Elementary Real Analysis: Second Edition (2008)

Wasn’t my favorite class haha

Decent Book but Boring.

I bought this book for a second semester course in real analysis. It manages to cover everything from sequences, to series convergence, to fourier and even differentation in several dimensions. Though it should be noted that the several dimensions chapters are just a tasting and I don't assume are satisfactory for a full semester course in mutivariable analysis. There is a chapter on metric spaces that I disn't go theough yet.I think that for anyone who wants to use it as a main text or supplemt it could be great.. our assigned text was Rudin's principles of mathematical analysis, and Rudin unfortunately doesn't write all steps of the proofs, which the bruckner couple(i found it nice that a couple wrote this book together.. oh the romance) and meyer manage to do(to write all proofs very meticulously).Overall highly recommended.

The book is really good. It provides a clear exposition of almost all basic real analysis topics. It is excellent as a complement for more advanced books, but limited for self study, because there isn't a solutions manual so that you can check your answers. It would be great if the authors could publish one (many of the other books the have written have one).

I am a Data Scientist by profession with CS and EE background, I have reached a point in my career where I needed to go beyond LSE based optimizations. Long story short, I realized I have to strengthen my concepts in sequences, convergence, sets, etc. before I can really appreciate Hilbert Spaces, and take a deeper dive into more cutting edge optimizations techniques.This book is like a story book, authors have accomplished a feat of unproportional amount to make it so intuitive and succinct. There are rare books that are written with such clarity and diligence towards readers. I highly recommend to those who are taking course in undergrad on this subject, specially to those who do self study, this is an extremely fundamental and critical subject and this book is equally spot on.

You will probably need some previous exposure to analysis to really appreciate this one but if you do not have such - you will have to take it on faith that this book is the ultimate real analysis reference to introduce you to the subject and help you master it in ways suitable to any further study that would need mathematical analysis.. Seriously.

Reasonably good book for beginners - authors are completely unresponsive to requests for additional information.

Really, this is one of the most pedagogical books I have read for elementary real analysis.Very highly recommended for everyone's library.

This is a review specifically on the how the printed version of this book looks (since it is free online in pdf format).Adequate is the best way to describe this. Production quality is not like that of your favourite textbook, but it is definitely in no way lacking. Still great value for its cost.It is soft cover with page quality that is not the white gloss, but rather the more fibrous paper you'd expect in a standard novel. It's all very adequate.The book is comparable in size to the Stewart's Calculus book which is nice (in comparison to some other mid-higher level undergrad books which come standard novel size).Of course, the real important stuff is the knowledge inside which is great, but since that is free online, I kept my score to the physical print's superficial qualities.

...mag man sich denken und ihm danach keine weitere Aufmerksamkeit mehr widmen. Der Gedanke ist bei der Menge an Büchern über die (reelle) Analysis, die es auf dem Markt gibt, nicht abwegig. Allerdings schafft dieses Buch recht gut den schweren Spagat zwischen mathematischer Exaktheit und Anwendbarkeit (nicht zu verwechseln mit der Numerik). Die Autoren versuchen in, wie ich finde, gelungener Weise abstrakte Formulierungen gekonnt so aufzubröseln, dass auf der einen Seite ihre mathematische Strenge nicht verloren geht, auf der anderen Seite der Leser aber mitgenommen wird und ihm gezeigt wird, wie man mit ihnen selber Mathematik betreiben kann. Daher verwundert es nicht, dass nach jedem noch so kurzen Abschnitt/Unterkapitel eine Fülle an Übungsaufgaben darauf warten, bearbeitet zu werden. Ein Bucher über Analysis liest man schließlich nicht wie einen Roman und rechtzeitige Überprüfungen, ob man die vorhergehenden Definitionen und Sätze überhaupt richtig aufgenommen hat, sollten einen davon auch abhalten und einen aktiven Lese- und Lernprozess fördern. Einziges Manko: es gibt keine Lösungen zu den Aufgaben. Dafür aber zu ausgewählten Aufgaben an jedem Kapitelende Notizen und Hinweise, die zu einer Lösung führen sollten. Wegen seiner verständlichen Formulierungen und Erklärungen ist dieses Buch sehr anfängerfreundlich.Das Inhaltsverzeichnis deckt folgende Themen ab:Chapter 1. Real NumbersChapter 2. SequencesChapter 3. Infinite sumsChapter 4. Sets of real numbersChapter 5. Continuous functionsChapter 6. More on continuous functions and setsChapter 7. DifferentiationChapter 8. The IntegralChapter 9. Sequences and series of functionsChapter 10. Power seriesChapter 11. Euclidean Space RnChapter 12. Differentiation on RnChapter 13. Metric SpacesIn der gedruckten Fassung gibt es zwei Versionen. Zum einen die hier beschriebene mit allen 13 Kapiteln in einem Band und eine zweibändige Ausgabe, die die Kapitel 1 bis 8 und 9 bis 13 abdeckt.