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Analysis with an Introduction to Proof Hardcover – Illustrated, 24 January 2013

by Steven Lay (Author)
4.2 4.2 out of 5 stars 99 ratings
Edition: 5th
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Analysis with an Introduction to Proof: Pearson New International Edition
Analysis with an Introduction to Proof: Pearson New International Edition
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For courses in undergraduate Analysis and Transition to Advanced Mathematics.

Analysis with an Introduction to Proof, Fifth Edition helps fill in the groundwork students need to succeed in real analysis―often considered the most difficult course in the undergraduate curriculum. By introducing logic and emphasizing the structure and nature of the arguments used, this text helps students move carefully from computationally oriented courses to abstract mathematics with its emphasis on proofs. Clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers make this text readable, student-oriented, and teacher- friendly.

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  1. ISBN-10
    032174747X
  2. ISBN-13
    978-0321747471
  3. Edition
    5th
  4. Publisher
    Pearson
  5. Publication date
    24 January 2013
  6. Language
    English
  7. Dimensions
    19.3 x 2.54 x 23.62 cm
  8. Print length
    408 pages
  9. See all details
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Product description

About the Author

Steven Lay is a Professor of Mathematics at Lee University in Cleveland, TN. He received M.A. and Ph.D. degrees in mathematics from the University of California at Los Angeles. He has authored three books for college students, from a senior level text on Convex Sets to an Elementary Algebra text for underprepared students. The latter book introduced a number of new approaches to preparing students for algebra and led to a series of books for middle school math. Professor Lay has a passion for teaching, and the desire to communicate mathematical ideas more clearly has been the driving force behind his writing. He comes from a family of mathematicians, with his father Clark Lay having been a member of the School Mathematics Study Group in the 1960s and his brother David Lay authoring a popular text on Linear Algebra. He is a member of the American Mathematical Society, the Mathematical Association of America, and the Association of Christians in the Mathematical Sciences.

Product details

  • Publisher ‏ : ‎ Pearson; 5th edition (24 January 2013)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 408 pages
  • ISBN-10 ‏ : ‎ 032174747X
  • ISBN-13 ‏ : ‎ 978-0321747471
  • Dimensions ‏ : ‎ 19.3 x 2.54 x 23.62 cm
  • Customer Reviews:
    4.2 4.2 out of 5 stars 99 ratings

About the author

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Steven R. Lay

Steven R. Lay

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Fio
5.0 out of 5 stars I thought this was a really good textbook for what could easily be a confusing subject
Reviewed in the United States on 28 December 2014
Verified Purchase
I thought this was a really good textbook for what could easily be a confusing subject. The author very carefully introduces all relevant definitions upfront and the chapters stack over one another (kind of like a Matryoshka doll). Everything is presented to the reader assuming little prior knowledge of calculus and a majority of the proofs are either built through logic or basic algebra. The book is written somewhat like an essay (in that there are introductions, 'paragraphs' and conclusions to each chapter) and proceeds in a linear manner.

There were some excellent visual aids which helped clarify the material at certain points. (In particular, I found the graphics for neighborhoods and the IVT to be very useful.) The combination of verbal, mathematical and visual descriptions often helped solidify exactly what was being described. There were also quite a few examples of how concepts could be used for other purposes (like on p. 218 in the 5th edition where the IVT is used to prove that every positive number has a positive nth root). I thought the applications were interesting and they definitely piqued my curiosity more than once.

The only thing I wish it included was answers to the practice problems (but maybe those are available elsewhere?). The back of the book only has 'hints' for selected problems but I felt like there weren't enough worked examples in the book to ensure you were grasping the concepts (enough to apply them, in any case).

However, I would overall recommend this book if you are interested in seeing concretely how some of the ideas you might take for granted in a calculus course could be derived from basic principles.
12 people found this helpful
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Sujaan
5.0 out of 5 stars Great book
Reviewed in Canada on 15 October 2013
Verified Purchase
Steven Lay's book is a good book for introductory analysis. I would highly recommend it to anyone starting analysis. It starts off with elementary set theory and reviews proof techniques like contrapositive. Also, Amazon delivered it within a week of ordering it. I am pleased both with the book and the speed of the delivery.
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Turtleman
5.0 out of 5 stars Extreme clarity. Good for self-study
Reviewed in the United States on 3 July 2015
Verified Purchase
I have tried
"Intro to Real Analysis" by Bartle & Sherbert,
"Elementary Analysis: the Theorem of Calculus" by Ross, and
"Intro to Analysis" by Roenlicht.

Most of Real Analysis books seem that the authors are trying to show off how smart they are.
Those books often have only 1st edition, which implies that they are not really interested on teaching.

This book (Lay's) is completely different from them.
The clarity of the book cannot be matched with any other real analysis textbooks I have tried.
The strength of the book is that it spends much time on emphasizing how theorems are used as "key elements" of proofs,
instead of showing just endless list of theorem-proof, lemma-proof, and corollary-proof.
Also, the end-of-chapter problems contain True/False questions to check "key elements", before starting proof questions.

This book is the stand-alone textbook for learning real analysis.
I recommend this book for self-study.
27 people found this helpful
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Dina T
5.0 out of 5 stars Very readable
Reviewed in Canada on 14 September 2013
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I am a student taking my first proof based course, and I find this textbook really clear and readable as an introductory real analysis text.
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Amazon Customer
4.0 out of 5 stars Getting me through analysis class
Reviewed in the United States on 18 October 2013
Verified Purchase
My class required a text by Bartlett/sherbet of which I can make neither head nor tails. This text is readable. It also has some great "guided" examples where the author gives you parts of the solution to help you along. My biggest beef with this and the other text is that there are so,few worked examples. I am a schaums lover. I want ALL the odd problems worked out !!! So sue me, but if you give a beginner a problem with no answer how am I supposed to know if I am getting it!? Still....at least I can understand it.
16 people found this helpful
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