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Real Analysis (Springer Undergraduate Mathematics Series)

Real Analysis (Springer Undergraduate Mathematics Series) [Kindle Edition]

John M. Howie
4.0 out of 5 stars  See all reviews (3 customer reviews)

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Product Description


From the reviews:

Written in an easy-to-read style, combining informality with precision, the book is ideal for self-study or as a course textbook for first-and second-year undergraduates.
Zentralblatt MATH
….the transition from the mysteries of real-analysis to the majesty of real analysis will be smoothed by this engaging, readable text.
The Mathematical Gazette

"This book is the distillation of Howie’s considerable experience in teaching the introductory real analysis course: he adopts a concrete, pragmatic approach ... . The most striking feature of Real Analysis is ... the author’s Ferrar-like concern for the reader’s understanding which shines through on every page of his carefully written and carefully paced text. ... There are numerous worked examples and some 190 accessible, impeccably pitched exercises ... another attractive feature is the inclusion of full names and dates for all mathematicians mentioned." (Nick Lord, The Mathematical Gazette, Vol. 85 (504), 2001)

"The book is a clear and structured introduction to real analysis. ... Fully worked out examples and exercises with solutions extend and illustrate the theory. Written in an easy-to-read style, combining informality and precision, the book is ideal for self-study or as a course textbook for first- and second-year undergraduates." (I. Rasa, Zentralblatt MATH, Vol. 969, 2001)

Product Description

Real Analysis is a comprehensive introduction to this core subject and is ideal for self-study or as a course textbook for first and second-year undergraduates. Combining an informal style with precision mathematics, the book covers all the key topics with fully worked examples and exercises with solutions. All the concepts and techniques are deployed in examples in the final chapter to provide the student with a thorough understanding of this challenging subject. This book offers a fresh approach to a core subject and manages to provide a gentle and clear introduction without sacrificing rigour or accuracy.

Product details

  • Format: Kindle Edition
  • File Size: 3130 KB
  • Print Length: 276 pages
  • Publisher: Springer; Corrected edition (27 Sep 2006)
  • Sold by: Amazon Media EU S.à r.l.
  • Language: English
  • Text-to-Speech: Enabled
  • X-Ray:
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Bestsellers Rank: #430,352 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
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Most Helpful Customer Reviews
3 of 3 people found the following review helpful
5.0 out of 5 stars The definitive introduction to analysis 5 April 2010
By Alpha
One of the difficulties faced by a student is to bridge the gap between the intuitive style of thinking in calculus and the more rigourous approach that is adopted in analysis. Howie's "Real Analysis" meets this challenge with flair. The "epsilon-delta" definitions that epitomize analysis are well motivated and well illustrated with excellent examples and exercises. Howie address the usual topics (sequences, series, continuity, limits, differentiation and integration), then applies them concepts by defining the exponential and circular functions in the formal language developed. And most importantly, I genuinely found it fun and entertaining. Highly recommended.
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5.0 out of 5 stars Real Analysis 2 May 2013
Format:Paperback|Verified Purchase
Useful textbook by a clear author. I will use it in my lessons. It is suitable for self study also
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0 of 4 people found the following review helpful
2.0 out of 5 stars Don't use is if you can help it 30 Jun 2013
Format:Paperback|Verified Purchase
Buy Haggarty instead!!! Don't bother with this. It doesn't even include Logic and Truth Tables, and what kind of Analysis are you going to do without that?
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Most Helpful Customer Reviews on (beta) 3.2 out of 5 stars  4 reviews
5 of 5 people found the following review helpful
4.0 out of 5 stars lacks exercises 14 Oct 2009
By Not Available - Published on
Format:Paperback|Verified Purchase
As you might already know this book is the basic of analysis, this is literally the introductory book to analysis. It goes into Sequences and Series, Functions and Continuity, Differentiation, Integrations etc (see "contents" for more detail).

The author of this book explicitly says that a prior knowledge on Calculus is expected before reading this book and he really means it. If you did your Calculus I (limit and derivative), Calculus II (integration), and Calculus III (multivariable) a year or two ago, you need to go review at least the topics that are covered in this book. Remember all the convergence/ divergence (Comparison Test, Limit Comparison Test, Ratio Test, Root Test, Lebeniz Test, P-test etc) tests that you did in Calculus II (?) The author manages to squeeze them all in 5 pages or so.

The major drawback of this book (for me) is lack of exercise. There are very few sections which have more than 10 problems, most have 6 or less. Here is a detailed data:

chapter 1 has 6 sections but only 24 problems
chapter 2 has 7 sections but only 44 problems
chapter 3 has 7 sections but only 37 problems
chapter 4 has 5 sections but only 17 problems
chapter 5 has 7 sections but only 27 problems
chapter 6 has 3 sections but only 19 problems
chapter 7 has 3 sections but only 19 problems
chapter 8 has 2 sections but only 1 problem
chapter 9 has 3 sections but only 1 problem

thankfully solutions to all these problems are available in the back of the book. These solutions are worked out well enough.

Another drawback of the book is that it does not inspire you. In most mathematics book (or any other course book for that matter) each chapter begins with a little bit of history, real life application or something that helps connect to the student. This book barely does that. Usually, the section starts with a theorem, followed by a proof or two, and finally two three examples.

Overall imo this book is more of a "study guide" than a textbook itself. The publisher say this book can be used for self study as well as course textbook. I will admit that this is an easy self study book but i would get a more detailed textbook to tag along with this, just in case.
17 of 26 people found the following review helpful
4.0 out of 5 stars British Style Math Book 10 Mar 2002
By A Customer - Published on
This is an introductory text of real analysis and it is kind of British Style (in term of the way they proved the theorems). Also, some advanced topics like "Metric" and "Generalized Riemann Integral" are not covered. If you really want to learn real analysis yourself, try Robert Bartle's "Introduction to Real Analysis", Manfred Stoll's "Introduction to Real Analysis", Apostol's "Mathematical Analysis" and Rudin's "Principle of Mathematical Analysis". Stephen Abbott's "Understanding Analysis" is also an excellent real analysis text.
4 of 10 people found the following review helpful
1.0 out of 5 stars The Worst Math Text Ever 5 May 2010
By Conor Jensen - Published on
This book was the example used by my mathematical writing professor as how NOT to write math texts. The formatting is strange, the theorems and definitions are buried in the text with no delineation whatsoever. There are typos throughout the book, sometimes in the middle of proofs, making the proofs even more difficult to follow.

The lack of exercises and examples are a little frustrating, as well, though this is typical of higher level math texts. I understand that the purpose of this book is to make analysis more accessible for undergraduates, but I feel that this book made the material more difficult than other, more advanced texts. Analysis is a challenging enough subject, and I feel that this book only exacerbates that.

My personal recommendation to anybody starting an analysis course, undergrad or grad is Principles of Mathematical Analysis by Walter Rudin. It's more advanced but far more thorough and illustrative in its proofs.
0 of 3 people found the following review helpful
4.0 out of 5 stars Good condition 15 Mar 2013
By Christine Peace - Published on
Format:Paperback|Verified Purchase
It's in good condition and I got it on time. It's not that big of a textbook, but it has all the important information that I need
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