Introduction to Real Analysis, 4th Edition 4th Edition by Robert G. Bartle (PDF)

Description

This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations, and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with additional examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: Introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible.

User’s Reviews

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

⭐This book provides a solid introduction to real analysis in one variable. The first two chapters introduce the basics of set theory, functions and mathematical induction. Also, the properties of real numbers are introduced here “borrowing” the concept and properties of field from abstract algebra.The following chapters deal with sequences and series of numbers, limits, continuity, differentiation, integration, sequences and series of function, in this order.I think the material is presented clearly and the results are proven rigorously throughout the entire book. There are a lot of worked-out examples and many exercises that will test the reader’s understanding. Solutions and hints to many (notice, not only the odd ones) of the problems are given in the back of the book. There is also an appendix on logic for those who might need to review the basics, and one on metric spaces and Lebesgue integrals for those students who want to go a bit farther.In my opinion, this book is not as good as Rudin’s book, but it does the job better than many other introductory books on the same topic. For a horrible book see Jiri Lebl’s text.Real analysis is hard, independently of the book you use. It requires a lot of care and hard work. This book does the best it can at clearing the path for you.

⭐I’m skeptical of all the 5 star reviews this book has. I would venture to guess that most of those reviews are coming from students who haven’t read other introductory Analysis texts, and so they don’t have any reference points outside of it.The text is certainly not terrible, but it strikes me as a typical example of what you can expect from the textbook industry. Quantity over quality. The material covers a lot of ground, but with very little emphasis on clarity. Statements such as “it follows from theorem a that x implies y” are littered in examples throughout the text, with no further explanation on why “it follows.” In some cases, when new concepts are introduced, I would have had no idea what the Authors’ were talking about had I not previously reviewed the concept in a better text (such as Abbott’s Understanding Analysis). I would expect this in more advanced texts, but not one that has “Introduction” in its title.It’s not that I expect Analysis to be easy. I just find texts like this to be wasteful of students time, because while you can eventually grasp the material, the task could have been quicker.

⭐This book is great. I am using it in my real analysis class right now and I’m very glad my professor chose this one. The book does a great job of explaining the material and the proofs don’t skip a lot of steps like I’ve seen before in other classes. The first chapter is a basic introduction to all the terminology that is used throughout the course and it is a nice reference whenever I need it. The back of the book contains a lot of hints and solutions to the problems, so when I am studying for a test it makes it a lot quicker and easier to review material. I’ve only gotten up through Chapter 4 in my class, but so far I don’t have any negative comments about it.

⭐Traditional kind of textbook that goes from intuition -> definition -> theorem -> proof. Many compares it to Abbott’s Understanding Analysis which is more like lecturing which is also good. But personally prefer this kind of organization.

⭐For undergraduate students, this book is one of the best introduction to Real Analysis. The nice thing about this book is there are many good examples for each Theorem which help you reinforce what you just read. I’ve been using this book for my first course in Introduction to Analysis, and I’m in love with it. The structure of the book is also very organized, and exercises are very relevant to each chapter. Excellent book for Introduction to Real Analysis.

⭐Taking my first graduate math class after years out of the classroom. This is the required text and I am not loving it. I find the text by Lay more readable. Also bought one by Mattuck that was an entirely different approach….very wordy. Have not found anything like a Shaums with many solved problems. Both of these texts show solutions for about a tenth of the problems they pose…..ah…for the days when I thought calc was difficult…..

⭐I really enjoyed using this book for my class. I kept it to use as a reference and its fantastic. The author uses the word “so” and “since” a bit too much.

⭐Great book! I have used it as a text book for a while now. It can be read at different level for math major students.

⭐Thank you amazon for making it available in a paperback edition. The book is extremely great and a absolute beginner can read and understand it with immense pleasure, It starts with basic sets function and ends up to Riemann integrals and some glimpse of Topology.If you love mathematics and the joy of discovering proofs and ideas go ahead you won’t regret.

⭐Mi libro favorito de introducción al análisis matemático.Cada tema es tratado con excelencia tanto en profundidad teórica como en ejemplos expuestos. Siempre que necesito regresar a pruebas de temas elementales, es éste mi libro preferido.Está edición contiene diversos temas complementarios y fundamentales.Además, la confección del libro es perfecta, con una muy duradera pasta dura y el papel utilizado es del mejor.Compre hace tiempo este libro para mi y no me dececiono en absoluto, y ahora compre 3 mas para unos amigos, el contenido del libro es estupendo, un curso introductorio estupendo de analisis, pero bastante deficil de digerir si es que planeas estudiarlo por tu cuenta (ser autodidacta). Excelente para matematicos y fisicos.El material es economico, pero bastante bueno, no pesa mucho y la tinta se ve muy bien (salvo en algunas hojas que estan un poco mas tenues).Tuve algunos problemas con uno de los libros que pedi pues la pasta venia dañado, aunque el vendedos a la hora de reclamarlo me respondio rapido y amablemente incluso me hizo un descuento.Lo recomiendo encarecidamente.A Classic book having strong mathematical rigor. Not an easy read. Excercises are coceptual. Background in basic Calculus, proof writing,algebra needed to study the book in detail. Takes time to complete each chapter but is enjoyable.

⭐It is a quality textbook for real analysis. It is so nicely written that there will no diffoculty in following it even without an instructor. Some bakground in calculus and algebra will be helpful as the book assumes this.

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