Analysis with an Introduction to Proof / Edition 3

Hardcover (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $1.99
Usually ships in 1-2 business days
(Save 98%)
Other sellers (Hardcover)
  • All (12) from $1.99   
  • New (3) from $98.52   
  • Used (9) from $1.99   
Close
Sort by
Page 1 of 1
Showing All
Note: Marketplace items are not eligible for any BN.com coupons and promotions
$98.52
Seller since 2015

Feedback rating:

(345)

Condition:

New — never opened or used in original packaging.

Like New — packaging may have been opened. A "Like New" item is suitable to give as a gift.

Very Good — may have minor signs of wear on packaging but item works perfectly and has no damage.

Good — item is in good condition but packaging may have signs of shelf wear/aging or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Acceptable — item is in working order but may show signs of wear such as scratches or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Used — An item that has been opened and may show signs of wear. All specific defects should be noted in the Comments section associated with each item.

Refurbished — A used item that has been renewed or updated and verified to be in proper working condition. Not necessarily completed by the original manufacturer.

New
Brand New Item.

Ships from: Chatham, NJ

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
  • Express, 48 States
  • Express (AK, HI)
$105.00
Seller since 2015

Feedback rating:

(217)

Condition: New
Brand new.

Ships from: acton, MA

Usually ships in 1-2 business days

  • Standard, 48 States
  • Standard (AK, HI)
$105.00
Seller since 2015

Feedback rating:

(217)

Condition: New
Brand new.

Ships from: acton, MA

Usually ships in 1-2 business days

  • Standard, 48 States
  • Standard (AK, HI)
Page 1 of 1
Showing All
Close
Sort by

Overview

Carefully focused on reading and writing proofs, this introduction to the analysis of functions of a single real variable helps readers in the transition from computationally oriented to abstract mathematics. It features clear expositions and examples, helpful practice problems, many drawings that illustrate key ideas, and hints/answers for selected problems. Logic and Proof. Sets and Functions. The Real Numbers. Sequences. Limits and Continuity. Differentiation. Integration. Infinite Series. Sequences and Series of Functions. For anyone interested in Real Analysis or Advanced Calculus.
Read More Show Less

Product Details

  • ISBN-13: 9780130898791
  • Publisher: Pearson
  • Publication date: 7/24/2000
  • Edition description: Older Edition
  • Edition number: 3
  • Pages: 341
  • Product dimensions: 7.01 (w) x 9.25 (h) x 0.30 (d)

Read an Excerpt

PREFACE:

Preface

A student's first encounter with analysis has been widely regarded as the most difficult course in the undergraduate mathematics curriculum. This is due not so much to the complexity of the topics as to what the student is asked to do with them. After years of emphasizing computation (with only a brief diversion in high school geometry), the student is now expected to be able to read, understand, and actually construct mathematical proofs. Unfortunately, often very little groundwork has been laid to explain the nature and techniques of proof.

This text seeks to aid students in their transition to abstract mathematics in two ways: by providing an introductory discussion of logic, and by giving attention throughout the text to the structure and nature of the arguments being used. The first two editions have been praised for their readability and their student-oriented approach. This revision builds on those strengths. Small changes have been made in many sections to clarify the exposition, and several new examples and illustrations have been added.

The major change in this edition is the addition of more than 250 true/false questions that relate directly to the reading. These questions have been carefully worded to anticipate common student errors. They encourage the students to read the text carefully and think critically about what they have read. Often the justification for an answer of "false" will be an example that the students can add to their growing collection of counterexamples.

As in earlier editions, the text also includes more than a hundred practice problems. Generally, these problems are not verydifficult, and it is intended that students should stop to work them as they read. The answers are given at the end of each section just prior to the exercises. The students should also be encouraged to read (if not attempt) most of the exercises. They are viewed as an integral part of the text and vary in difficulty from the routine to the challenging. Those exercises that are used in a later section are marked with an asterisk. Hints for many of the exercises are included at the back of the book. These hints should be used only after a serious attempt to solve an exercise has proved futile.

The overall organization of the book remains the same as in the earlier editions. The first chapter takes a careful (albeit nontechnical) look at the laws of logic and then examines how these laws are used in the structuring of mathematical arguments. The second chapter discusses the two main foundations of analysis: sets and functions. This provides an elementary setting in which to practice the techniques encountered in the previous chapter.

Chapter 3 develops the properties of the real numbers R as a complete ordered field and introduces the topological concepts of neighborhoods, open sets, closed sets, and compact sets. The remaining chapters cover the topics usually included in an analysis of functions of a real variable: sequences, continuity, differentiation, integration, and series.

The text has been written in a way designed to provide flexibility in the pacing of topics. If only one term is available, the first chapter can be assigned as outside reading. Chapter 2 and the first half of Chapter 3 can be covered quickly, again with much of the reading being left to the student. By so doing, the remainder of the book can be covered adequately in a single semester. Alternatively, depending on the students' background and interests, one can concentrate on developing the first five chapters in some detail. By placing a greater emphasis on the early material, the text can be used in a "transitional" course whose main goal is to teach mathematical reasoning and to illustrate its use in developing an abstract structure. It is also possible to skip derivatives and integrals and go directly to series, since the only results needed from these two chapters will be familiar to the student from beginning calculus.

A thorough treatment of the whole book would require two semesters. At this slower pacing the book provides a unified approach to a course in foundations followed by a course in analysis. Students going into secondary education will profit greatly from the first course, and those going on to graduate school in either pure or applied mathematics will want to take both semesters.

I appreciate the helpful comments that I have received from users of the first two editions and reviewers of the third. In particular, I would like to thank Professors Michael Dutko, Ana Mantilla, Marcus Marsh, Carl Maxson, Stanley Page, Doraiswamy Ramachandran, Ernie Solheid, David Trautman, Kevin Yeomans, and Zbigniew Zielezny. I am also grateful to my students at Lee University for their numerous suggestions.

Steven R. Lay
Cleveland, TN

Read More Show Less

Table of Contents

1. Logic and Proof.
2. Sets and Functions.
3. The Real Numbers.
4. Sequences.
5. Limits and Continuity.
6. Differentiation.
7. Integration.
8. Infinite Series.
9. Sequences and Series of Functions.
References.
Hints for Selected Exercises.
Index.
Read More Show Less

Preface

PREFACE:

Preface

A student's first encounter with analysis has been widely regarded as the most difficult course in the undergraduate mathematics curriculum. This is due not so much to the complexity of the topics as to what the student is asked to do with them. After years of emphasizing computation (with only a brief diversion in high school geometry), the student is now expected to be able to read, understand, and actually construct mathematical proofs. Unfortunately, often very little groundwork has been laid to explain the nature and techniques of proof.

This text seeks to aid students in their transition to abstract mathematics in two ways: by providing an introductory discussion of logic, and by giving attention throughout the text to the structure and nature of the arguments being used. The first two editions have been praised for their readability and their student-oriented approach. This revision builds on those strengths. Small changes have been made in many sections to clarify the exposition, and several new examples and illustrations have been added.

The major change in this edition is the addition of more than 250 true/false questions that relate directly to the reading. These questions have been carefully worded to anticipate common student errors. They encourage the students to read the text carefully and think critically about what they have read. Often the justification for an answer of "false" will be an example that the students can add to their growing collection of counterexamples.

As in earlier editions, the text also includes more than a hundred practice problems. Generally, these problems are notverydifficult, and it is intended that students should stop to work them as they read. The answers are given at the end of each section just prior to the exercises. The students should also be encouraged to read (if not attempt) most of the exercises. They are viewed as an integral part of the text and vary in difficulty from the routine to the challenging. Those exercises that are used in a later section are marked with an asterisk. Hints for many of the exercises are included at the back of the book. These hints should be used only after a serious attempt to solve an exercise has proved futile.

The overall organization of the book remains the same as in the earlier editions. The first chapter takes a careful (albeit nontechnical) look at the laws of logic and then examines how these laws are used in the structuring of mathematical arguments. The second chapter discusses the two main foundations of analysis: sets and functions. This provides an elementary setting in which to practice the techniques encountered in the previous chapter.

Chapter 3 develops the properties of the real numbers R as a complete ordered field and introduces the topological concepts of neighborhoods, open sets, closed sets, and compact sets. The remaining chapters cover the topics usually included in an analysis of functions of a real variable: sequences, continuity, differentiation, integration, and series.

The text has been written in a way designed to provide flexibility in the pacing of topics. If only one term is available, the first chapter can be assigned as outside reading. Chapter 2 and the first half of Chapter 3 can be covered quickly, again with much of the reading being left to the student. By so doing, the remainder of the book can be covered adequately in a single semester. Alternatively, depending on the students' background and interests, one can concentrate on developing the first five chapters in some detail. By placing a greater emphasis on the early material, the text can be used in a "transitional" course whose main goal is to teach mathematical reasoning and to illustrate its use in developing an abstract structure. It is also possible to skip derivatives and integrals and go directly to series, since the only results needed from these two chapters will be familiar to the student from beginning calculus.

A thorough treatment of the whole book would require two semesters. At this slower pacing the book provides a unified approach to a course in foundations followed by a course in analysis. Students going into secondary education will profit greatly from the first course, and those going on to graduate school in either pure or applied mathematics will want to take both semesters.

I appreciate the helpful comments that I have received from users of the first two editions and reviewers of the third. In particular, I would like to thank Professors Michael Dutko, Ana Mantilla, Marcus Marsh, Carl Maxson, Stanley Page, Doraiswamy Ramachandran, Ernie Solheid, David Trautman, Kevin Yeomans, and Zbigniew Zielezny. I am also grateful to my students at Lee University for their numerous suggestions.

Steven R. Lay
Cleveland, TN

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)