Reviews (1)

Great introduction to the theory of toposes.
When Goldblatt's book first hit the stands, it was blasted by reviewerswho had a geometric predilection. They claimed that Goldblatt hadtrivialized this essentially rich geometric subject by giving aset-theoretic treatment.Read more

Subjects:  1. Logic    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Toposes    6. Mathematics / Logic   

Reviews (4)

The latest cutting edge research on Elliptic Curve Cryptography
First, the reviews dated below (July 25, 2002, July 29, 2000 [Lee Carlson] and January 31, 2000) are refering to Blake, Seroussi and Smart's first book: Elliptic Curves in Cryptography: London Mathematical Society Lecture Note Series 265, not the new book Advances in Elliptic Curve Cryptography, London Mathematical Society Lecture Note Series 317.
too much math
This is a fairly complete treatment of elliptic curve cryptography. It suffers from a very uneven treatment. The chapters on implementation are well written and easy to read. The material on the logarithm problem, however, is much too advanced and will only be accessible to research mathematicians. A big omission in the book are protocols such as signatures and encryption.

Good compact book on elliptic curves in cryptography
This book gives a good summary of the current algorithms and methodologies employed in elliptic curve cryptography. The book is short (less than 200 pages), so most of the mathematical proofs of the main results are omitted.The authors instead concentrate on the mathematics needed to implementelliptic curve cryptography. The book is written for the reader with someexperience in cryptography and one who has some background in the theory ofelliptic curves.A reader coming to the field for the first time mightfind the reading difficult. The authors do give a brief summary in Chapter1 on the idea of doing cryptography based on group theory. They then moveon to discuss finite field arithmetic in Chapter 2. The reader is expectedto know some of the basic notions of multiprecision arithmetic forintegers. The authors choose to work with 2^16. Psuedocode is given fordoing modular arithmetic with Montgomery arithmetic given specialattention. The last section of the chapter gives a good summary ofarithmetic in fields of characteristic 2. Chapter 3 discusses verycompactly arithmetic in elliptic curves. This is where the reader shouldalready have the background in the theory of elliptic curves, since thereading is very fast and formal. The authors do a good job of summarizinghow modular polynomials come into play in elliptic curve cryptography andgive some explicit examples of these polynomials. The most importantchapter of the book is Chapter 4, where the authors give a discussion ofhow to implement elliptic curves efficiently in cryptosystems. This chapteris nicely written and pseudocode appears many times with lots of niceexamples. This chapter serves as background for the next one on thediscrete logarithm problem using elliptic curves over finite fields. TheMOV attack, the anomalous attack, and the baby step/giant step methods arediscussed very nicely. Random methods, such as the tame and wild kangarooare discussed at the end of the chapter. Read more

Subjects:  1. Computer security    2. Mathematics    3. Number Theory    4. Public key cryptography    5. Science/Mathematics    6. Security    7. Security - General    8. Applied mathematics    9. Coding theory & cryptology    10. Data security & data encryption    11. Mathematics / Number Theory   

Editorial Review

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Reviews (12)

Daughter of Jackson's Fans responds (Robert Jackson)
I have met one of the authors, Dr. John Conway, at Princeton University. Dr. Conway was consulted by my Father, Robert Jackson, of Jackson's Difference Fans,(a 1937 Princeton alumnus -Chemical Engineering with Honors). Although I, myself, am not a math inclined individual, the explanations found in various sections of the book have been used in the history courses I teach on the middle and high school grade levels. They are designed for the beginner and the advanced math intrigued mind.
very nice, but wishing for a clean up
This is an 'almost done' type of book. I like the way the subject is handled. The pictures and the thoughts that go with them are really good food for thought. Still, when I read the text, I get the feeling that this book was rushed to press. One more review by the author could have helped. I get this feeling because the text does not always follow the illustrations. It neither does much to elaborate on them or to completely discuss what has been included.

Gets off to a strong start
Conway and Guy start this book with an enticing survey of how numbers pervade the English language, showing the hidden (or not-so-hidden) numerical roots of common words. They also mention other numbering systems, including the Roman numerals, Greek, Egyptian, and cuneiform Babylonian - numbers that persist in our 60-based measures of minutes and seconds, in both time and angle.
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Subjects:  1. Mathematics    2. Number Systems    3. Number Theory    4. Popular works    5. Science/Mathematics    6. Theory Of Numbers    7. Mathematics / Number Theory   

Editorial Review

Bernhard Riemann was an underdog of sorts, a malnourished son of aparson who grew up to be the author of one of mathematics' greatestproblems. In Read more

Reviews (66)

My own bit of random noise
In the unlikely event that someone might have been misled by a previous reviewer, who claimed to have found an error so serious that forced her to stop reading, a gentle reminder that ln(x) and log(x) are used interchangeably by mathematicians and other numerically-literate bipeds to denote the natural logarithm, at least when there is no possible confusion on the logarithm basis. This is not to say that you will not find any typos in this book -- you might or you might not -- but this one doesn't even deserve that name.
Quick&Dirty
NOT for the faint of (math) heart.I have started reading it a second time, trying to be a bit more careful as I hit the later chapters.This, for me, is where the trouble starts.I have to admit that I probably will not really understand the depth of the problem, although I do, as a very old one-time math major, appreciate its significance.
Amazing book
This is a really great book. Of course, it is an introduction to the Riemann hyphotesis, but you will enjoy reading (a lot). Actually reading this book is like reading a mystery novel. ... Read more

Subjects:  1. Algebraic Geometry    2. Biography / Autobiography    3. Geometry - Algebraic    4. History & Philosophy    5. Mathematics    6. Number Theory    7. Science/Mathematics    8. Scientists - General    9. Theory Of Numbers    10. Mathematics / Advanced   

Reviews (39)

Awesome book on sacred geometry
I love this book!It is the first time I've read on the subject, and it is chockful of so much eye opening info.I enjoy it so much that I am making a cliff notes book for myself and illustrating it just for fun.This may sound wierd, but as an artist, sacred geometry has changed the way I see the world and my art, it is changing my life.I recommend to all, though you have to have a somewhat academic vocabulary base to truly understand this book.

Fantastic author
He knows his subject. The man can write, he is simply brilliant. He has such an enlightened way of connecting all the dots while keeping you interested in very complex principles.
excellent content, great for the lay reader
the only thing i would add to what others have said is that it really only makes sense if read in order.
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Subjects:  1. Astronomy - General    2. Mathematics    3. Number Theory    4. Philosophy    5. Philosophy & Social Aspects    6. Science/Mathematics    7. Popular astronomy    8. Science / General   

Reviews (3)

Good book on a standard subject
I thought this book was a very good book on elementary number theory. It covered all the standard topics for such a book. The author was clear in his presentation of topics.

Not a bad book, but horribly expensive
I had to get this book for an undergraduate class in number theory, so I had no choice but to shell out the cash. Price aside, it really is a decent textbook. It is easy enough to understand for even a non math person, and there is a nice range of easy, medium, and hard problems. Still, although I haven't looked at too many other textbooks, I bet you could find a book just as good for half the price.

Plenty of choices...
Another thin book on a standard subject with horrendous price. Another cheap effort hope to reap in good cash. Look elsewhere, plenty of choices. ... Read more

Subjects:  1. Education    2. Elementary    3. Mathematics    4. Number Theory    5. Mathematics / Number Theory   

Reviews (1)

A wonderful insight into number theory
In general, this book gives a comprehensiveaccount on elementary number theory. The first few chapters include some fundamental concepts like divisibility and congruences (i.e. a simple kind of modular arithmetic), aswell as famous yet basic theorems like the fundamental theorem ofarithmetic. Important topics in number theory such as Diophantineequations, fractional approximations for irrational numbers and Quadraticfields are there, and if you're interested in magic squares, I'd like tosay that a whole chapter is devoted to it. Read more

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

Reviews (6)

Excellent intro book on number theory
Ever since my undergraduate days aeons ago, I have always had an aversion to any number theory, but Jones and Jones have changed my mind completely.In the last year, I came across a few articles that made me want to learn more about the topic, but wasn't sure where to start, as I wanted a book that had proofs that I could follow, and yet also gave me some motivation to dive into more complicated mathematics such as elliptic curves.Elementary Number Theory fit the bill perfectly and has served as a wonderful introduction to the subject that I could follow and enjoy.
Great buy for aspiring cryptographers
I bought this book while studying cryptography, a field that relies heavily on Number Theory for inspiration and from which it draws many, if not most, of its constructions. Most books on Cryptography summarily relegate the relevant number-theoretic aspects to short appendices that fail to build any intuition about what is going on. This book delivers precisely what is missing: a very readable, easily accessible introduction to the main topics of number theory that leaves the reader with a much better idea of how everything fits together. The book is very well suited for self-study, and includes answers to all exercises. Nicely explained
I used this book as a reference book to review the basic number theory that I tend to foreget while I was in graduate school.I hope I had that book while I was undergraduate, because the all the proofs are clearly written.The exercises are all meaningful, but it will be nice to include some challenging problems.I highly recommend this book to any undergraduate or even bright high school students who want a quick introduction to number theory. ... Read more

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

Reviews (2)

Excellent Text on Factorization
This is one of the most compact and best organization of material on the subject of factorization and primality. Just the facts mam, just the facts.
This book gives you the juicy bits you want for factoring and primality testing.It skips all the theory and presents the algorithims before you to observe and play with.For the amateur, this is an excellent firstbook. ... Read more

Subjects:  1. Factorization (Mathematics)    2. History    3. Linear Algebra    4. Mathematics    5. Number Theory    6. Numbers, Prime    7. Science/Mathematics    8. Algebraic number theory    9. Mathematics / Number Theory    10. Science-History   

Reviews (8)

Superb Introduction for the Mathematical Sophisticate
This classic deserves its reputation but be warned that it is not an introduction for mathematical neophytes. The authors take detours (which sometimes are looks ahead) from the main path of development that the sophisticate will enjoy but the novice may not be able to recognize as detours. Examples are the geometry of numbers (introduced in chapter 3), the Farey dissection of the continuum, and trigonometric sums.
excellent introduction
For a statistician like me who has a fair background in pure math, and who needed at some point to know a couple of things in number theory, it is definitively the best book. It covers a wide variety of topics explained succinctly and clairly.

One of the greatest
First of all, let me say this about the one star review. Do not let yourself be infuenced by lesser mathematicians. Idiots in my opinion. To give this book one star, you must posses some special kind of mediocracy. Keep your stupidity to yourself Lucas.
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Subjects:  1. Chemistry - General    2. Mathematics    3. Number Theory    4. Science    5. Science/Mathematics    6. Mathematics / Number Theory   

Reviews (4)

Gives an intuitive feel for numerical methods
Chances are, if you have a degree in engineering of any kind, you have seen all of the numerical methods outlined here before. However, the purpose of this book is not just to detail how to perform different kinds of calculations. Instead, the author is attempting to give you an intuitive feel for the mathematics as well.
Like no other book on numerical methods I have read.
I sympathise with the reviewer who said this is one of the few The Purpose of Computing is Insight, Not Numbers
Throughout the book, that motto is repeated.Read more

Subjects:  1. Applied    2. Data processing    3. Mathematics    4. Number Theory    5. Numerical analysis    6. Science/Mathematics    7. Mathematics / General    8. Mathematics for scientists & engineers   

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

Subjects:  1. Automorphic forms    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Algebra    6. Algebraic geometry    7. Calculus & mathematical analysis   

Reviews (2)

A good book
This is a nice book that introduce the reader in a nicely way to Galois and Field theory. This book not only concentrate in the classic topics but also covers so much about areas not covered in other books. For example the topics of normality and separibility and pure separability are very well covered and the concepts of infinite extensions; among many others. This books also contains a nice feature and is tons of examples and exercises. Definitely a very good book. I took the course of Galois Theory with this text and I learned a lot.

An excellent book for begginers
This book provides a lot of examples to demonstrate the theorems in the book. So you can understand the theorems without much difficulty. Besides, the author gave many details of theproofs in this book. Although it mayhurt the concisity of the book, for the begginers, it is very useful. ... Read more

Subjects:  1. Algebra - General    2. Algebraic Fields    3. Algebraic Number Theory    4. Galois theory    5. General    6. Mathematics    7. Number Theory    8. Science    9. Science/Mathematics    10. Fields & rings    11. Groups & group theory    12. Mathematics / Algebra / General    13. Science-General   

Reviews (6)

Best book on the subject
I am currently finishing my third year of undergraduate math at Brown University, and have just completed a course that used this particular book.I have to say it's the most WELL WRITTEN math book I've ever read, and I've read many, many math books by now (more than I'm willing to count as I'm typing this).Professor Rosen (and Ken Ireland, God rest his soul) have made a book that has both fun and interesting problems as well as clear explanations of proofs in the text.It does of course require that you know the basics of abstract algebra (in particular, one is expected to know that "1" is a unit and therefore cannot be prime, so of course when we discuss problems involving factorization into primes, one will of course ignore the number 1).One is also expected to know the basics of formal logic (i.e. understanding how a proof by induction works, how a proof by contradiction works, and knowing that any proper subset of the natural numbers will have a least element), and I choose to point this out simply because MrBigBeast's review makes it obvious that all these facts were not understood.Despite the fairly large amount of assumed knowledge (this is a book intended for advanced undergrads and first year grad students, afterall), this book takes one on an amazing adventure through the depths of elementary number theory, as well as introduces you to very advanced topics in both algebraic and analytic number theory (ever want to know about Zeta Functions?This book treats the topic quite nicely, making a fairly difficult concept accessible).Truly a gem of a book and worth buying even if you never use it for a course.

Great Book
I'm currently an undergrad math and phsyics major at Brown, and I loved this book.Rosen is a great teacher and a great writer.As per the post below mine, the submitter is being overly nitpicky.If a reader cannot realize that unique factorization of Z+ extends to Z or understand immediately the nature of "1", then perhaps the reader shouldn't be trying to learn advanced number thoery.As per using the conclusion in the proof, it's called proof by induction.It's easy and trivial enough that I'm sure they didn't want to waste the readers time going through the incredibly obviouse steps.
Covers many important areas
I have devoted a good portion of my life to the study of mathematics in general, especially algebra and number theory.This book is an extraordinary reference to many areas of number theory and extremely approachable.The book can be studied on its own or as a companion piece to more specialized texts such as Marcus's Number Fields. ... Read more

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Theory Of Numbers    5. Mathematics / Number Theory    6. Zahlentheorie   

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

Reviews (1)

Incredible implications for physics and mathematics
At first it seemed this book was [spendy] but once I bought it I had no regrets. Mastering the material, means that one gets a glimpse at the potential exquisite simplicity of the p-adics. You also get a real sense that the proof of the greatest problem of all - the Riemann Hypothesis - is not far away if Haran's philosophy is pursued just one step further.... ... Read more

Subjects:  1. Algebraic Geometry    2. Calculus    3. Functions, Zeta    4. Geometry - Algebraic    5. Mathematics    6. Number Theory    7. Probability & Statistics - General    8. Science/Mathematics    9. p-adic analysis    10. Algebra    11. Complex analysis    12. Mathematics / Number Theory    13. Mathematics | Probability & Statistics    14. Quantum physics (quantum mechanics)    15. Stochastics    16. Theoretical methods   

Subjects:  1. Algebra - General    2. Calculus    3. Mathematics    4. Modular groups    5. Science/Mathematics    6. Siegel domains    7. Theory Of Functions    8. Mathematics / Algebra / General    9. Mathematics / Calculus    10. Mathematics-Algebra - General    11. Mathematics. Automorphic functions    12. Number theory   

Reviews (3)

all about understanding RSA
The book revolves around RSA. The motivation for the book is that the reader wants to understand public/private key cryptography, where this is represented by the seminal RSA algorithm.
Excellent introduction
This book is a very readable introduction to the theory of numbers. The author manages to concentrate in a relatively short book and with a very clear and pleasant style the material necessary to understand the mathematics underneath the RSA cryptosystem. No previous knowledge ofadvanced mathematics is assumed. Perhaps not enough for mathematicians, butmore than rewarding for the rest of us. It reminds me a bit of the style ofM. Gardner. Books on mathematics can be very dull without the style ofexposition of Mr. Coutinho. Highly recommended !

multiplication
multiplicatio ... Read more

Subjects:  1. Cryptography    2. Cryptography/Access Control    3. Mathematics    4. Number Theory    5. Programming - Algorithms    6. Science/Mathematics    7. Theory Of Numbers   

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