Real Mathematical Analysis

by Charles C. Pugh

Overview

Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

Product Details

ISBN-13:	9780387952970
Publisher:	Springer New York
Publication date:	03/01/2002
Series:	Undergraduate Texts in Mathematics Series
Edition description:	1st ed. 2002. Corr. 2nd printing 2003
Pages:	440
Product dimensions:	9.21(w) x 6.14(h) x 1.00(d)

Table of Contents

Real Numbers
• A Taste of Topology
• Functions of a Real Variable
• Function Spaces
• Multivariable Calculus
• Lebesgue Theory
• Index

Editorial Reviews

From the reviews:

C.C. Pugh

Real Mathematical Analysis

"The book contains more than 500 carefully worked exercises the level of which varies from straight-forward to challenging (the text can thus serve as a source book for examples and exercises in real analysis). The book can be highly recommended as an introduction to real analysis."—ZENTRALBLATT MATH

"This introduction to undergraduate real analysis is based on a course taught … by the author over the last thirty-five years at the University of California, Berkeley. … The exposition is informal and relaxed, with a number of pictures. The emphasis is on understanding the theory rather than on formal proofs. The text is accompanied by very many exercises, and the students are strongly encouraged to try them." (EMS Newsletter, June, 2003)

"This one is … a pleasure to read, contains many exercises (about 500) and includes full proofs following an intuitive introduction of new ideas. I should add here that Pugh succeeds in transferring his love and enthusiasm for this material to the reader. … As a mathematics student, I would have loved to have this as a textbook to be taught my first analysis course. As a teacher … I would love to use it as lecture notes." (Adhemar Bultheel, Belgian Mathematical Society - Simon Stevin Bulletin, Vol. 11 (1), 2004)

"The author of this undergraduate text believes that real analysis is the jewel in the crown of pure mathematics. … This text is based upon many years of teaching the analysis course at Berkeley. The exposition is chatty and easygoing, while managing to cover all of the basic ideas carefully and thoroughly. … The text is complemented by an excellent index and frequent suggestions for further reading. I can recommend this book to serious undergraduates who want to get into real analysis … ." (Gerry Leversha, The Mathematical Gazette, Vol. 88 (551), 2004)

"This book is a new introduction to undergraduate real analysis. … The exposition is informal and relaxed, with an excellent selection of more than 500 exercises. The occasional comments from mathematicians … make the text really enjoyable. … To sum up, this undergraduate … textbook contains a wealth of information. It is written in a concise, but always clear and well-readable way. … It should have a great appeal to the students of (under) graduate courses as well as to budding pure mathematicians." (Ferenc Móricz, Acta Scientiarum Mathematicarum, Vol. 69, 2003)

"Pugh’s book … is not a typical book. … it very successfully (and atypically) manages to convey the look and feel of an engaging classroom lecture while maintaining the highest level of rigor and care. … This makes this well-crafted book very appealing as a resource for an honors section, but it also should be in any undergraduate library as a source of ideas and supplementary problems for faculty or as a challenge for strong students. An excellent book in an excellent series. Highly recommended." (J. Feroe, CHOICE, September, 2002)

"This book is suited for a two-semester course in real analysis for upper-level undergraduate students who major in mathematics. … The book is very well written. The style is lively and engaging. Intuition is stimulated and metaphors are used throughout the book, without compromising rigor. … The exercises are numerous and they vary from straightforward to very challenging … . This is a book for the highly motivated student. He/she will get from this book a good grasp of analysis: concepts and techniques." (Sherif T. El-Helaly, Mathematical Reviews, 2003 e)

"The book under review is an introduction to the basics of real analysis. … A special feature of the exposition is its emphasis on the explanation of mathematical concepts by figures … . The book can be used for self-study. … The book can be highly recommended as an introduction to real analysis." (Joachim Naumann, Zentralblatt MATH, Vol. 1003 (3), 2003)

"In this new introduction to undergraduate real analysis, the author takes a different approach … by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples, and occasional comments from mathematicians … . This book is based on the honors version of a course that the author has taught many times, over the last thirty-five years, at the University of California, Berkeley." (L’ Enseignement Mathematique, Issue 1-2, 2002)

From the Publisher