Elementary Analysis

Rating:
Summary: Entirely mediocre
Review: A solid, if limited, textbook. The author provides an entry level approach to analysis without much use of more abstract topological concepts like metric spaces. A decent book for the reader who desires this type limited approach. Even in that light it is hardly spectacular as the author's logic often does not flow as clearly as in alternate texts

This book might be better viewed as an auxiliary text beside a classic like Rudin or the very good Real Mathematical Analysis by Charles Pugh.

Rating:
Summary: Not for the easily discouraged
Review: I am using this book in an undergraduate analysis class. I have to say that the book is very good. The author takes time to prove all the theorems and there are about 10-15 exercises for each section with random solutions in the back. Sometimes he skimps on the proofs and at times it is hard to follow his logic. But overall I would recommend this for anyone interested in analysis who has a good background in calculus. He starts with basic properties of numbers but then jumps pretty quickly into sequences, series and the rest of calculus. Put your thinking caps on for this one!

Rating:
Summary: a truly well-written text on elementary analysis
Review: I used this book for the analysis sequence at cal poly for my undergraduate coursework. This is one of the best books i've read. In addition to the standard material for a two-quarter course, it concluded some nice topological supplementary like compactness, open/closed sets and continuity that got me interested in general topology. Included in the back are the much appreciated hints for the exercises. Excellent and radical approach to Riemann-Stielje Integrals in the integration section. Good for an intro. to proofs in general.

Rating:
Summary: Wanna get started on real analysis? This is the one!!
Review: I used this book in my junior year.It will be helpful to read this book if you have taken some sort of "proofs" class before. This book jumps straight into sequences and later on into series. So if you have had exposure to these concepts in some elementary calculus courses, then you will ease into the book very easily.This is a real math book, and so the book starts with axioms, then some definitions and then theorems and proofs. Ken also includes some sections on metric spaces and point-set topology, and shows how real analysis and the latter are inter related.However, it is not necessary to have had any point-set topology to follow the proofs.To get a full appreciation of the subject matter, it is a must to do the exercises, and Ken provides partial proofs in the back, ample examples in each section. This book is dull, if you'll let it be.There were times when I struggled with the matter, especially in the point-set topology sections, but in the end it paid off. I give it five stars. Money well spent!

Rating:
Summary: Wanna get started on real analysis? This is the one!!
Review: I used this book in my junior year.It will be helpful to read this book if you have taken some sort of "proofs" class before. This book jumps straight into sequences and later on into series. So if you have had exposure to these concepts in some elementary calculus courses, then you will ease into the book very easily.This is a real math book, and so the book starts with axioms, then some definitions and then theorems and proofs. Ken also includes some sections on metric spaces and point-set topology, and shows how real analysis and the latter are inter related.However, it is not necessary to have had any point-set topology to follow the proofs.To get a full appreciation of the subject matter, it is a must to do the exercises, and Ken provides partial proofs in the back, ample examples in each section. This book is dull, if you'll let it be.There were times when I struggled with the matter, especially in the point-set topology sections, but in the end it paid off. I give it five stars. Money well spent!

Rating:
Summary: Excellent introduction to analysis
Review: Of the many analysis books I have seen, I think this is one of the best for the student approaching the subject for the first time.

It is mathematically rigourous, yet develops the major concepts of analysis in a leisurely (in the good sense of the word) way with interesting and sometimes unusual examples.

Beginners will especially appreciate the quality exercises and the solution guide in the back.

The style of this book is a bit similar to Spivak's *Calculus* in that the author is a bit wordy. I find Ross' presentation more direct and less pretentious than Spivak--and far less intimidating.

This is definitely the best introductory analysis book I know of for self-study. A student who masters the material in this book will be well prepared to tackle Rudin and other classic works in real analysis.

Rating:
Summary: a truly well-written text on elementary analysis
Review: the "elementary analysis: theory of calculus" text by kenneth A. Ross is truly a gem among analysis texts, not for it's complicated, indigestable technojargons, but rather for it's simplistic, "pristine" approach. more often than not, this genre of textbook is written to be more teacher-friendly than student-friendly. this text has been structured in such a way as to provide an optimal learning experience.

what a magnificient text, ... , i am truly sorry for giving you a negative evaluation (1/5). the book is in excellent shape. LOVE IT!

Rating:
Summary: If You Can Find a Better Than This, Let Me Know
Review: The book is rigorously written and is extremely good for math majors. I don't think this book is very suitable for non-math majors however, since they might think it's too dull. The book does not go on and on like some math textbooks with non-essential talk. It gets into the material right the way. The proofs have been carefully chosen so that they're as simple and as elegant as possible. Topology is treated in optional sections, and the focus of the book is sequences. Indeed, the treatment of sequences is very thorough. Also, many notions are also defined in terms of sequences. However, proofs that this definition and the usual delta-epsilon definition are equivalent is given. The style of writing is clear, concise, and avoids uncessaary discussion. Proofs are given out in full and are seldom left to the readers as an exercise. In keeping with the style of this book, historical facts and references are not provided. I think this book should be a must-have for all math undergrads.