The Way of Analysis, Revised Edition: . (Jones and Bartlett Books in Mathematics) Revised Edition

I read all the reviews on this book before writing. I have read about 3 chapters of the book. I believe this is how a book aimed to teach should be written. Some of the reviewers believed that the book was too verbose. These folks must be geniuses I really wonder about their intelligence. I have read Walter Rudin's book on some ones recommendation, It just sucked. Rudin is not a book from which you can learn analysis. It is one of the crappiest books ever written. It probably makes for a good reference but if the material was learnt it is more than likely u will not need a reference. If you are like me self studying analysis you will love this book. Like one of the reviewers said, this book is an easy read.Analysis was developed over centuries and without sufficient motivation and examples it is just impossible to come to grips with the subject. A bit more explanation never hurt anyone and this book has a lot of detail and points out subtleties that are easily missed if you read some of the other books on analysis. One example is the difference between a limit point and the limit of a sequence. I did not know the difference till I read this book. I bet you some of the geniuses that read Rudin believe they are the same.I also liked the development of Reals as equivalence classes of sequences of rationals it makes so much sense to do it that way. Rudin in his infinite wisdom chose to develop the real numbers as a field/dedikind cuts, go figure.For any undergraduate or graduate student looking at analysis for the first time this is a book one must have.

The current mathematics text landscape is a troubling one: Most of the standard texts are great as references, but are often not very effective at conveying the material to a student approaching a subject for the first time. Refreshingly, this book does not suffer from this failing; instead, it is packed full of explanation, examples, context, and informational asides. In fact, it is so crammed full of text that often the actual point often becomes lost amid the explanation. This renders the text almost useless as a reference because it requires so much trudging to get to the point. I very much enjoyed some of the insights provided by this book, but ultimately I found it too much of an effort to sort out the central message from all the other fluff; I ultimately abandoned this book for a cleaner treatment.I you're trying to learn Analysis on your own, this may be a good starting point. If you're actually taking a class, this book is likely overkill in the exposition department. If you're looking for a reference, look elsewhere. In any case, you may want to consider Abbott's absolutely brilliant book Understanding Analysis, which manages to be a great presentation that succeeds all around.

Pros:It explains a lot of the motivation of why we are studying something, and it helps you grasp the idea intuitively.The proofs are easy to follow, explaining in detail.Clear explanation and good example problems.It is definitely recommended for self studying.Cons:In a way, it's "too explanatory." It feels like I am reading a lecture and honestly, it's a little slow for some easy to grasp concepts.It gets tiring after a while, so this is the reason I did not give it 5 stars.Summary:It's a great book; easy to follow, intuitive motivations and explanations and the arguments flow so it is recommended for people who actually spend time reading their math book. You might find it boring if you are pretty smart, because it explains a lot more than what is necessary.

Excellent! This is all you need to know about this book: it is efficient. No it does not mean that it uses fewer words, it is somewhat chatty. It is efficient in that once you do the exercises and learn the corresponding material, it will stick and you won't find yourself wasting your precious energy deciphering notation. What a waste of time that would be. The content is not hidden by anything, and this will allow you to find the way, and the how of analysis.

This book works best if you think of it as a substitute for class lectures, while working through exercises and material from a more traditional text. In that role, it's truly excellent, and a fast, pleasant read, despite its bulk.The bits on approximation in function spaces are particularly well motivated, and include a juicy excursion into convolutions.Highly recommended for undergrad analysis students with time for some extra reading.Just make sure you have an actual textbook on hand for exercises and reference. Browder is good for the latter, Pugh for the former, and Rudin does both.

To anyone that is looking to take a first course to Analysis, this book is a great buy. It offers a smooth read with well organized and detailed Proofs. The book is easy to read as well since the Author tends to go into extra detail that some may not, in order to provide the reader with great depth in understanding the thought process involved in Analysis.Great Book.

Although I found some of the notation to be different from what I am used to seeing, it is equivalent and easy to comprehend.The content is comprehensive and I though it was easy to read. Its probably not what would be considered as a main text for a class in Analysis, but it makes a valuable adjunct to almost any of the standard texts. I like it.

Most books on mathematics simply dump concepts,equations and examples and let you figure out what to do. Not this one. The book is written in a passionate manner where the author takes pains to explain why we are going in a particular direction and the goals. The style is extremely lucid and informal, something unusual for a subject that is steeped in formal mathematics. Yet the author presents, explains and covers all the formal theorems, concepts etc . The book also has excellent exercises. A truly noteworthy achievement. I would highly recommend this to anyone (especially self-study) trying to learn this subject.

El estilo es demasiado narrativo, para ser un libro que pretende conservar un rigor matemático. Esto se nota sobretodo en las demostraciones. Además, algunos temas se tratan con bastante superficialidad, como la construcción de los números reales. Esperaba que fuese un buen complemento de libros como "Mathematical Analysis" de Bernd S.W. Schröder, "The Real Numbers and Real Analysis" de Ethan D. Bloch o "Basic Real Analysis" de Houshang H. Sohrab", todos ellos adquiridos por mi en Amazon.