and optional quadratic variation [M] for a square integrable (local) martingale is studied. Next, [M] is generalized sufficiently to complete the development of the Ito calculus. The general Ito Formula is applied to such problems as the Kalman-Bucy Filter and the Bayesian Filter of Kallianpur-Striebel.
The book wraps up with an introduction to excursion theory. The premise here is that we want to study those times for which a Markov process visits a compact set. The theory leads to some nice results, including a proof of the embedding theorems of Skorokhod and Azema-Yor along with applications to potential theory and the general study of local time.
A Great Book.......2005-01-15
This book and its companion volume are a well organized and relatively easy-to-read introduction to a wide variety of ideas in stochastic processes. It is not only a great reference (I always keep it on my desk) but it also has a solid expositional style that fully motivates concepts as they are introduced. The Ito Calculus volume goes deeper than a number of other books on topic including information on integration wrt to a general semimartingale instead of just BM and even an introduction to stochastic calculus on manifolds. My only complaints about the book are that it is separated into two volumes which can be kind of a pain and that its coverage of the SDE/PDE relationship is weak. I would recommend reading Karatzas&Shreeve in addition to this book to fill in some the SDE/PDE details and to get another point of view on the somewhat difficult topic of stochastic analysis
Pretty accessible.......2002-02-04
The parts of this book I've read have been clear and accessible for someone with an undergraduate degree in mathematics and some knowledge of stochastic processes. It doesn't needlessly multiply the jargon like some books, and it focuses mainly on the one-dimensional case so that the intuition isn't constantly obscured by matrix notation. Many subjects also have chatty introductions that offer intuition and a bit of relief from the hard work involved in learning this subject.
Book Description
Now available in paperback, this celebrated book remains a key systematic guide to a large part of the modern theory of Probability. The authors not only present the subject of Brownian motion as a dry part of mathematical analysis, but convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively presentation of the theory of Markov processes. Together with its companion volume, this book equips graduate students for research into a subject of great intrinsic interest and wide applications.
Customer Reviews:
Definitive Introduction of Brownian Motion and Markov Processes.......2005-08-15
The authors have compiled an excellent text which introduces the reader to the fundamental theory of Brownian motion from the point of view of modern martingale and Markov process theory. I highly recommend this book for anyone who wants to acquire and in-depth understanding of Brownian motion and stochastic calculus.
The book is fairly self-contained, although the reader should prepare herself with some prerequisite material. Rudin's "Real and Complex Analysis" 3rd edition and Norris's "Markov Chains" provide a good basis. You'll also need a solid understanding of the basic properties of Laplace transforms as is covered in an undergraduate course on differential equations (e.g. Schiff's "The Laplace Transform").
Rogers and Williams begin Chapter 1 of the 2nd edition of their first volume 'Foundations' by exploring Brownian motion from several different modern viewpoints. This is intended to help the reader develop an intuition about Brownian motion and related diffusions. They then move on to explore the well-known features of Brownian motion, including the strong Markov property, the Reflection principle, the Blumenthal Zero-One Law and the Law of the Iterated Logarithm.
The section on Brownian motion in higher dimensions is very nice and I enjoyed the applications of Brownian motion to complex analysis. I particularly liked the Ito's Rule-style proof of the Maximum Modulus Principle.
The authors close out Chapter 1 with detailed introductions of Gaussian and Levy Processes.
In the chapter on Brownian motion, the authors make several forward references to Chapter 2, which covers the prerequisite material from measure theory, probability theory, and stochastic processes needed for both volume I and II. If you found these forward references a bit unsettling, it is quite reasonable to first read Chapter 2 (sections 1-5), then read Chapter 1, and then finish up with canonical Brownian motion section at the end of Chapter 2.
Chapter 3 is a wonderful treatment of Markov processes and requires that the reader have an appreciation of the classical theory of Markov chains. In the first section of Chapter 3, the basic theory of operator semigroups is covered and the authors prove the famous Hille-Yosida Theorem.
The next section covers the 'base case' of operator semigroups. Rogers and Williams refer to these as Feller-Dynkin semigroups. (Ethier and Kurtz simply call these Feller semigroups in their book "Markov Processes: Characterization and Convergence".) Each Feller-Dynkin semigroup is shown to be realized by strong Markov process. Continuous Levy processes are then characterized as a nice application of the Feller-Dynkin theory.
The highlight of the next section is the Feynmac-Kac formulas. These are presented from the Markov process point of view (computing generators of transformed Markov processes), not from the usual PDEs point of view. Since the authors don't have Ito's Rule available in this first volume, they establish Feynman-Kac using the theory of additive functionals.
The final sections of the book deal with Markov processes with values in a countable state space. Ray processes and the Martin boundary are introduced, however as I began read this material, I felt that the authors believed that I already knew why Ray Theory is so important. I felt this last material would have been a bit better motivated with more of a tie-in to the theory of harmonic functions and the Dirichlet problem. However, the proof of Ray's Theorem is very elegant and really solidifies the reader's understanding of the Hille-Yosida Theorem.
Several of the sections wrap up with a small set of exercises. There are also exercises sprinkled throughout the text (several of which the authors plead with you to work through). The exercises have been thoughtfully selected and reinforce the material.
A Beautiful Survey of Markov Processes.......2005-01-29
This book, the first in a two volume set, is a wonderful survey of some of the most important results in modern mathematics. The books begin with Brownian motion, review results from measure theory, and proceed all the way up to the general theory of Markov processes. As a researcher in econometrics and finance, I have found these books incredibly useful.
Several things really set these books apart. First, the authors do a great job motivating the subject matter, giving the reader a sense of why technical topics are important. Although mathematical purists may quibble with this, it gives readers with backgrounds outside of pure mathematics a really useful perspective, and makes the progression of topics flow smoothly throughout the two volumes. Second, these books actually manage to provide motivation and intuition without sacrificing rigor, which is truly an amazing accomplishment. Finally, the price is outstanding--I would challenge anyone to find a text in this area that covers half as much ground for less than twice the price of R&W's books!
While on a similar technical level to Karatzas and Shreve, these books offer much more breadth and intuition at the cost of a few technical details and little treatment of PDEs (this is really my only complaint). Both are indispensible references, but Rogers and Williams is one of the finest mathematical texts I have encountered.
A Great Book.......2005-01-15
This book and its companion volume are a well organized and relatively easy-to-read introduction to a wide variety of ideas in stochastic processes. It is not only a great reference (I always keep it on my desk) but it also has a solid expositional style that fully motivates concepts as they are introduced. The Ito Calculus volume goes deeper than a number of other books on topic including information on integration wrt to a general semimartingale instead of just BM and even an introduction to stochastic calculus on manifolds. My only complaints about the book are that it is separated into two volumes which can be kind of a pain and that its coverage of the SDE/PDE relationship is weak. I would recommend reading Karatzas&Shreeve in addition to this book to fill in some the SDE/PDE details and to get another point of view on the somewhat difficult topic of stochastic analysis
A Great Book.......2003-01-01
This is a great book. It is not difficult to read. The style is very informal and at times actually humourous. It does not follow the definition-lemma-proof way of doing things at the expense of leaving simple definitions out, but these can be easily found somewhere else. The book contains an enormous amount of information, and the authors are clearly men of great knowledge and depth. The book is very nicely produced (from a 1st edition) by Cambridge U Press. Very clearly printed, and at a low price for the volume. I highly recommend both volumes to anyone who works in stochastic processes, or mathematical finance (assuming one wants to learn things, rather than just talk about them).
Excellent Treatment of Theory of Diffusion, Martingales, Ito.......2001-11-19
Although not an easy read, this book contains a wealth of information on diffusion, martingales and Ito calculus. Reading difficulty is comparable to Karatzas/Shreve. Mastery of topics included enables the reader to get understanding of most of the current research papers in this field.
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Principles of Computational Fluid Dynamics
Pieter Wesseling
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Computational Methods for Fluid Dynamics
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ASIN: 3540678530 |
Book Description
The book is aimed at graduate students, researchers, engineers and physicists involved in fluid computations. An up-to-date account is given of the present state of the art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary methods. Attention is given to the difficulties arising from geometric complexity of the flow domain. Uniform accuracy for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Unified methods for compressible and incompressible flows are discussed. A treatment of the shallow-water equations is included. A basic introduction is given to efficient iterative solution methods. Many pointers are given to the current literature, facilitating further study.
Customer Reviews:
good for the experienced.......2002-09-18
hi all,
this book is not appropriate for the beginners to CFD so i don't recommend it for the instructors who are looking for a introduction book. The tensor notation is also not easy to grasp for the not experienced. Besides the language of the book is not clear and not enough to let the reader apply without referring to another book. This is probably because the book has covered a lot of CFD concepts so deep explanation on every item is not provided.
However I would recommend this book for experienced CFD'ers since it covers many concepts and it can be used as a good referring material.
Book Description
This is an updated English translation of "Cohomologie Galoisienne", published more than 30 years ago as one of the very first Lecture Notes in Mathematics (LNM 5). It includes a reproduction of an influential paper of R. Steinberg, together with some new material and an expanded bibliography.
Average customer rating:
- very complete and useful
- review for Computational Inelasticity - J.C. Simo
- Absolutely amazing
- Absolutely Accept No Substitute
- Right on target yet someting missing
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Computational Inelasticity (Interdisciplinary Applied Mathematics)
J.C. Simo , and
T.J.R. Hughes
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ASIN: 0387975209 |
Book Description
A description of the theoretical foundations of inelasticity, its numerical formulation and implementation, constituting a representative sample of state-of-the-art methodology currently used in inelastic calculations. Among the numerous topics covered are small deformation plasticity and viscoplasticity, convex optimisation theory, integration algorithms for the constitutive equation of plasticity and viscoplasticity, the variational setting of boundary value problems and discretization by finite element methods. Also addressed are the generalisation of the theory to non-smooth yield surface, mathematical numerical analysis issues of general return mapping algorithms, the generalisation to finite-strain inelasticity theory, objective integration algorithms for rate constitutive equations, the theory of hyperelastic-based plasticity models and small and large deformation viscoelasticity. Of great interest to researchers and graduate students in various branches of engineering, especially civil, aeronautical and mechanical, and applied mathematics.
Customer Reviews:
very complete and useful.......2007-07-25
I bought this book several years ago, and keep going back and study more in it. As usual, I didn't read it from front to back. Instead I started from the middle, jumped around and then settled for chapter 7. That's mainly a review of continuum mechanics, and one of the reasons I keep this book handy. It is very comprehensive and very clear. I think the reason Simo and Hughes could explain things so clear is because they just really deeply understood it. There is hardly any superfluous talking or name dropping, it's all just clear, well printed math and neat little diagrams that lets you get the point. Somehow I understood chapters 8 and 9 much better by first reading chapter 10 on nonlinear viscoelasticity, finally getting the idea of dissipative processes in solids, and how one can actually compute all this. Recently I studied more of the first part of the book: finally this stuff about yield surfaces makes sense. It's a real mystery buster. Another thing that makes this book very useful are the boxes: detailed algorithms, neatly printed, that actually work if you turn them into computer code. In general, this book is not for total beginners, but if you understand the very basic mathematical underpinnings for continuum mechanics, this will bring you to the next level. If you get stuck, read around in other books, but go back to this one, because that's were you will understand.
review for Computational Inelasticity - J.C. Simo.......2007-03-09
the book is in excellent condition and reached me well before the estimated time. Worth the money...Great transaction and look forward for many more ahead on Amazon.
Absolutely amazing.......2006-09-30
I strongly recommend this book. It gives insights that no other books give. A solid mathematical background and a wide scope are the fundamental book characteristics.
Absolutely Accept No Substitute.......2002-06-24
This book is really well organised, and the theory is well presented, particularly Chapter 1. It is among the few which I highly recommend, and it is value for money.
Right on target yet someting missing.......2000-01-08
The book had been in the making at Stanford for some time. I happened to use a manuscript of it in 1991 at Virginia Tech. I was pleasantly surprised how quickly a student could pick up relevant aspects of compuatational plasticity from this book; the book has a style of its own. We have successfully used the book in programming the integral (or endochronic) hardening rule with the incremental theory of plasticity. The book surely makes a useful companion to a plasticity textbook.
It is disheartening to see that the numerical schemes for the integration of the constitutive equations of the endochronic theory are missing from the book.
Book Description
This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus. Jeffrey Stopple pays special attention to the rich history of the subject and ancient questions on polygonal numbers, perfect numbers and amicable pairs, as well as to the important open problems. The culmination of the book is a brief presentation of the Riemann zeta function, which determines the distribution of prime numbers, and of the significance of the Riemann Hypothesis.
Download Description
This undergraduate introduction to analytic number theory develops analytic skills in the course of studying ancient questions on polygonal numbers, perfect numbers and amicable pairs. The question of how the primes are distributed amongst all the integers is central in analytic number theory. This distribution is determined by the Riemann zeta function, and Riemann's work shows how it is connected to the zeroes of his function, and the significance of the Riemann Hypothesis. Starting from a traditional calculus course and assuming no complex analysis, the author develops the basic ideas of elementary number theory. The text is supplemented by series of exercises to further develop the concepts, and includes brief sketches of more advanced ideas, to present contemporary research problems at a level suitable for undergraduates. In addition to proofs, both rigorous and heuristic, the book includes extensive graphics and tables to make analytic concepts as concrete as possible.
Customer Reviews:
One of my favorite math books.......2007-06-24
A little background on me. I have just finished my freshman year of high school, and this was my first book on number theory. However, I have read many other math texts. In the beginning of the book there are some new concepts introduced, but they are not too hard to understand. The middle is refreshing as it involves a lot of calculus, which the student is most likely familiar with. The latter part consists of a variety of new ideas, and the theorems can get quite lengthy. I do not fully understand all of them myself. The book is well written and also includes the history of many mathematical problems.
For the senior math undergraduate.......2006-02-03
A great book for senior undergraduates in mathematics or anyone with some background in calculus and complex numbers. Proofs are at a level where a careful reading makes them clear, and the author tells the reader when he is not being rigorous. Historical background and logical development of topics makes this a good read too. Most surprising to me was how the author tied in topics from prior chapters into later chapters--he didn't just jump from one topic to the next willy-nilly, but made the book flow as a whole. Problems given to the reader were helpful though sometimes too hard for me, a math major.
A great bridge to analytic number theory.......2005-07-19
There seems to be a huge gap between the mathematical background required to understand a book on elementary number theory and that required to understand most books dealing with analytic number theory. This book assumes no familiarity with complex variables. The writing feels a bit like Silverman's "Friendly Introduction to Number Theory" and Derbyshire's "Prime Obsession." Stopple includes plenty of experiments for Mathematica and Maple. I think this could be a useful textbook for an undergraduate number theory course. The last few chapters include elliptic curves (mention is made of their L-functions and the Birch and Swinnerton-Dyer conjecture) and binary quadratic forms. I recommend this book to anyone who can read (and for those who can't, this book is good motivation to become literate).
Book Description
This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. The first five chapters treat elementary concepts such as divisibility, congruence and arithmetical functions. The topics in the next chapters include Dirichlet's theorem on primes in progressions, Gauss sums, quadratic residues, Dirichlet series, and Euler products with applications to the Riemann zeta function and Dirichlet L-functions. Also included is an introduction to partitions. Among the strong points of the book are its clarity of exposition and a collection of exercises at the end of each chapter. The first ten chapters, with the exception of one section, are accessible to anyone with knowledge of elementary calculus; the last four chapters require some knowledge of complex function theory including complex integration and residue calculus.
Customer Reviews:
Introduction to Analytic Number Theory.......2006-08-21
The reason I bought this book was to understand an elementary proof of the prime number theorem. Actually, it contains only an outline of an elementary proof. But the book introduces methods for the proof with awesome clarity. It must have been much greater if we could see the detailed elementary proof of the prime number theorem written by Apostol. He gives a reference to An Introduction to the Theory of Numbers by G.H. Hardy and E.M. Wright for the detailed proof, but the reader may be required to do unnecessary guessing (which is believed to be good in learning math, but seems to be nothing but trouble for me) to go through it.
Amazing.......2006-01-28
This book is absolutely incredible. The topics covered range from some very elementary topics on the theory of certain basic arithmetic functions, to much more advanced topics such as the theory of Dirichlet L-Functions. I have never seen a clearer explanation of the characters associated with finite Abelian groups, and the L-functions associated with Dirichlet Characters, than that provided by this book. Apostol makes even the most difficult concepts seem clear and simple. As an added bonus, the end-of-chapter exercises range from moderately difficult to almost excruciatingly so (but still very fun to work on) and give the reader excellent experience in solving problems in this field. With all this said, it should be pointed out that, as another reviewer stated, this book should not be read until the reader has already had a good deal of previous exposure to number theory. I myself would recommend the book of Hardy and Wright. As a second text on number theory, and an introduction to the aspects of number theory related to function theory and analysis, I believe that Apostol's book is the best that anyone could possibly hope for.
Exceptional readability.......2005-09-27
You normally dont talk so much about readability of a book on Math, but of all the other books on number theory that I've seen, this is quite a page turner. Strikes just the right ballance between theory, proofs and examples. As mentioned somewhere in the book, one of the aims of the author is to arouse reader's interest in number theory..which this book will certainly do..especially since its main emphasis is on prime numbers.
Unsurpassed SECOND text on number theory.......2004-06-29
The amazing positives of this book are accurately described in the other reviews so I will skip them. There is no negative, but the other reviewers assert that the reader needs no prior exposure to number theory. I completely disagree.
While this book does quickly cover elementary number theory, a reader new to this field will quickly feel lost. Without more exposure and a good prior feel for elementary number theory, the use of analytic techniques will seem ad hoc instead of following a logical pattern. By way of example, three areas covered in this book that are not part of analytic number theory and for which the reader would do better to learn from a less sophisticated text are the Fermat-Euler Theorem, Diophantine equations, and quadratic reciprocity.
Excellent texts for a first exposure to number theory are, from simpler to more difficult:
1. Elementary Number Theory by Underwood Dudley
2. An Introduction to the Theory of Numbers by Niven, Zuckerman and Montgomery
3. An Introduction to the Theory of Numbers by Hardy and Wright
Apostol's book on analytic number theory is a classic that may never be surpassed. It is a marvelous second book on number theory.
well presented, delightfully written.......2001-12-06
I think that there will be little harm if the title of the book is changed to 'Introduction to elementary number theory' instead. The author presumes that the reader has not any knowledge of number theory. As a result, materials like congruence equation, primitive roots, and quadratic reciprocity are included.
Of course as the title indicates, the book focusses more on the analytic aspect. The first 2 chapters are on arithmetic functions, asymptotic formulas for averaging sums, using elementary methods like Euler-Maclaurin formula .This lay down the foundation for further discussion in later chapters, where complex analysis is involved in the investigation. Then the author explain congruence in chapter 4 and 5. Chapter 6 introduce the important concept of character. Since the purpose of this chapter is to prepare for the proof of Dirichlet's theorem and introduction of Gauss sums, the character theory is developed just to the point which is all that's needed. ( i.e. the orthogonal relation). Chapter 7 culminates on the elementary proof on Dirichlet's theorem on primes in arithmetic progression. The proof still uses L-function of course, but the estimates, like the non-vanishing of L(1) , are completely elementary and is based only on the first 2 chapters.
The author then introduce primitve roots to further the theory of Dirichlet characters. Gauss sums can then be introduced. 2 proofs of quadratic reciprocity using Gauss sums are offered. The complete analytic proof, using contour integration to evaluate explicitly the quadratic Gauss sums, is a marvellous illustration of how truth about integers can be obtained by crossing into the complex domains.
The book then turns in to the analyic aspect. General Dirichlet series, followed by the Riemann zeta function, L function ,are introduced. It's shown that the L- functions have meremorphic continuation to the whole complex plane by establishing the functional equation L(s)= elementary factor * L(1-s). The reader should be familiar with residue calculus to read this part.
Chapter 13 may be a high point of this book, where the Prime Number Theorem is proved. Arguably, it's the Prime Number Theorem which stimulate much of the theory of complex analysis and analyic number theory. As Riemann first pointed out, the Prime Number Theorem can be proved by expressing the prime counting function as a contour integral of the Riemann zeta function, then estimate the various contours. The proof given in this book , although not exactly that envisaged by Riemann , is a variant that run quite smoothly. As is well known , a key point is that one can move the contour to the line Re(s)=1, and to do this one have to verify that zeta(s) does not vanish on
Re(s)=1.The proof , due to de la vale-Poussin, is a clever application of a trigonometric identity. Unfortunately, the method does not allow one penetrate into the region 0
The last Chapter is of quite differnt flavour, the so-called additive number theory. Here the author only focusses on the simplest partition function ---the unrestricted partition. However interesting phenomeon occur already at this level. The first result is Euler's pentagonal number theorem, which leads to a simple recursion formula for the partition function p(n). 3 proofs are given. The most beautiful one is no doubt a combinatorial proof due to Franklin. The third proof is through establishing the Jacobi triple product identity, which leads to lots of identites besides Euler's pentagonal number theorem. Jacobi's original proof uses his theory of theta functions, but it turns out that power series manipulaion is all that's needed.
The book ends with an indication of deeper aspect of partition theory--- Ramanujan's remarkable congrence and identities ( the simplest one being p(5m+4)=0(mod 5) ). To prove these mysterious identites, the "natural"way is to plow through the theory of modular functions, which Ramanujan had left lots more theorem ( unfortunately most without proof). However an elementary proof of one these identites is outlined in the exercises.
This book is well written, with enough exercises to balance the main text. Not bad for just an 'introduction'.
Book Description
This book thoroughly examines the distribution of prime numbers in arithmetic progressions. It covers many classical results, including the Dirichlet theorem on the existence of prime numbers in arithmetical progressions, the theorem of Siegel, and functional equations of the L-functions and their consequences for the distribution of prime numbers. In addition, a simplified, improved version of the large sieve method is presented. The 3rd edition includes a large number of revisions and corrections as well as a new section with references to more recent work in the field.
Customer Reviews:
An extraordinary Book.......2002-06-12
Ever since I first read about the prime number theorem, I have been roaming the mathetmatical landscape, looking for the best proof of this result. I believe this book has it. It's not the simplest or the shortest proof, but it gives the deepest understanding of why the prime numbers behve like they do. In addition to this, it shows you the historical perspective in these proofs. All too often today math books give one short and slick proofs that leave you wondering how on earth they came up with it. In this book, however, one can almost feel the thoughts going through Riemann and Dirichlet's heads as they came up with the theorems. This book also has the proof of Dirichlet's theorem and Vinogradov's partial proof of the ternary goldbach conjecture. The vinogradov and following sections are considerably harder, partly because they were not written by Davenport himself. Anyway, if you're serious about Analytic number theory and how mathematicians think, this books needs to be on your bookshelf.
A good historical approach to Analytic Number Theory.......2000-12-26
I like this book because it gives you a good understanding of where the difficulties in the subject are. It takes a historical approach, following more or less the same steps that the original discoverers of these results took. Today we have very slick proofs for many of these results, and it is sometimes hard to understand why it took so long to discover them in the first place, but this book will give you this understanding; Dirichlet in particular practically had to invent Analytic Number Theory to prove his theorem on primes in an arithmetic progression.
The book works up gradually to each result, for example proving Dirichlet's theorem first for a prime modulus (as Dirichlet did himself), then the general modulus. In most cases it proves first the result for all primes (zeta function) and then the generalization for primes in an arithmetic progression (L function), pointing out which parts generalize easily and which cause special difficulties.
Some of the more advanced results covered are exponential sums, Vinogradov's theorem that every large odd number is the sum of three primes, and Bombieri's theorem about the average distribution of primes in arithmetic progressions.
I haven't seen the previous (1980) edition; this new edition seems to be lightly revised from the previous one. The last chapter is up-to-date and gives a brief survey of new results and of new books on the subject.
Book Description
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques.
The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
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Elementary and Analytic Theory of Algebraic Numbers (Springer Monographs in Mathematics)
Wladyslaw Narkiewicz
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ASIN: 3540219021 |
Book Description
This book gives an exposition of the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. The following topics are treated: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. Each chapter ends with exercises and a short review of the relevant literature up to 2003. The bibliography has over 3400 items.
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