Introductory Real Analysis (Dover Books on Mathematics) 1st Edition by A. N. Kolmogorov (PDF)

Description

This volume in Richard Silverman’s exceptional series of translations of Russian works in the mathematical science is a comprehensive, elementary introduction to real and functional analysis by two faculty members from Moscow University. It is self-contained, evenly paced, eminently readable, and readily accessible to those with adequate preparation in advanced calculus.The first four chapters present basic concepts and introductory principles in set theory, metric spaces, topological spaces, and linear spaces. The next two chapters consider linear functionals and linear operators, with detailed discussions of continuous linear functionals, the conjugate space, the weak topology and weak convergence, generalized functions, basic concepts of linear operators, inverse and adjoint operators, and completely continuous operators. The final four chapters cover measure, integration, differentiation, and more on integration. Special attention is here given to the Lebesque integral, Fubini’s theorem, and the Stieltjes integral. Each individual section — there are 37 in all — is equipped with a problem set, making a total of some 350 problems, all carefully selected and matched.With these problems and the clear exposition, this book is useful for self-study or for the classroom — it is basic one-year course in real analysis. Dr. Silverman is a former member of the Institute of Mathematical Sciences of New York University and the Lincoln Library of M.I.T. Along with his translation, he has revised the text with numerous pedagogical and mathematical improvements and restyled the language so that it is even more readable.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I find this a great introduction to real analysis. Contrary to what one reviewer has suggested, I think the book is fairly rigorous. It is true that some details are omitted, but they can always be filled up by the reader. In fact, this is the one of the most fun parts of reading the book!To give a concrete example: One reviewer has suggested that the theorem “Every infinite set has a countable subset” is proved without stating that the axiom of choice is required. This is certainly a serious lapse of rigour, BUT, in a later page, the author explains the axiom of choice (and several equivalent assertions) and also touches upon the fact that there are some very deep set theoretic questions, not yet fully resolved, concerning this axiom. He goes on to say “The axiom of choice will be assumed in this book. In fact, without it, we will be severely hampered for making various set-theoretic constructions”. It is evident that the above theorem is one such construction.This book emphasizes an intuitive approach to the subject, something which in my opinion is neglected by far too many books. Rigour is necessary but never sufficient to acheive proficiency in math!

⭐This is a very good intermediate math book. I used it to write my undergraduate monograph and it actually helped a lot (I’m an economics student). However, it is difficult to understand without the help of other books. In fact, if you want to use this book I recommend to get also: “Topology” by Munkres and “The Way of Analysis” by Robert Strichatz. They all make a very useful math kit and if you are thinking in a Ph.D. in economics they can help you a lot if you read them (not all, buy selected chapters) before you start the math review at the begining of the Ph.D. program.

⭐A classic in real analysis! Recommended!

⭐Compra muy favorable y a la espera de otras obras similaresI don’t really know how to rate this book. The content is great, but the Kindle format is terrible. Most of the equations are low quality, small, images, which makes viewing with a dark background ugly, and scaling impossible (increase font size does not increase equation size).1 star for Kindle5 for book

⭐I knew that It’s a classic, must read. (Although I don’t understand it at all.) I think you should have some knowledge about mathematical analysis before you read this.

⭐I love the Dover books. This one helped with my capstone. Great read too.

⭐Came as promised. I would order from seller again.

⭐The only reason why I did not give it 5 stars is because it contains aboslutely no clue about most of the problems. Some people might argue that this forces you to go through the problems rather than to look at the solution at the first signs of failure. I beg to differ, I think that solutions help greatly to those who are learning by themselves be it for the first time or to gain a sounder knowledge of the subject (the latter is my case) and provide with good examples of rigour. One is always free to think of alternative ways, or maybe only solutions to odd (or even) exercises could have been included (As Kreyszig did on his book on Functional Analysis).Apart from this, I liked the book very much, written in the usual russian style. I would have liked it to include more material on spectral theory of operators however. I would certainly reccommend this book. Maybe not for beginner on the subject (for this I would go for Kreyszig’s without doubt) but certainly for someone who has been exposed to Functional Analysis at some point and wishes to review or simply study it in more depth.

⭐I studied maths at university some years ago and have kept on reading sporadically since. This is quite possibly the clearest, easiest to read maths book I have ever read. It does cover a lot of material fairly quickly (more than the title might suggest) but never feels rushed and the logical structure of the book makes perfect sense.

⭐Great book. Helped me a lot

⭐El contenido es de excelencia. Todo es explicado a detalle y las pruebas fueron de una profundidad muy correcta, a mi parecer.Los temas tratados y la variedad también constituyen una parte muy atractiva del libro.Lo único que no me agradó fue la baja calidad de la impresión y del papel utilizado. Fuera de ello, un excelente libro.This book is an excelent text for math and physics students. since in bot cases is necesary know on real analysis.The topics are very well exposed the Authors developed details when is necesary.

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