Subjects:  1. Automorphic forms    2. Calculus    3. Geometry - Algebraic    4. L-functions    5. Mathematics    6. Number Theory    7. Science/Mathematics    8. Mathematics / Number Theory   

Reviews (8)

A Worthy Number Theory Text
We used this book in an number theory course I took recently.Burton is a skilled writer, and his book is extremely easy to read even for those devoid of "mathematical maturity".There is a student solutions manual, but I recommend that you abstain from buying it.Many of the exercises have generous hints provided.In fact, Burton probably overdoes it in the hint department.Some of the exercises are ruined that way.Nonetheless, Burton provides excellent exercise sets.Some of the problems are trivial, some aren't.He is careful to point out certain themes that recur in number theory in the text and the exercises.
as a start.. perfect
I bought this book to study number theory on my own. (but let me say I had great knowledge about the material b4 I got into it). I studied the first three chapters on my own, and it was great experience, but then I had to stop cuz I did not have any free time to continue. From the first three chapters, I rank this book 5 stars!
Adequate introductory text at an outrageous price.
This text has served me through my first course in number theory.It follows the traditional "definition - theorem - proof - example - exercises" format throughout it's sections.For some flavor, it even throws in a little history behind the mathematics it presents.This book, however, IS NOT worth the ridiculous price that McGraw Hill has retailers charging; nothing in it is that spectacular (well, not spectacular at all, really). ... Read more

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Mathematics / Number Theory   

Subjects:  1. Applied    2. Curves on surfaces    3. Data processing    4. Geometry - Differential    5. Geometry, Differential    6. Mathematics    7. Number Theory    8. Science/Mathematics    9. Textbooks    10. Geometry    11. Mathematical & statistical software    12. Mathematics / Geometry / General   

Subjects:  1. Algebra - General    2. General    3. Homology theory    4. Local fields (Algebra)    5. Mathematics    6. Number Theory    7. Science/Mathematics    8. Algebraic number theory    9. Fields    10. Fields & rings    11. Lokaler Körper    12. Mathematics / Algebra / General    13. Mathematics / Number Theory    14. Mathematics-Algebra - General   

Reviews (4)

Excellent book on problems
This is a very useful book for anyone studying number theory. It's especially helpful for amatuer mathematicians learning on their own. This one is the same as the older edition with more hints and more detailed explanation. But WOULDN'T IT BE GREAT TO LEAVE A little room for the readers to think on their own?! You will reap the benefit from thinking hard as well as working hard!

Amazing!!
Best book of it's kind that I've ever read.I found it to be extremely helpful.I even read it at night before I go to bed because its so entertaining.I thoroughly enjoyed it and would recommend it to anyone who is studying this.

Won't become a classic.
A problem book is always helpful to students. But this one is sloppy. Besides the supplementary problems at the end of each chapter, most problems are boring or break-ups of theorems, and there isn't much enlightment or warmth or lucidity in presentation of the materials. I do find though, the author's other book, "Problems in analytic number theory", is far superior to this one. ... Read more

Subjects:  1. Algebra - General    2. Algebraic number theory    3. Mathematics    4. Number Theory    5. Problems, exercises, etc    6. Science/Mathematics    7. Mathematics / Number Theory   

Reviews (1)

Good Reference
This is an EXCELLENT reference manual. Its a "bit" mathematical, but does need to be updated regarding turbo codes. ... Read more

Subjects:  1. Coding Theory    2. Computers - General Information    3. Discrete Mathematics    4. Information Theory    5. Mathematics    6. Number Theory    7. Programming - Systems Analysis & Design    8. Science/Mathematics    9. Set Theory    10. Algebra    11. Algebraic geometry    12. Algebraic number theory    13. Applied mathematics    14. Combinatorics & graph theory    15. Mathematics / Number Theory   

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Analytic number theory    5. Mathematics / Number Theory    6. Mathematics | Pure Mathematics   

Reviews (1)

Definitive text
This is the definitive text on the theory of primes in the form x^2 + ny^2. Problems with simple formulation like this (which primes can be written in that form, and for what n?) make the class field theory interesting and worth understanding. Those with interest in prime numbers would greatly appreciate the topics presented. Recommended for those with a strong background in number theory and algebra. ... Read more

Subjects:  1. Algebra - General    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Algebraic number theory    6. Mathematics / Algebra / General   

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Complex analysis    5. Groups & group theory    6. Mathematics / Number Theory   

Reviews (3)

Winner of the 2006 Mathematical Association of America Beckenbach Book Prize
"Thoroughly engaging... Accessible to a very broad audience... While the theorems covered may not be new to research mathematicians, I would wager that very few of us have seen them proven in quite this way." -- American Mathematical Monthly [http://www.maa.org/reviews/reallycount.html]
Outstanding exposition
I was introduced to this book by a talk that one of the authors (Arthur Benjamin) gave at the MAA Mathfest in Albuquerque in August of 2005.The talk was one of the very best mathematics talks that I've ever attended.Everyone in the audience could follow what was going on, and we all left with an understanding of the basic approach to combinatorial identities used in this book.The authors' approach is to prove combinatorial identities by defining a quantity and then obtaining different formulas for that quantity.One formula becomes the left hand side of an identity while another formula becomes the right hand side.
Lovely author
I haven't read this book yet, but I have a signed copy after seeing Jenny Quinn speak at the 2005 meeting of the Northwest chapter of the Mathmatics Association of America.If her written work is anything like her speaking, then this should be a great book.Her combinatorial proofs are an interesting approach to old equations, and she presents them in a very clear manner.A most enthusiastic lady. ... Read more

Subjects:  1. Combinatorics    2. Counting & Numeration    3. Discrete Mathematics    4. Mathematics    5. Reference    6. Science/Mathematics    7. Combinatorics & graph theory    8. Mathematics / Combinatorics    9. Number theory   

Editorial Review

Until about 1975, logarithms were every scientist's best friend. They were the basis of the slide rule that was the totemic wand of the trade, listed in huge books consulted in every library. Then hand-held calculators arrived, and within a few years slide rules were museum pieces.Read more

Reviews (44)

Compelling and easy to read
I know calculus but I didn't know much about some of the history of mathematics. How easy is to learn a complex theme in the words of this author. A fascinating book about an important number, browsing the history of logarithms, then some of the history of calculus and finally the history of Leonhard Euler, and the first appearance of "e". Obviously you find mathematics in this book, but presented in a easy-to-understand way.

A must read for math or EE major
This is by far the BEST book that I have read about math. It definitely helped me to understand some of the important concepts in applied math and electrical engineering fields. I'd strongly recommend this book!

Good Balance of Math and History
For me, this book had the exact right balance of math and history. There is some mathematical discussion but nothing to scare anyone who has taken calculus. The historical discussion really helps one understand how mathematical thought has evolved over the last few hundred years. ... Read more

Subjects:  1. History & Philosophy    2. History Of Mathematics    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. History of Science and Medicine, Philosophy of Science    7. History of science    8. Mathematics / History   

Reviews (4)

chimpanzee oven mitts
I have a background in logic but absolutely none in elementary number theory or abstract algebra and I am using this as a first-time study guide. I find it very good. I have to mull over some of the proofs and examples since certain shortcuts are not immediately evident to me, but everything is generally clear and easy to follow. There are very few historical remarks which may or may not be a bonus for some. And as Dover does, they are practically giving this thing away.

Won't Be Over Your Head
The other reviews pretty much say it all.The book begins with a pedestrian approach to the topic and then gradually becomes more complex.Should be accessible to most readers.

Excellent text by expert in the field
George Andrews is the reigning expert on partitions in the mathematical community who has written many seminal papers on the subject over the past half-century! If you don't know what partitions are in the theoretical sense, don't worry, the text provides ample introduction.I don't think you can find a more elementary introduction to the difficult, but extraordinarily powerful and elegant theory of partitions. The book covers the basics of number theory well, but it is the chapters on partitions that make this text stand out. It covers the Rogers-Ramanujan identities as well as the Jacobi triple product identity. It is rare in the mathematical community that an expert in a subject also writes a ground-level introductory text - but that's what you have here.Thanks to the dover edition, it's now quite affordable. ... Read more

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Mathematics / General   

Reviews (3)

I only wish I could give more stars...
This is the best introduction-level mathematics textbook I have ever read, and I have read (and own) many.Every theorem and definition is well-motivated, and problems for the reader are interspersed within the text to make sure that every subtle nuance of the exposition is understood.Though introductory, Gouvea manages to incorporate some relatively advanced topics, (as far as undergraduate mathematics goes) such as the Weierstrass Preparation Theorem, local rings, and analysis in C_p.All this and the topic at hand is fascinating to boot.p-adic numbers are perfect for anyone wishing to pick up an amazingly interesting topic not found in most undergraduate or graduate courses.In conclusion, I recommend this book to the set of people interested in p-adic numbers, and its complement.

enthousiasm-adique
You're curious about beautifull topics in math, but reading a classical texbook, browsing through a list of lemma and therorems just get you sleep ? Read this one. The idea behind theorems, and why and how they came aliveare so nicely exposed that thisbook can replace your favoritebed timeone.

This is a wonderful book for several reasons.
This book really grabbed me on a number of points.First, in addressing a rather abstract topic (often not included in a basic undergraduate curriculum) it does a good job trying to compute concrete examples.Itstays broad, as not to lose the reader on the messy details of anyparticular part of the theory.Hence the book is good even for studentswho are a little weak on their background.It is well-organized andexposed for an introductory-level text.Read more

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Theory Of Numbers    5. p-adic numbers    6. Algebra    7. Algebraic number theory    8. Mathematics / Number Theory    9. absolute values on fields    10. p-adic analysis    11. valuations   

Subjects:  1. Forms, Modular    2. Geometry - Algebraic    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Mathematics / Number Theory   

Subjects:  1. Applied    2. Bifurcation theory    3. Differential Equations    4. Engineering - General    5. Mathematics    6. Number Theory    7. Science/Mathematics    8. Calculus & mathematical analysis    9. Mathematics / Applied   

Reviews (2)

Absolutely essential reference
This long book is sort of the equivalent of an extremely long review paper, with innumerable references. It is the only work of its kind on Theory of Numbers. Written in the early 1920s, it is still the only place where one can find information on who did what in various topics of number theory, and many of those topics are still fertile ground for further research. So if one wants to do research on any topic in theory of numbers, or on related aspects of algebra, topology, Ramsey Theory, theory of graphs, etc. one *must* have Dickson's book handy. It's expensive; if you're lucky, a colleague or your departmental library may have a copy handy for you, but if not, go ahead and spend the money to buy it. It has been of great use to me.

Not what you might expect.
The author was himself an expert in number theory and modern algebra (as it was) in his day.These volumes were published in 1919-23 so don't expect the latest results. In fact, the terminology won't even be the same since much of the theory has undergone a great deal of mollycoddling and reformulation...publish or perish, you know. Read more

Subjects:  1. History & Philosophy    2. Mathematics    3. Number Theory    4. Science/Mathematics   

Reviews (1)

Respectable and enjoyable guide to pre-Gaussian number theory
When someone like Weil sets out to write a history of number theory it is destined to be the standard reference for decades to come. But this is not only an authoritative reference everyone loves to cite--it is also delightfully readable. It is not a substitute for a textbook (although Weil hints at this possibility is the preface), but even for readers with only a modest background in number theory this book will be a source of insight and joy.
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Subjects:  1. History    2. History & Philosophy    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Theory Of Numbers    7. Mathematics / Number Theory    8. Mathematics-History & Philosophy   

Reviews (2)

One of the most beautifully written math books
This book is basically all you need to learn modern algebraic number theory. You need to know algebra at a graduate level (Serge Lang's Algebra) and I would recommend first reading an elementary classical Algebraic number theory book like Ian Stewart's Algebraic Number Theory, or Murty and Esmonde's Problem's in Algebraic Number theory.

10 stars if I could.
After having no fun with Lang's text "Algebraic Number Theory" I began seking out something more complete and which was full of quality exposition.As a result of Amazon's approach to marketing towards members, I was recommended this book and decided quickly that I must have it.This book is marvelously well written, examples are kept to an un-overwhelming minimum, the problems are not trivial (at least to me) and in fact I feel this is the kind of book on par with, say, Paulo Ribenboim's "Classical Theory of Algebraic Numbers" since these are both the type of book you would want to take with you on a long trip or as Paulo says, "while stranded on a desert island".This book is by no means intended for those who are not fluent in both Number Theory as well as Algebra, both at the graduate level and obviously for those who are Mahematically gifted.I highly recommend this book to graduate students interested in Algebraic number theory as well as those needing a splendid reference. ... Read more

Subjects:  1. Algebraic Number Theory    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Arithmetic Algebraic Geometry    6. Mathematics / Number Theory   

Reviews (4)

Reviewing the numbers!
Haven't read through the entire book yet but so far there are a lot of theorem equations I've never heard before that are very interesting to consider.I've been trying to find my own way to find any possible prime number and this book is very helpful in showing you whats already been done and could influence you to maybe think of an equation or method yourself (for finding prime numbers that is).Other than that.I don't have too much detailed information on this book yet.

Compendium of unconnected number factoids
This a dictionnary comprised of number theory factoids. Admittedly it is well researched, but I found it dry and hard to get into. You must know quite a bit of number theory to appreciate the subject matter, which will limit the appeal of the book to the layman.
A Mathematical Comedy
This book is a mathematical comedy. For most of us prime numbers have no value beyond a bit of curiosity -- if you're into cryptology of course then you're looking at a horse of an entirely different color.
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Subjects:  1. History & Philosophy    2. Mathematics    3. Number Theory    4. Numbers, Prime    5. Reference    6. Science/Mathematics    7. Mathematics / General   

Subjects:  1. History & Philosophy    2. Mathematical Analysis    3. Mathematics    4. Number Theory    5. Numbers, Prime    6. Science/Mathematics    7. Theory Of Numbers    8. History of specific subjects    9. Mathematics / Number Theory    10. Prime numbers    11. Primzahlen    12. Primzahlenvereteilung    13. distribution of primes    14. primes in progressionve