How to Prove It

Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 9781139450973
Release Date: 2006-01-16
Genre: Mathematics

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.

How to Prove It

Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 0521675995
Release Date: 2006-01-16
Genre: Mathematics

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.

How to Prove It

Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 0521446635
Release Date: 1994-11-25
Genre: Mathematics

Many mathematics students have trouble the first time they take a course, such as linear algebra, abstract algebra, introductory analysis, or discrete mathematics, in which they are asked to prove various theorems. This textbook 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 "scratchwork" sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. Numerous exercises give students the opportunity to construct their own proofs. 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.

How to Read and Do Proofs

Author: Daniel Solow
Publisher: John Wiley & Sons
ISBN: 1118164024
Release Date: 2013-07-29
Genre: Mathematics

The inclusion in practically every chapter of new material on how to read and understand proofs as they are typically presented in class lectures, textbooks, and other mathematical literature. The goal is to provide sufficient examples (and exercises) to give students the ability to learn mathematics on their own.

Mathematical Proofs

Author: Gary Chartrand
Publisher: Pearson
ISBN: 9780134766461
Release Date: 2018-04-19
Genre: Mathematics

This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. For courses in Transition to Advanced Mathematics or Introduction to Proof. Meticulously crafted, student-friendly text that helps build mathematical maturity Mathematical Proofs: A Transition to Advanced Mathematics, 4th Edition introduces students to proof techniques, analyzing proofs, and writing proofs of their own that are not only mathematically correct but clearly written. Written in a student-friendly manner, it provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as optional excursions into fields such as number theory, combinatorics, and calculus. The exercises receive consistent praise from users for their thoughtfulness and creativity. They help students progress from understanding and analyzing proofs and techniques to producing well-constructed proofs independently. This book is also an excellent reference for students to use in future courses when writing or reading proofs. 0134746759 / 9780134746753 Chartrand/Polimeni/Zhang, Mathematical Proofs: A Transition to Advanced Mathematics, 4/e

Journey into Mathematics

Author: Joseph J. Rotman
Publisher: Courier Corporation
ISBN: 9780486151687
Release Date: 2013-01-18
Genre: Mathematics

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.

Introduction to Mathematical Structures and Proofs

Author: Larry J. Gerstein
Publisher: Springer Science & Business Media
ISBN: 9781461442653
Release Date: 2012-06-05
Genre: Mathematics

As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor—and the flexible thinking—required to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader. The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers). Solutions for even numbered exercises are available on springer.com for instructors adopting the text for a course.

Book of Proof

Author: Richard H. Hammack
Publisher:
ISBN: 0989472116
Release Date: 2016-01-01
Genre: Mathematics

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.

100 mathematical proof

Author: Rowan Garnier
Publisher: John Wiley & Son Ltd
ISBN: 047196199X
Release Date: 1996
Genre: Mathematics

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

Writing Proofs in Analysis

Author: Jonathan M. Kane
Publisher: Springer
ISBN: 9783319309675
Release Date: 2016-05-28
Genre: Mathematics

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.

The Art of Proof

Author: Matthias Beck
Publisher: Springer Science & Business Media
ISBN: 1441970231
Release Date: 2010-08-17
Genre: Mathematics

The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.

Proofs and Fundamentals

Author: Ethan D. Bloch
Publisher: Springer Science & Business Media
ISBN: 9781461221302
Release Date: 2013-12-01
Genre: Mathematics

The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.

A Friendly Introduction to Mathematical Logic

Author: Christopher C. Leary
Publisher: Lulu.com
ISBN: 9781942341079
Release Date: 2015-07-27
Genre:

At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Godel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises."

Theoremus

Author: L. P. Cruz
Publisher: CreateSpace
ISBN: 1505921457
Release Date: 2015-01-02
Genre: Mathematics

This concise textbook will teach mathematics students the art of proving theorems. Using a simple approach, it will provide them the mechanics to solve challenging proof exercises. Students are first taught to be sensitive to fallacious claims so they could form valid assertions. The book shows the proper use of logic and its deduction rules. It is an effective tool for improving students' skills in formulating sound mathematical arguments. What is more is that the student can get all of these in one sitting.

Understanding Mathematical Proof

Author: John Taylor
Publisher: CRC Press
ISBN: 9781466514911
Release Date: 2016-04-19
Genre: Mathematics

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.