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This is a translation of Landau's famous Elementare Zahlentheorie with added exercises by Paul T. Bateman and Eugene E. Kohlbecker.This three-volume classic work is reprinted here as a single volume ... Read more

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After completing his famous Foundations of Analysis (See AMS Chelsea Publishing, Volume 79.H for the English Edition and AMS Chelsea Publishing, Volume 141 for the German Edition, Grundlagen der Analysis), Landau turned his attention to this book on calculus. The approach is that of an unrepentant analyst, with an emphasis on functions rather than on geometric or physical applications. The book is another example of Landau's formidable skill as an expositor. It is a masterpiece of rigor and clarity. ... Read more

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The meaning of analysis
This book would more correctly be described as a book on analysis, because of the completeness of its proofs. It assumes you know just arithmetic of natural numbers, integers, rational, real and complex numbers-that is to say, just how to sum, multiply, subtract and divide. Edmund Landau wrote a masterpiece, because nothing is left without proof. You will not find a single step missing. From arithmetic to all the concepts of calculus, like differentiation, integration, infinite series and sequences, this book contains the mathematics that most mathematicians should know presented in a perfect way. It is not easy reading, though. Landau strives to reach the perfect axiomatic presentation, so like Euclid's "Elements" the book is the clear and beautiful presentation of a doctrine. I dare say that no book in analysis approaches Euclid's ideal of presentation better than Landau's, never in the past and never in the future. What you will find in this book is, in its best appearance, truth, that will not change even in a thousand years. ... Read more

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Two volumes in one. In this edition there has been added to Landau's monumental work on prime-number theory two of Landau's papers, a guide to the work and an Appendix by Paul T. Bateman. The text is in German. ... Read more

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Why does $2 \times 2 = 4$? What are fractions? Imaginary numbers? Why do the laws of algebra hold? And how do we prove these laws? What are the properties of the numbers on which the Differential and Integral Calculus is based? In other words, What are numbers? And why do they have the properties we attribute to them? Thanks to the genius of Dedekind, Cantor, Peano, Frege and Russell, such questions can now be given a satisfactory answer. This English translation of Landau's famous Grundlagen der Analysis-also available from the AMS-answers these important questions. ... Read more

Customer Reviews (12)

A Complete Rubbish
I got very upset when I finished reading the book. The book contains a complete rubbish not worthy of reading. The author was a fool for taking pride in proving such a theorem as: If x1/x2>y1\y2, then y1/y2y1\y2, then x1y2=x2y1. Therefore y1/y2 Decent book, but it should have done more
This little book is quite peculiar. It tries to give a detlailed account of the natural, rational, real, and complex numbers, and the book tries to prove many of the small theorems that govern the arithmitic for these numbers. In all honesty, when I read this book a year ago I enjoyed it. However, now that I am more mathematically mature, I'm not too sure if I would enjoy it now. This book essentially uses induction ad nauseum and uses basic algebraic manipulation throughout the entire book. While these things arn't in themselves bad, anyone who is slightly mathematically mature (lets say at least one proof-based course) would easily be able to do many of these proofs in a mater of seconds. This is simply a result of the nature of the material that this book deals with. I'm not geniunely expecting to see complicated proof methods in here. However, these proofs offer little mathematical knowledge to the reader.
Another thing that I am confused with is the style that this book is written in. This book has less soul than Baby Rudin! While I am a fan of terse mathematical exposition, I feel that presenting this material in the brutal fashion that it does is a waste. I will not be using this book as a reference, so there is no point to have it in this terse style. Landau even said himself that this book is written for first year university students who are taking a calculus course. Maybe the students he was writing for are used to reading this style of math, but I do not feel that the theorem, proof, lemma style works very well here. Why present seemingly simple material in this terse style? It almost seems as if he wishes to make this material seem more difficult then it actually is. This book will only be used as a learning tool, and so I wish he had not written this book as if he was expecting it to be used as a reference. Not only that, I don't believe that a first year university student would gain much from having no motivation whatsoever.

When I had bought this book, I read many of the reviews and thought that this book would tell me everything I everwanted to know about numbers. Sadly, it doesn't, and so here is some extra material that I feel would make this book worth having.

I wish this book gave detailed descriptions on how all of the numbers are constructed. He really only tells us how the reals are constructed via Dedekind Cuts. If he used the Von Neumann construction to make the natural numbers, equvilance classes to contruct the integers, etc... then I feel that this extra material would make this book a must-have (definitely 5 stars). However, this book takes for granted most of these, and as a result we are left with a handful of theorems that amount to proving trivialities. If you happen to find a book that includes this material, it would be a very good book to have!

While I can not truly reccomend this to anyone, what it does it does well, and I did learn a few things too (so three stars). However, I wish that I had found a more detailed book that went into more material than this one does. If you are considering buying this book, my advice to you is to find a different book that covers this material and more. It will be a much more rewarding experience. Unfortunately, I do not know of such a book. If you happen to come across one, please let me know!

The reals from the integers via Dedekind cuts.
This book dates from 1951 but it's still a satisfactory place to see how the real (and even complex) numbers can be developed from the integers. A quick read.

A good book of its kind, BUT---
I give this book one star, not because it's a bad book--of its kind,it is not--but to sound a warning and to counter some of the rave reviews here. In the preface to his famous calculus text, the great Richard Courant speaks of a "smug and presumptuous purism" which had crept into the mathematics texts of his time and place (Germany, '20s and '30s). I suspect he had Landau's "completely rigorous" (and in my opinion, completely unreadable) calculus text. "Foundations of Analysis" is cut from the same monk's-hairshirt cloth. IF you really like math books that consist almost 100% of "definition-axiom-theorem-proof; definition-axiom-theorem-proof" style writing, and that defy the reader to penetrate a completely closed system of elegantly presented and almost contemptuously concise pure truths (or at least, pure deductions from axioms), then Landau is definitely for you, or at least worth a serious try. But if you like math books that containbase, ignoble, impure elements such as motivation, intuitive insight, historical information about the development of the number concept, or just an occasional prose oasis, you're better off looking elsewhere (e.g. Feferman, Mendelson, Henkin-Smith-et al). By comparison to Landau, Hardy's "Pure Mathematics" seems chatty and chummy; it's also a much better book which gives more insight into the foundations of analysis in its first chapter than the whole of "Foundations". To my mind, Landau's book is, to quote a very old joke, not so much "rigor" as rigor mortis.

Very nice book.
Ever wonder how many of those field axioms in the front of your calculus/analysis book were redundant and what were essential? Are you a skeptic, who is not sure that you can really derive the complex numbers from Peano's axioms? Are you someone who does not know what the hell Peano's axioms are, even though you do know what an Axiom is? Then this book is for YOU!

This book proves the properties of the complex numbers and some of their subsets, (positive integers, integers, rationals, and reals). The proofs are quite rigorous, and provide an excellent foundation for which to study calculus, real or complex analysis. I thought it was a wonderfull read, and surprisingly accessible, given its hieroglyphic initial appearance.

If you decide to read this book in several sittings, I recommend being sure you cover each of the small sections. If you can't finish a full section, restart the section. I think that if you do it that way the results will seem more cohesive. ... Read more

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Landau's monumental treatise is a virtual encyclopedia of number theory and is universally recognized as the standard work on the subject. The text is in German. ... Read more

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This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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This Book Is In German. ... Read more

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This volume is produced from digital images created through the University of Michigan University Library's large-scale digitization efforts. The Library seeks to preserve the intellectual content of items in a manner that facilitates and promotes a variety of uses. The digital reformatting process results in an electronic version of the original text that can be both accessed online and used to create new print copies. The Library also understands and values the usefulness of print and makes reprints available to the public whenever possible. This book and hundreds of thousands of others can be found in the HathiTrust, an archive of the digitized collections of many great research libraries. For access to the University of Michigan Library's digital collections, please see http://www.lib.umich.edu and for information about the HathiTrust, please visit http://www.hathitrust.org ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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This Book Is In German. ... Read more

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Landau's classic book on the foundations of analysis is presented in its original German, with a German-English dictionary as an appendix. One intent of this edition is to provide the English-speaking mathematician with an opportunity to learn some mathematical German. Of course, a pleasant by-product is having Landau's exposition on the construction of the real numbers from the natural numbers using Dedekind cuts. The book is written in an extremely telegraphic style, with few words outside the ``Theorem-Proof'' motif, making the German notably simpler than in more advanced texts. Thus, the student who begins this book with little or no knowledge of German will gain the experience of successfully reading an entire book in mathematics and with it a feeling for the language and a well-ingrained mathematical vocabulary. (Note: The English edition of the book is available as Foundations of Analysis). ... Read more

Customer Reviews (1)

Clarity, completeness, even a glossary...
I read this book because Michael Spivak recommended it in his "Calculus" (another 5 star book). Good books on analysis can be hard to find (Bressoud's "A Radical Approach to Real Analysis", Stephen Abbot's "Understanding Analysis" being two). Edmund Landau's beautifully complete works on Calculus and Analysis are rare finds indeed. Landau's careful and cogent development of mathematical concepts is worth the price of a book, alone. Unfortunately, as far as I am able to determine this book is no longer available in English. No problem - this edition includes a complete glossary of mathematical terms...mathematicians should be able to read German, Russian, and, if possible, Japanese and Chinese because so many works of importance are published in these languages. The German necessary to get through a book like this is not that hard to pick up - especially when the editors have made it so convenient. ... Read more

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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 496 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more

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This digital document, covering the life and work of Edmund Georg Hermann Landau, is an entry from Contemporary Authors, a reference volume published by Thompson Gale. The length of the entry is 1367 words. The page length listed above is based on a typical 300-word page. Although the exact content of each entry from this volume can vary, typical entries include the following information:

• Place and date of birth and death (if deceased)
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