Analysis With An Introduction to Proof, 5th Edition 5th Edition by Steven Lay (PDF)

Description

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.

User’s Reviews

Editorial Reviews: 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐I would not wish this text on anyone!1. This text features incomplete proofs that leave too much to the imagination of the beginning analysis student.2. The author asks us to prove important theorems as part of the exercises.3. We are repeatedly referred back to previous exercises and to theorems by number, rather than by descriptive names. Referring students to theorem numbers fails to evoke recall of past material.I am about to FAIL my advanced calculus 1 class trying to learn from this book. I pray that my future classes will not use texts that are written this way.

⭐I am writing this review after having taken my intro to analysis course and my Real Analysis I course as an undergrad and finally feel like I can give some thoughts on where I think this book does well. I used this text for my into to analysis course which was mostly focused on logic, structure of proofs, and then got into sets, functions, convergence of a sequence, and basic topology. I have to say I actually really liked this book as an intro to proofs, logic, and even the topology section isn’t bad. Past that I am not sure I can recommend this text. The definitions just aren’t as intuitive as Abbot’s Into to Analysis text for some of the more advanced topics like continuity, functional limits, uniform convergence, and differential calculus. The definitions and proofs shown in Abbot’s book are definitely more elegant and intuitive than this text. In conclusion, I would highly recommend chapters 1-4 of this text for an intro to proofs and logic class (and maybe even as a second reference if your struggling with proofs in real analysis), but for a first-semester real analysis course, stick to Abbot.

⭐It sucked.It’s too low level. The focus on the course was mainly how to do epsilon delta proofs, induction, prove something about some function using sequential continuity, prove something using the IVT, MVT, difference quotient, and then integration.The course was not ultra relevant, but I guess it was required. We almost never used the text, and when I did I used it to see the proof of some Theorem for how the author did it vs what my prof was doing. The author did a better job. I still don’t care for this book. I would return it. I also have the likes of baby Rudin, which could serve as a reference in the least.

⭐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.

⭐Quite often Mathematics textbooks can be a challenge to read and absorb without actual lectures from a Professor/Master. This book however, is very good and really does not need supplemented learning time.I have been rather surprised by how good this book is. Gives exact references in proofs. Each section builds off each other in a very linear fashion.I am very glad my professor choose this textbook for my Real Analysis 1 lecture.

⭐When I received this item it had water damage. It was still readable, but there was no mention of the damage. I rented it used so I’m not complaining, just warning.

⭐Book is in bad condition for being a rental. The binding is nearly falling apart. It’s useable but can’t believe it’s in this condition and being rented out.

⭐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.

⭐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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