Product Description
This Book Is In German. ... Read more

Product Description
This Book Is In German. ... Read more

Product Description
This Book Is In German. ... Read more

Product Description
An Unabridged, Digitally Enlarged Printing Of The Second Edition. ... Read more

Product Description
Bernhard Riemanns Werk hat bis heute wesentlichen Einfluß auf die Entwicklung der Mathematik genommen. Seine Ideen sind überraschend modern und prägen die heutige mathematische Forschung. Die Gesammelten Abhandlungen (1892) samt Supplement von 1902 waren seit langer Zeit vergriffen. R. Narasimhan hat die mühevolle Edition dieser Neuausgabe übernommen. Es können nur einige Höhepunkte genannt werden: - H. Weils Kommentare über Riemanns Habilitationsschrift - C.L. Siegel über Riemanns Nachlass zur analytischen Zahlentheorie - W. Wirtingers berühmter Vortrag beim internationalen Mathematikerkongress Heidelberg 1904 über Riemanns Vorlesungen über die hypergeometrische Reihe. Neben diesen historischen Würdigungen von Riemanns Werk gibt es aktuelle Beiträge, insbesondere zur Mechanik und über "shock waves" von S. Chandrasekhar, N. Lebovitz und P. Lax. Raghavan Narasimhan gibt in einer ausführlichen Einleitung eine Würdigung, insbesondere des funktionentheoretischen Werks von Bernhard Riemann. Ferner sind Fotos und zahlreiche Nachträge zum Lebenslauf aufgenommen worden. Eine Bibliographie mit mehr als 800 Literaturstellen erarbeitet von E. Neuenschwander und W. Purkert rundet diese Werkausgabe ab. Dieser Band ist ohne Zweifel ein Höhepunkt in der "Blauen Reihe" gesammelter Werke des Springer-Verlags. ... Read more

Product Description
This digital document is an article from Encyclopedia of Philosophy, 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 21897 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.Explores major marketing and advertising campaigns from 1999-2006. Entries profile recent print, radio, television, billboard and Internet campaigns. Each essay discusses the historical context of the campaign, the target market, the competition, marketing strategy, and the outcome. ... Read more

Product Description
From its history as an elegant but abstract area of mathematics, algebraic number theory now takes its place as a useful and accessible study with important real-world practicality. Unique among algebraic number theory texts, this important work offers a wealth of applications to cryptography, including factoring, primality-testing, and public-key cryptosystems.A follow-up to Dr. Mollin's popular Fundamental Number Theory with Applications, Algebraic Number Theory provides a global approach to the subject that selectively avoids local theory. Instead, it carefully leads the student through each topic from the level of the algebraic integer, to the arithmetic of number fields, to ideal theory, and closes with reciprocity laws. In each chapter the author includes a section on a cryptographic application of the ideas presented, effectively demonstrating the pragmatic side of theory.In this way Algebraic Number Theory provides a comprehensible yet thorough treatment of the material. Written for upper-level undergraduate and graduate courses in algebraic number theory, this one-of-a-kind text brings the subject matter to life with historical background and real-world practicality. It easily serves as the basis for a range of courses, from bare-bones algebraic number theory, to a course rich with cryptography applications, to a course using the basic theory to prove Fermat's Last Theorem for regular primes. Its offering of over 430 exercises with odd-numbered solutions provided in the back of the book and, even-numbered solutions available a separate manual makes this the ideal text for both students and instructors. ... Read more

Customer Reviews (3)

A Mature and Concrete Introduction to Algebraic Number Theory
I used this book in a one on one course in algebraic number theory in my fourth year of college.We finished just before ramification.

My background at the time included a year of undergraduate linear algebra, a year of undergraduate abstract algebra, a semester of intro. graduate algebra, intro. Galois theory, and intro. commutative algebra. The only things I used were Galois theory, my second abstract algebra course, and my second linear algebra course.Commutative algebra helped, but wasn't necessary in that abstract setting.

Organization: The book is very well organized with helpful appendices on abstract algebra basics (Groups, Rings, Fields) and Galois theory. The first chapter is slow-paced and provides a strong historical background for the material.A reviewer below suggested that there were "logical leaps" in the text--I never found such stuff, and I am always very picky about details. The author uses easy propositions that are assigned for homework sometimes, but they're mostly straightforward.

Exercises: They range from straightforward to quite thought-invoking... I remember one in particular, a starred problem, in which I had to use three "tricks" to solve.

Content: I like this book a lot.It's not super abstract on the level of Lang, but has hints of great generality throughout, and it's not some trivial algebraic number theory full of history, anecdotes, useless junk book with "Fermat's Last Theorem" misleadingly stated in the title somewhere.This book has a lot of stuff on applications to cryptography. The book covers things including

- Euclidean domains and unique factorization,
- special cases of FLT,
- Dirichlet's Unit Theorem,
- geometry of numbers,
- ideal class group,
- ramification,
- basics of class field theory,
- reciprocity laws.

It's a really nice all-around introduction. You need to be mature enough to read this book--the problems require that the reader is familiar with the relevent math. I was really impressed with the organization of this book--with topics like these, it's hard to have a nice balance of generality with concrete and useful results. This is for people not ready to appreciate Lang's book.

Worst textbook ever!
I am a graduate student specializing in Ring Theory and I have to tell you this is the absolute worst book I have ever had. Not only does the author make these humongous jumps in each section, he also has massive logical gaps. There are plenty of errors in the text starting right from the first section. You could easily spend a whole year deciphering (with a massive headache) the first chapter. The author is definetly wrong in assuming that all you need is a basic undergraduate number theory class and basic abstract algebra. You could have 2 comprehensive years of graduate modern algebra and still not be ready for the massive logical gaps in the book. Sure if we were all Galois and Eulers, the book would be easier, but I'd bet they'd even be scratching their heads often enough. My advice is stay away from the text at all cost. You'll regret paying the outrageous price for a text that is worth firepaper.

BUY THIS BOOK!
I learned a tremendous amount about Algebraic Number Theory from this excellent source. I have looked at other books that just skim the topics. This one covers them in depth and even has applications to cryptography (the author shuld have put that in the title). Even more advanced topics such as the higher reciprocity laws are covered with rigorous detail and extreme clarity. I read the AMS review for this book by Charles Parry and it is right on! This book should replace the old standards such as Janusz's and Marcus' books for instance. I'd say that this is a gem to be enjoyed. ... Read more