos,Lakatos Imre
Pages: 174
ISBN: 0521290384
Release: 1976
Editor: Cambridge University Press

DESCRIPTION OF THE BOOK:

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

Journey into Mathematics

Journey into Mathematics
Available:
Author: Joseph J. Rotman
Pages: 256
ISBN: 9780486151687
Release: 2013-01-18
Editor: Courier Corporation

DESCRIPTION OF THE BOOK:

This treatment covers the mechanics of writing proofs, the area and circumference of circles, and complex numbers and their application to real numbers. 1998 edition.

Logic Sets and the Techniques of Mathematical Proofs

Logic  Sets and the Techniques of Mathematical Proofs
Available:
Author: Brahima Mbodje Ph. D.
Pages: 356
ISBN: 9781463429676
Release: 2011-06-01
Editor: AuthorHouse

DESCRIPTION OF THE BOOK:

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.

Reverse Mathematics

Reverse Mathematics
Available:
Author: John Stillwell
Pages: 200
ISBN: 9780691196411
Release: 2019-09-24
Editor: Princeton University Press

DESCRIPTION OF THE BOOK:

" This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics. "--

100 Mathematical Proof

100  Mathematical Proof
Available:
Author: Rowan Garnier,John Taylor
Pages: 317
ISBN: UOM:39076001859920
Release: 1996-08
Editor: John Wiley & Son Limited

DESCRIPTION OF THE BOOK:

"Proof" has been and remains one of the concepts which characterises mathematics. Covering basic propositional and predicate logic as well as discussing axiom systems and formal proofs, the book seeks to explain what mathematicians understand by proofs and how they are communicated. The authors explore the principle techniques of direct and indirect proof including induction, existence and uniqueness proofs, proof by contradiction, constructive and non-constructive proofs, etc. Many examples from analysis and modern algebra are included. The exceptionally clear style and presentation ensures that the book will be useful and enjoyable to those studying and interested in the notion of mathematical "proof."

Mathematical Analysis and Proof

Mathematical Analysis and Proof
Available:
Author: David S G Stirling
Pages: 253
ISBN: 1904275400
Release: 2009-05-14
Editor: Horwood Publishing

DESCRIPTION OF THE BOOK:

This fundamental and straightforward text addresses a weakness observed among present-day students, namely a lack of familiarity with formal proof. Beginning with the idea of mathematical proof and the need for it, associated technical and logical skills are developed with care and then brought to bear on the core material of analysis in such a lucid presentation that the development reads naturally and in a straightforward progression. Retaining the core text, the second edition has additional worked examples which users have indicated a need for, in addition to more emphasis on how analysis can be used to tell the accuracy of the approximations to the quantities of interest which arise in analytical limits. Addresses a lack of familiarity with formal proof, a weakness observed among present-day mathematics students Examines the idea of mathematical proof, the need for it and the technical and logical skills required

A Transition to Advanced Mathematics

A Transition to Advanced Mathematics
Available:
Author: Douglas Smith,Maurice Eggen,Richard St. Andre
Pages: 416
ISBN: 0495562025
Release: 2010-06-01
Editor: Cengage Learning

DESCRIPTION OF THE BOOK:

A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Mathematical Proofs

Mathematical Proofs
Available:
Author: Gary Chartrand,Albert D. Polimeni,Ping Zhang
Pages: 400
ISBN: 0321797094
Release: 2013
Editor: Pearson College Division

DESCRIPTION OF THE BOOK:

Normal 0 false false false Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book 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. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.

Q E D

Q E D
Available:
Author: Burkard Polster
Pages: 64
ISBN: 190426350X
Release: 2006-11-01
Editor: Wooden

DESCRIPTION OF THE BOOK:

'Q.E.D.' presents some of the most famous mathematical proofs in a charming book that will appeal to non-mathematicians and experts alike.