Introduction to Real Analysis

by Robert G. Bartle, Robert G. Bartle

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, analyse 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 addition 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.

Genres: Mathematics, Textbooks, Science, Reference, Academic, Nonfiction

416 pages, Hardcover

First published March 24, 1982

Reviews

[Ron · Rating 3 out of 5]

This book was used in my Real Analysis course. The subject would be hard to learn from this book alone, but lucky for me I had a great teacher at San Jose State University. For those trying to use the book, I do have some electronic copies materials of theorems and study notes that I put to help me in my studies. Contact me if you want copies of those materials.

[Bilgewater · Rating 1 out of 5]

Ouch! Trying to learn analysis with this book alone is probably impossible, and definitely not enjoyable. Mix this with Haaser & Sullivan's title and maybe Rudin's book and you stand a fair chance of walking away with a solid foundation... so you can move on to Folland's Abstract Algebra book, or perhaps even give yourself a fatal aneurysm attempting some problems from Dummit & Foote's Abstract Algebra book.

[afloatingpoint · Rating 4 out of 5]

The book is very well written, logically organized and easy to read.

[Ana · Rating 4 out of 5]

top 5 books that made me cry

[Urobuchi Gen · Rating 2 out of 5]

This textbook only covers the most basic stuffs in mathematical analysis (I don't know why the title is "real analysis") yet a more advanced text like baby rudin is even more comprehensible than this crap. The writing style of the author(s) is simply paradoxical: He keeps skipping crucial steps in the proofs of theorems which makes easy thing complicated. When you begin to think that he might just be lazy or love simplicity, then you may suddenly encounter a horribly lengthy paragraph where everything could be replaced by statements in logical symbols. The ONLY good thing about this book is that it has a lots of examples where Rudin and other authors are stingy to provide.

[Dhiraj Kumar · Rating 4 out of 5]

It's a sufficient but not a necessary book.
If you are really interested in learning analysis then Rudin a better book. To give you an analogy: this book is like rational numbers and Rudin like real numbers and we know real number fills the gaps between rational number.

[James · Rating 4 out of 5]

How strange... That math textbooks are available for review. Oh well, neat. This one's a real page turner!

[Jaci · Rating 5 out of 5]

This is a good analysis book. I recommend it.

[Shozab Qasim · Rating 5 out of 5]

I would definitely recommend it for a first course in Analysis - or if you wish to learn the subject matter yourself. The presentation is clear and the text is equipped with multiple examples to ensure that one grasps the fundamental concepts.

I would especially recommend it for people who are in a hurry to learn the relevant bits of real analysis in order to study some other (more, but not necessarily) technical subject that require or utilise analytic notions like the supremum and infimum of sets, epsilon-delta proofs, sequences or limits etc.

[Rhys Tilford · Rating 5 out of 5]

Woah! This class has been a wild ride. I loved Calculus and I may yet learn to love its related proofs but I'm not quite there. I venerate my professor though so that makes all the difference. In Calculus I, I once called her the Queen of Calculus so this year I'm emailing her a Spotify link to the song "God Save the Queen". I also had one delusionship with a friend who was taking the class with me so that played a role in keeping me engaged. 😂

[Klaire Hoang · Rating 1 out of 5]

Horrible solution. No systematic approach. All steps are messy and explained badly. The author wants to run a marathon, taking the reader from A to Z, skipping all the important B C D E D G H I J K L M N O P Q R S T U V W X Y in between

[Mukesh · Rating 5 out of 5]

awesome book

[Bal Bahadur]

Good and Best Book

[SUBRAT PANIGRAHI]

.

[Joseph]

Well

[Shai S. · Rating 3 out of 5]

I thought this book explained the real number things pretty well. Will remember peaks and the monotone subsequence theorem.

[fedya · Rating 1 out of 5]

unintuitive. feels like slugging through cliff’s notes.

[Justin · Rating 2 out of 5]

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 Abbot'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.

[Ashley]

Textbook for this fall's analysis course.

[Hahn hahn · Rating 4 out of 5]

buku babon heuheu

[Duddy Septiadi]

amazing

[Qothrotun Nada · Rating 3 out of 5]

buku edisi ketiga yang dipakai saat kuliah anril 1 dan anril 2. hmm. belum semua dipelajari saat kuliah S1.

[Maftul Fahrul · Rating 4 out of 5]

buku yang pernah dipake kuliah, bagus tampilannya, gak terlalu tebal, dan enak dibaca.

[Tue Le · Rating 4 out of 5]

This is a decent textbook. But given the difficulty of the subject matter, you will most likely need a competent professor, unless you are a mathematical prodigy.