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Introduction to Analysis (Dover Books on Mathematics) [Paperback]

Maxwell Rosenlicht
3.9 out of 5 stars  See all reviews (30 customer reviews)

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Book Description

February 1, 1985 0486650383 978-0486650388
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. Rigorous and carefully presented, the text assumes a year of calculus and features problems at the end of each chapter. 1968 edition.

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Introduction to Analysis (Dover Books on Mathematics) + Introduction to Topology: Third Edition (Dover Books on Mathematics) + A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 254 pages
  • Publisher: Dover Publications (February 1, 1985)
  • Language: English
  • ISBN-10: 0486650383
  • ISBN-13: 978-0486650388
  • Product Dimensions: 8.5 x 5.3 x 0.5 inches
  • Shipping Weight: 8 ounces (View shipping rates and policies)
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (30 customer reviews)
  • Amazon Best Sellers Rank: #55,964 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
129 of 134 people found the following review helpful
5.0 out of 5 stars a bargain May 30, 2001
Buying this book is a no-brainer. It's only [price]. Unlike many dover books, it's not a reprint of a hundred year old text or dominated by 19th century style formal manipulations with indices running everywhere and no actual analysis or rigorous proofs. It covers the key topics of elementary real analysis (ie advanced calculus, or calculus with real proofs), which is basic to almost all fields of mathematics. In order to focus on the main ideas and definitions, it leaves out many topics and definitions (like functions of bounded variation, absolute continuity, lebesgue integration, differential forms, lebesgue covering lemma, f.i.c. etc.), so you should definitely have a more complete and comprehensive text like Apostol or Rudin (I prefer Apostol, although Rudin has complementary strengths). But for those omissions, Rosenlicht is quite a bit more readable than Apostol, which is best worked through methodically (since it contains a lot of results explicitly presented, its primary strength). Because it's both short and readable and focused, you can get through it reasonably quickly. Modern secondary school education teaches students to skip over the cursory material on elementary set theory, number systems, and strangely named but apparently obvious concepts like associativity and other field axioms, and to jump straight to the various sections with formulas in outlined boxes and procedure recipes for performing calculations. These rote recipes typically lack any conceptual unity and students are not often worse for wear forgetting or only superficially grasping previous ideas. This is a good way to never actually learn any legimate mathematics. Real math works on the principle of A->B->C->.... A proof (or your understanding of a mathematical concept) is only as strong as the weakest link in a chain. Read more ›
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63 of 64 people found the following review helpful
Introduction to Analysis by Maxwell Rosenlicht is another bargain from Dover Publications. I used this inexpensive mathematics reprint to help fill in gaps in my background before tackling more advanced mathematics. I found the first 150 pages to be challenging, but manageable. I had less success with the last 100 pages.

My college work was limited to applied mathematics, but in recent years I have developed some familiarity with metric spaces, topology, and analysis. (I previously reviewed Metric Spaces by Victor Bryant and Introduction to Topology by Bert Mendelson.)

Throughout his text Rosenlicht emphasizes how the same idea or theorem can be formulated in various ways. I found his approach to be quite helpful in clarifying more abstract representations of key ideas.

The first two chapters review set theory and the real number system and should be familiar to many readers. However, Chapter 3 (Metric Spaces) and 4 (Continuous Functions) are critical and require substantially more effort. My pace slowed dramatically.

For the reader new to metric spaces, Chapter 3 will likely be challenging, although metric space concepts are not really that difficult, just unfamiliar.

Rosenlicht demonstrates how statements concerning the open subsets of a metric space can be translated into statements concerning closed subsets, or alternatively into ones concerning sequences of points and their limits. Rosenlicht closes Chapter 3 with definitions and discussions of Cauchy sequences, completeness, compactness, and connectedness.

Rosenlicht begins Chapter 4 by illustrating that the familiar epsilon-delta definition of continuity of functions can be reformulated using the metric space open ball concept, or by using open subsets in metric spaces.
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23 of 24 people found the following review helpful
5.0 out of 5 stars An excellent introduction to real analysis January 22, 1998
A very readable book. Any student with two years of calculus should be able to read this with understanding. Starts with metric spaces, and proceeds through differentiation, integration, interchange of limits, implicit functions. A kinder and gentler introduction, yet rigorous.
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30 of 33 people found the following review helpful
5.0 out of 5 stars Gets right to the point with no waste of time! April 26, 1998
By A Customer
In the beginning the faint of heart should beware. This book takes no time in getting to the deeper underpinnings of analysis. This makes the reader learn and become comfortable far quicker then the average book, although it can be frustrating for the first month. However, past the introduction, Rosenlicht gives an unmatched exposition of difficult material and is far more readable than most. Definately the best book in analyis for the money! Great as a stand alone text or as a supplement to a beginners course in analysis such as Russell Gordon, "Real Analysis: An Introduction." Every student should own a copy (is $8 all that much?)
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25 of 28 people found the following review helpful
3.0 out of 5 stars Solid introduction to analysis December 27, 2004
By K.
I used this book in conjunction with Little Rudin while studying analysis. While Rudin provided deeper insight, it provided almost no motivation or exposition. Rosenlicht and Little Rudin are very good complements to one another. I found Rosenlicht much easier to learn from, but use Rudin as a reference now that I understand the theory.
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16 of 17 people found the following review helpful
5.0 out of 5 stars still one of the best September 23, 2003
By A Customer
The book was written in 1960s, and is still one of the best. The presentation is exceptionally clear; treatment of metric spaces and elementary topology is superb. Plenty of counterexamples and good (doable) exercises (some with useful hints). The print is a bit small, but you'll get used to it. Worth every penny. More math texts should be as short, inexpensive and good as this one. Highly recommended.
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Most Recent Customer Reviews
5.0 out of 5 stars Clear introduction to analysis
I'm considering applying to PhD programs in economics and purchased this for review. I also want to build on what I learned in high school and as an undergrad at UCLA. Read more
Published 3 months ago by Norman Oro UCLA 93
1.0 out of 5 stars 2013 Important Books edition ILLEGIBLE!
Make sure you get the Dover edition. The print in the Important Books edition looks like a 40th generation photocopy done on a first generation photocopier! Read more
Published 3 months ago by James E. Anderson
5.0 out of 5 stars Well written math book.
Great introduction to analysis as the title indicates. Reviews basic mathematical ideas from elementary school and builds up to more advanced undergraduate math topics.
Published 4 months ago by Amir Aczel
2.0 out of 5 stars Great Book - Terrible Printing
The author, Dr. Rosenlicht, has done an excellent job on the textbook. The printing, however, is nearly unreadable. Read more
Published 6 months ago by Slllade
1.0 out of 5 stars blotchy type
While the exposition in this book is excellent - it is sometimes unreadable - especially problematic are the superscripts and subscripts. Read more
Published 7 months ago by rivertech
2.0 out of 5 stars Dated.....collectors maybe, but not if you are enrolled in an analysis...
Not worth it. I am in an intro to Analysis course and figured sometimes classic material benefits from classic presentation.......but not this time..... Read more
Published 9 months ago by J. Stevens
1.0 out of 5 stars I can't believe I paid money for this
To be clear, this rating is based on the quality of THIS VERSION of the book. The text itself is a quality textbook, but the quality of this particular printing is atrocious. Read more
Published 9 months ago by bonehead
5.0 out of 5 stars Incredibly concise and understandable introduction to analysis
This is one of the best (if not the best) introduction to analysis I've read. If I have one criticism of some mathematical authors is that sometimes 'elegance' gets priority over... Read more
Published 14 months ago by Diego Alonso Cortez
5.0 out of 5 stars Perfect
Quick and perfect. The book is exactly as it was described in the advertisement. It was sent as quickly as I could expect.
Published 17 months ago by garnier
5.0 out of 5 stars Excellent, great value
Great for learning introductory analysis. The book is concise and thorough, the proofs given are clear and easy to follow.
Published 18 months ago by Huey
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