Summaries and Customer Reviews are supplied by Amazon.com
Summary:
This book outlines an elementary, one-semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.
Customer Reviews:
Average Customer Rating:
Adequate, but missing solutions is frustrating.
Customer Rating:
It's a good introductory book, but it leaves a prodigious amount of the Theorems as exercises. This makes studying out of the book very difficult in a time crunch. Still, easy to understand the explanations that are given.
A book which is too unfocused for beginners
Customer Rating:
I attempted to teach out of this book and my students found it difficult since many of its exercises aren't properly prefaced in the sections for which they were intended. The ordering of the ideas is also haphazard and the general presentation assumes far more mathematical knowledge and familiarity with basic concepts than can be gleaned from its pages alone. An extension to the introductory section on set theory and mappings would be helpful to the presentation. Many sections are unnecessarily chatty in the wrong places and unfocused. It is an inexpensive book, but Bartle and Sherbert's masterful introduction is well worth 5 times its price.
Super user-friendly well written analysis book delightful to read!
Customer Rating:
I currently own Baby Rudin, Kolmogorov and Fomin, Marsden, John Royden, Probability and Analysis and this book I think if this book provides a solutions manual, it will be the best self-study book. Sure Rudin is elegant and very general in a sense that it covers huge amount of materials through pithy and concise yet rigorous proofs but this is exactly why i don't think it is a good book to start.
When i started with Rudin because of its fame, I was very frustrated because of the density of the book. It is very heavy reading that you need to explicate in your head to understand. This is all good and well if you already grasp the idea but for first time learners rudin should be used as a reference. ( i am sure lots of people disagree, this is just my view).
This book on the other hand is super friendly and when you read it, it does the explicating of the ideas for you. it is as if you are listening to a professor who does the thinking for you. OF COURSE this is not GOOD for learning how to proof stuff. That, one must learn by himself. However, When one wants to learn the ideas and grasp the general overview and the beauty of analysis, it serves one well.
I recommend this book to anyone who wants to leisurely yet rigorously learn analysis. usually, those two words are oxymorons but this book combines them - leisure and rigor come together.
A great book!
Customer Rating:
As a student of an introductory analysis course which used this book, I would like to share my perspective to all those who might find it helpful. No doubt, this is a great book which encouraged me to read back through all the project sections. Abbott manages to do two things which I have not seen in many other analysis books: firstly, he manages to be very thorough with every topic he presents, thus there are no confusing interludes, nor does he jump from easy topics to hard topics within the length of a page. Secondly, the problems are all very well thought out, I can guarantee that there is no "busy work" in this book. Each problem is worth looking at and so encourages students to test themselves outside of any assigned work. As has been said before, this book is an investigation into the reasoning behind this reworking, which enables students to formulate correct definitions even when they have no prior experience with a concept. Abbott's book is a very effective approach to introductory analysis, encouraging true thought and understanding over busy work or memorization, which, as a student I am very thankful for. Again, read correctly, this book will create a lasting love for the subject, and will encourage any diligent student to think beyond the scope of the book.
Great for the basics: You will be glad you bought it
Customer Rating:
I have studied analysis with at least two other books "Introduction to Real Analysis" by Michael J. Schramm and "Principles of Mathematical Analysis", by Walter Rudin.
Abbott's presentation is the best in terms of concept building for beginners (Schramm is good too).
Abbott's presentation is limited to the real number line R. But that is not a bad thing, it is a good thing. The reader can understand the concepts by associating them with a field that is familiar to most of the analysis' beginners.
Sometimes the presentation in the book is not as formal as it is done in other books but it never gets too informal.
The proofs are clear, the exercises clarify the concepts learned in each sub-chapter and work on new concepts as well.
I really think I learned much more from this textbook than what I have learned from any other analysis' textbook before.
If you are taking a class that will be using this book, you will be glad you bought it.
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