Subjects:  1. General    2. Mathematics    3. Science/Mathematics    4. History of mathematics    5. Number theory   

Reviews (1)

A Landmark Writing, mainly of historical value
The author, L. E. Dickson, was a distinguished algebraist and number theorist in the first half of the 20th century. With collaborators, he compiled this "history", in three volumes, to get himself acquainted with the subject and to launch research on this topic (considered as important in other countries) in the US.
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Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Mathematics / Number Theory   

Reviews (7)

All about quadratric number fields, but little else
From 1962, this is a detailed account of quadratic number fields, and makes a fair introduction to the theory of number fields of any degree. Ideal theory (restricted to the quadratic case) is well covered in plenty of detail. Gauss's classic theory of binary quadratic forms is also included. nice text, but somewhat hard to read
This book gives a nice treatment of the theory of quadratic number rings and fields.It also covers a few other topics like class field theory and the Dirichlet problem.It requires surprisingly little algebra, but this makes some parts of the text seem to drag if you already know the algebra he covers.Not really recommended for independent study, since some arguments are a bit confusing, and it has few examples.

Advanced, but now dated. Still useful.
This is definitely an advanced book. But no book claiming to be advanced can hold that title for long since mathematical research is progressive. As advanced as the book is, it'sjust an introduction to advanced number theory now, and dated in places.This book was orginally published as "A Second Course in Number Theory " in 1962. I own several books by Harvey Cohn and I appreciate his writing style. He writes with the complete book in mind and every chapter and paragraph is cohesively developed. His writing (between the numerous equations, tables and proofs) is lucid and conversational with historical motivation. He places a strong emphasis on ideal theory, and quadratic fields. In this regard the book is almost redundant given his "Class Field Theory" book. Read more

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

Subjects:  1. Forms, Modular    2. General    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. q-series   

Subjects:  1. General    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Theory Of Numbers    6. Algebra    7. Mathematics / General    8. Mathematics / Number Theory   

Reviews (1)

The easiest introduction to field extensions I've read
This is the easiest-to-read introduction to abstract algebra and, in particular, field extensions, that I have ever seen. It is easier to follow than Artin's famous little book, and has easy but useful problems to allow you to check your understanding.
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Subjects:  1. Algebra    2. Algebra - General    3. Algebra, Abstract    4. Geometry    5. Mathematics    6. Number Theory    7. Problems, Famous    8. Science/Mathematics    9. Mathematics / Number Theory    10. Mathematics-Algebra - General   

Reviews (4)

Difficult book but great topic coverage
Solid coverage of proofs relating to Fermat's Last Theorem up to Kummer's Theory.You will find proofs for n=2, n=3, n=4, n=5, and n=7.Requires solid background in Algebraic Number Theory.For example, you should already have a good understanding of the Quadratic Law of Reciprocity, Quadratic Fields, and Congruences.If you don't, I recommend Elementary Number Theory for Congruences and the Quadratic Law of Reciprocity and Stark's An Introduction to Number Theory for Quadratic Fields.I would also recommend starting out with Edward's Book on Fermat's Last Theorem which includes detailed coverage of Kummer's Theory.

Great selection of material, difficult book
I find that this is a great book if you are an instructor or have a solid background in algebraic number theory.If you are unfamiliar with the Legendre Symbol, Gaussian integers, or the Law of Quadratic Reciprocity, you may wish to start out with a book such as Elementary Number Theory.If your are familiar with Algebraic Number Theory and wish to study in detail the Fermat Last Theorem proofs up to Kummer's Theory, this is a great book.I would recommend starting out with Edward's Book (Fermat's Last Theorem), for analysis of Euclid's proof of N=3.I found this very useful as an example of applications of Gaussian integers and Eisenstein integers.Ribenboim is one of the top experts about Fermat's Last Theorem and he is to praised for putting these beautiful proofs down.Even so, I would recommend purchasing other books to help explain this one.I found Stark's book very helpful in understanding Quadratic Fields.

"Amateur" mathematicians, that is !
If, like me, you were fascinated to hear that Fermat's so-called "last theorem" had been proven in 1995, then read Simon Singh or Amir Aczel's books popularizing the proof in outline, you probably wanted something more.Read more

Subjects:  1. Algebraic Geometry    2. Fermat's last theorem    3. Geometry - Algebraic    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. Algebraic number theory    8. Fermat    9. Mathematics / Number Theory   

Reviews (1)

Very good exposition
Liu's book has two distinct parts to it. The first 7 chapters combine to give a wonderful exposition of the language of schemes; the other chapters are of a specialised nature and concentrate on arithmetic curves. I will talk about the former. (So when I say "this book", I am only referring to the first 7 chapters)Read more

Subjects:  1. Geometry - Algebraic    2. Mathematics    3. Science/Mathematics    4. Algebraic geometry    5. Mathematics / Geometry / Algebraic    6. Mathematics | Pure Mathematics    7. Number theory   

Reviews (2)

Well worth the price
A nice, interesting book with a lot of useful information on probabilistic structural analysis, but does not follow the current industrial practice that is leaning towards stochastic FEA and FORM/SORM based limit state analysis. If you want to understand modern structural reliability theory, or plan to work in probabiistic design, I would strongly reccomend the textbooks by Haldar & Mahadevan. In short, Prof. Elishakoff's book will be a nice companion volume, but not a main reference. Cant beat the price, though.

Review
This book is a very lucidly written one in the area of probabilitisticapplications in mechanics and vibratrions.The first chapter is anintroduction in to the history of probability and its roots.The bookbegins with an introduction to probability and probability distributionsand this is covered in the initial couple of chapters.The second chapterdeals with the basics of probability involving set thory.The third andfourth chapters deals with the basic concepts of probability and deals withdifferent probability distributions in practice.In the next couple ofchapters the concepts of derived distributions are covered.The concept ofderived distributions along with transformations used are covered in thefourth and fifth chapters.The theory of random functions are covered inthe sixth chapter.Then the application of probability and stochasticprocesses to structural mechanics for example stability, vibration theoryhave been covered.The final chapter is on the random number generation. It deals with Monte Carlo simulation of probability distributions andrandom functions. ... Read more

Subjects:  1. Engineering - Civil    2. General    3. Probabilities    4. Probability & Statistics - General    5. Science    6. Science/Mathematics    7. Structural analysis (Engineeri    8. Structural analysis (Engineering)    9. Technology & Industrial Arts    10. Number theory    11. Science: General Issues    12. Technology / Engineering / Civil   

Reviews (4)

tough problems => good for the student
The motivation of explaining Fermat's Last Theorem is a nice device by which Stewart takes you on a tour of algebraic number theory. Things like rings of integers, Abelian groups, Minkowski's Theorem and Kummer's Theorem arise fluidly and naturally out of the presentation.
Very clear introduction to Algebraic Number Theory
This book is a very clear intoductino to ANT.It is a good first step for many reasons.One: it stays with algebraic number fields that are extensions of Q, the rational numbers.You get a good feel for the subject.When you go to more advanced books Q is replaced by other fields (P-adic, function fields, finite fields,..).
thoughts from an amateur
good overview of algebraic number theory as it applies to FLT, however not exactly pitched at beginners.you'll want to have a grounding in abstract algebra & linear algebra at the minimum.still, even if you don't, you can get a good sense of the "big picture" and a high-level understanding of the advances in mathematics that were directly or indirectly related to attempts to solve FLT.overall a fascinating read if you're a math geek who wants something a little deeper than Simon Singh's pop treatment of Wiles' proof. ... Read more

Subjects:  1. Algebraic Geometry    2. Algebraic number theory    3. Fermat's last theorem    4. Geometry - Algebraic    5. Mathematics    6. Number Theory    7. Science/Mathematics    8. Theory Of Numbers    9. History of mathematics   

Reviews (4)

Childrens book
The book has a very nice overview of Fibonnaci in daily life, written for children age 10 - up.
Good Book For Kids
A good intro book on Fibinocci numbers, but not whatI was looking for. This book is geared toward middle school students.

A good starter
This book is a good starter.It provides a good introduction on what is a Fibonacci Series, the analysis of such and where Fibanacci numbers occur in nature and our lives.It even has a decient introduction on Lucas Numbers.However, it is just that, a good starter which I would whole heartedly recommend for a high school student that is just about to discover how wonderful math subjects can be. To get a more in depth presentation, one will have to refer to a receintly published paper on the subject or refer to a graduate text. ... Read more

Subjects:  1. Education    2. Fibonacci numbers    3. Mathematics    4. Number Theory   

Reviews (1)

An Incredibly Beautiful Book
I was given this book as a present and have now read it over ten times.Lovely images and good mathematics.Lundy covers the numbers 1-12 in detail, listing their relationships to music, geometry and Pythagorean number theory, as well as some cultural background.She does this without sounding either too 'symbolic' or too 'mathematical'.Each number is presented with its own compound illustration, and these are - to put it plainly - quite awesomely well executed.The book then goes off into Magic Squares, Gematria and other esoterica again managing to stay neat, informative and historical.Finally there are extensive appendices.I utterly commend this rare, beautiful and fascinating book to anyone with even a passing interest in numbers. ... Read more

Subjects:  1. General    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Mathematics / General   

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.
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

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

Subjects:  1. Computer Books: General    2. Computer Science    3. Computers    4. Computers - General Information    5. Number Theory   

Subjects:  1. Advanced    2. Differential Equations    3. Exponential sums    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. Analytic number theory    8. Mathematics / Advanced    9. Mathematics / Number Theory    10. Mathematics-Advanced    11. Mathematics-Differential Equations   

Subjects:  1. Algebra - Linear    2. Forms, Modular    3. Geometry - Algebraic    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. Eichler-Selberg trace formula    8. Eisenstein series    9. Hecke operator    10. Hecke-Weil theory    11. Mathematics / Number Theory    12. Primitive form   

Editorial Review

This may surprise those who have trouble carrying the remainder in division orfiguring out a 15 percenttip on a $20 lunch bill, but according to mathematician andpsychologist Stanislas Dehaene, mathematics is an inborn skill. In Read more

Reviews (8)

Good book
This book is a tour de force of neurology as it applies to mathematics. From anectodes and case studies of mathematical greats and autistic calculating prodigies to brain scans and theory of the evolution of our calculating ability.
Amazing, objective research scores an A!
Fascinating. That's the word I've been using to describe this book. From the information on numerical experiments with animals to the solid evidence presented for the hardwired concept of numbers from birth, the author ties together an amazing work. Quality science, excellent entertainment
I received this book as a gift.I skimmed it and left it unread for months.I thought it was a cash-in on Steven Pinker's excellent The Language Instinct.But no!Read more

Subjects:  1. Cognitive Psychology    2. General    3. Mathematical ability    4. Mathematics    5. Neuropsychology    6. Number concept    7. Philosophy Of Mathematics    8. Psychological aspects    9. Psychology    10. Study and teaching    11. Theory Of Numbers    12. Number theory    13. Psychology & Psychiatry / Cognitive Psychology    14. Psychology | Cognitive   

Reviews (3)

Can't Get Enough
This is the most concise, humourous book on the history of numbers you will read. Asimov is at his peak with this one. The last couple of chapters lost my interest, but the rest is well worth the money. Written for the layman, but enough fuel for the enthusiast.

One of my favorite books
Every time I read this book (I've read it at least 4 times) I get to achapter that I've read before and I say, "I don't think I'll read thischapter, I'll just skip it and go on to the next one..."But then Iend up reading that chapter and I will think to myself, "That chapterwas AWESOME!Why would I ever think of skipping it?"I love thisbook, I find it hard to put down.Asimov has a way of explainingmathematical concepts in a very compelling way.I'm sad that the book isout of print - I can't find the copy that I read back in high school - surewould love to pick up another copy.As mentioned else where this book is acompilation of articles written by Asimov, mostly in the 60's.

Number "facts," history & theory; includes Math Biographies
The late Issac Asimov's thoughts on various numbers, series and numerically interesting subjects, including Euler's "e," the origin of the "Arabic numerals" and lots about various largenumbers, including Googols and the transfinite numbers.Read more

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Non-Classifiable    5. Sale Books   

Reviews (3)

what!
I had this as a textbook in a junior level number theory course, and I am sorry to say that it is the worst textbook I have yet used.This book contained very little actual information and even less mathematics. I'm sad to say that it read like a book whose purpose is to sell you another book.I would have to say that the real message of the book is:
Extremely well-motivated and clear introduction
This is a very pleasant introduction to number theory. Each chapter is preceded by a preview and concluded by a discussion to make the main ideas clear and well-motivated and to show how things fit in the big picture by discussing the historical development. The book starts with the very basics and moves via some pearls like the four square theorem and quadratic reciprocity to a culmination with algebraic number theory. A readable and elementary introduction to algebraic number theory is especially valuable today because, as Stillwell argues in his preface, this is the proper setting in which to learn of rings and ideals. Nowadays, of course, the custom is to pull these concepts out of a hat in the mysterious context of "abstract algebra" where there is no apparent reason to introduce them whatsoever. Fortunately, Stillwell has provided us with an equally enjoyable book on algebra, so now we can only hope that some day the curricula will change accordingly.

Illuminating and down to earth
One of the best introductory books I've seen. It is concise, and yet very illuminating and down to earth, leading very nicely into the beginnings of algebraic number theory. ... Read more

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Theory Of Numbers    5. Mathematics / Number Theory   

Subjects:  1. Algebra    2. Algebra - Linear    3. Forms, Quadratic    4. General    5. Mathematics    6. Matrices    7. Number Theory    8. Probability & Statistics - General    9. Science/Mathematics    10. Theory Of Numbers    11. Algebraic number theory    12. Arithmetic Theory of Fields    13. Arithmetic Theory of Rings    14. Mathematics / Number Theory    15. Quadratic Forms