# introduction to proof in abstract mathematics dover books on mathematics

**Download Book Introduction To Proof In Abstract Mathematics Dover Books On Mathematics in PDF format. You can Read Online Introduction To Proof In Abstract Mathematics Dover Books On Mathematics here in PDF, EPUB, Mobi or Docx formats.**

## Introduction To Proof In Abstract Mathematics

**Author :**Andrew Wohlgemuth

**ISBN :**9780486141688

**Genre :**Mathematics

**File Size :**69. 54 MB

**Format :**PDF, Docs

**Download :**338

**Read :**912

This undergraduate text teaches students what constitutes an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. 1990 edition.

## Journey Into Mathematics

**Author :**Joseph J. Rotman

**ISBN :**9780486151687

**Genre :**Mathematics

**File Size :**33. 78 MB

**Format :**PDF, ePub, Docs

**Download :**684

**Read :**349

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.

## An Introduction To Abstract Mathematics

**Author :**Robert J. Bond

**ISBN :**9781478608059

**Genre :**Mathematics

**File Size :**63. 76 MB

**Format :**PDF, ePub, Mobi

**Download :**188

**Read :**414

Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher- level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments.

## Introduction To Real Analysis

**Author :**Michael J. Schramm

**ISBN :**9780486131924

**Genre :**Mathematics

**File Size :**22. 96 MB

**Format :**PDF, ePub

**Download :**222

**Read :**1125

This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.

## Introduction To Analysis

**Author :**Maxwell Rosenlicht

**ISBN :**9780486134680

**Genre :**Mathematics

**File Size :**76. 84 MB

**Format :**PDF

**Download :**656

**Read :**650

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.

## Fundamentals Of Mathematics

**Author :**Bernd S. W. Schröder

**ISBN :**0470551380

**Genre :**Mathematics

**File Size :**82. 42 MB

**Format :**PDF, ePub

**Download :**158

**Read :**1109

An accessible introduction to abstract mathematics with an emphasis on proof writing Addressing the importance of constructing and understanding mathematical proofs, Fundamentals of Mathematics: An Introduction to Proofs, Logic, Sets, and Numbers introduces key concepts from logic and set theory as well as the fundamental definitions of algebra to prepare readers for further study in the field of mathematics. The author supplies a seamless, hands-on presentation of number systems, utilizing key elements of logic and set theory and encouraging readers to abide by the fundamental rule that you are not allowed to use any results that you have not proved yet. The book begins with a focus on the elements of logic used in everyday mathematical language, exposing readers to standard proof methods and Russell's Paradox. Once this foundation is established, subsequent chapters explore more rigorous mathematical exposition that outlines the requisite elements of Zermelo-Fraenkel set theory and constructs the natural numbers and integers as well as rational, real, and complex numbers in a rigorous, yet accessible manner. Abstraction is introduced as a tool, and special focus is dedicated to concrete, accessible applications, such as public key encryption, that are made possible by abstract ideas. The book concludes with a self-contained proof of Abel's Theorem and an investigation of deeper set theory by introducing the Axiom of Choice, ordinal numbers, and cardinal numbers. Throughout each chapter, proofs are written in much detail with explicit indications that emphasize the main ideas and techniques of proof writing. Exercises at varied levels of mathematical development allow readers to test their understanding of the material, and a related Web site features video presentations for each topic, which can be used along with the book or independently for self-study. Classroom-tested to ensure a fluid and accessible presentation, Fundamentals of Mathematics is an excellent book for mathematics courses on proofs, logic, and set theory at the upper-undergraduate level as well as a supplement for transition courses that prepare students for the rigorous mathematical reasoning of advanced calculus, real analysis, and modern algebra. The book is also a suitable reference for professionals in all areas of mathematics education who are interested in mathematical proofs and the foundation upon which all mathematics is built.

## A Logical Introduction To Proof

**Author :**Daniel W. Cunningham

**ISBN :**9781461436317

**Genre :**Mathematics

**File Size :**63. 83 MB

**Format :**PDF, ePub

**Download :**193

**Read :**1088

The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.

## A Bridge To Advanced Mathematics

**Author :**Dennis Sentilles

**ISBN :**9780486482194

**Genre :**Mathematics

**File Size :**25. 21 MB

**Format :**PDF, Mobi

**Download :**194

**Read :**354

"This helpful "bridge" book offers students the foundations they need to understand advanced mathematics, spanning the gap between practically oriented and theoretically orientated courses. Part 1 provides the most basic tools, examples, and motivation for the manner, method, and material of higher mathematics. Part 2 covers sets, relations, functions, infinite sets, and mathematical proofs and reasoning. 1975 edition"--Provided by publisher.

## An Introduction To Algebraic Structures

**Author :**Joseph Landin

**ISBN :**0486659402

**Genre :**Mathematics

**File Size :**58. 26 MB

**Format :**PDF, Docs

**Download :**232

**Read :**1023

As the author notes in the preface, "The purpose of this book is to acquaint a broad spectrum of students with what is today known as 'abstract algebra.'" Written for a one-semester course, this self-contained text includes numerous examples designed to base the definitions and theorems on experience, to illustrate the theory with concrete examples in familiar contexts, and to give the student extensive computational practice.The first three chapters progress in a relatively leisurely fashion and include abundant detail to make them as comprehensible as possible. Chapter One provides a short course in sets and numbers for students lacking those prerequisites, rendering the book largely self-contained. While Chapters Four and Five are more challenging, they are well within the reach of the serious student.The exercises have been carefully chosen for maximum usefulness. Some are formal and manipulative, illustrating the theory and helping to develop computational skills. Others constitute an integral part of the theory, by asking the student to supply proofs or parts of proofs omitted from the text. Still others stretch mathematical imaginations by calling for both conjectures and proofs.Taken together, text and exercises comprise an excellent introduction to the power and elegance of abstract algebra. Now available in this inexpensive edition, the book is accessible to a wide range of students, who will find it an exceptionally valuable resource. Unabridged, corrected Dover (1989) republication of the edition published by Allyn and Bacon, Boston, 1969.

## An Introduction To Mathematics

**Author :**Alfred North Whitehead

**ISBN :**9780486821382

**Genre :**Mathematics

**File Size :**50. 94 MB

**Format :**PDF, ePub

**Download :**449

**Read :**1076

Concise volume for general students by prominent philosopher and mathematician explains what math is and does, and how mathematicians do it. "Lucid and cogent ... should delight you." — The New York Times. 1911 edition.