From: dlrenfro@gateway.net (Dave L. Renfro) Subject: Re: good basic analyis texts Date: 6 Jul 2000 01:18:32 -0400 Newsgroups: sci.math Summary: [missing] Larry Mintz [sci.math Wed, 05 Jul 2000 04:55:23 GMT] wrote > I am looking for some good texts on with the following topics > [1]point set topology > [2] metric spaces > [3] basic topology > [4] set theory > [5] measure and integration theory > Probably under the heading of "real" analysis. I find a hole in > my pysche when it comes to do these proofs ,since I am rather > new at it. The farthest I've gone was basic stuff. I've used > Calculus by Michael Spivak. Basically want a text that goes beyond > that. > > Books with good examples and good explanation of topics so I can > learn it on my own. > > Anyone know of some good available texts ? I recommend the following books. Irving Kaplansky, SET THEORY AND METRIC SPACES, Chelsea Publishing Company, 1977. [A very engaging text that manages to cover a lot of the *flavor* of the subject in just a few pages.] Ralph P. Boas, A PRIMER OF REAL FUNCTIONS, 4'th edition (revised and updated by Harold P. Boas), The Carus Mathematical Monographs #13, The Mathematical Association of America, 1996. [Any serious math student should spend some time with this book.] Andrew M. Bruckner, Judith B. Bruckner, and Brian S. Thomson, REAL ANALYSIS, Prentice-Hall, 1997. [Excellent choice of *interesting* topics and lots of historical remarks to motivate the material. (Something virtually absent from Royden, Rudin, etc.)] Wendell Fleming, FUNCTIONS OF SEVERAL VARIABLES, Springer-Verlag, 1977. [Advanced calculus of several variables at a slightly higher level than the traditional advanced calculus text. Covers Lebesgue integration, differential forms, etc. Probably the "advanced calculus text" appropriate for someone whose elementary calculus was from Spivak's book.] Kenneth Hoffman, ANALYSIS IN EUCLIDEAN SPACE, Prentice-Hall, 1975. [Excellent choice of topics, n x n matrices (identified with R^(n x n)) crop up often in ways that other textbooks seem to overlook, doesn't pretend that the complex numbers don't exist, an excellent introductory treatment of normed spaces, and an introduction to Lebesgue integration (measurable functions are obtained as the normed space completion of the continuous functions with the L^1 norm).] George F. Simmons, INTRODUCTION TO TOPOLOGY AND MODERN ANALYSIS, Krieger Publishing Company, 1982. Given what you wrote, I'd recommend the Simmons book the strongest. Here are some reviews of Simmons' book from amazon.com: ################################################################### Reviewer: Kevin R. Vixie from Los Alamos, New Mexico I became aquainted with this book many years ago and I still read it ... and send students off to read it. The book is written by an incredible expositor who was and still may be at Colorado College in Colorado. It is always the book that first comes to mind when someone asks for a reference on any of the subjects it covers. These include point set topology, analysis (Not including integration or measure theory), and operator theory. It is introductory. This merely makes you wish the author would have written several advanced sequels to this amazing book. This book has my highest recommendation. Every mathematics student should own a copy. ################################################################### ################################################################### Reviewer: Kiran K Garimella from USA This book was on a recommended list for a grad course in Analysis (we followed Rudin's book) that I took several years ago. I was absolutely captivated by the introduction, and the great introductory sections of each chapter. I am not a mathematician, but I have always loved mathematics (esp. analysis and topology). For me to remember this book and the author is testimonial enough. Because of such books, my dream is to go back to school a few years from now to pursue a degree in math. I would give this book 6 stars! ################################################################### ################################################################### Reviewer: A reader from Cambridge, MA This is the best book on analysis and point-set topology I know of. It is a model of mathematical exposition: completely rigorous but always letting the reader in on the thought process that ultimately results in the formalism. This is a very rare combination in a math book! Particularly recommended for independent study. ################################################################### ################################################################### Reviewer: peter_heisen@mercer.com from Washington Crossing, PA I used this "text book" in a course in Topology at Swarthmore College in 1964. The writing is so good that I still enjoy picking it up - surprisingly often - and reading anywhere in the book. The combined asthetics of the mathematics and the writing is wonderful. ################################################################### Dave L. Renfro