Subjects:  1. Education / Teaching    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Teaching Methods & Materials - General    6. Teaching Methods & Materials - Mathematics   

Reviews (7)

Good text but unfortunately often misused
This book is popularly used for an introductory course in number theory, which also often serves as an introduction to proofs. This is how I came across this text and in that context it fails. To the author's credit, however, he never intended the book to be used in this manner and he states that in the beginning. This book was designed for non-math majors (and perhaps eager high-school students) and is clearly aimed towards them.
A Valuable Book!
I admit that this book might not be suitable especially for pure mathematicians. But I very much liked Silverman's way of writing: He cast questions and encourage readers to tackle them! Indeed, this is a unique number thoery book written in that way.

A reallyfriendly, enjoyable introduction to number theory
I very much enjoyed this book.The book is indeed an excellent and "friendly" introduction to number theory.Dr. Silverman writes in a conversation style.I felt like I had a friendly tutor standing over my shoulder explaining not only how the mathematics worked, but, more importantly, why the topics he described or was about to describe are important and their relevancy in either the world of mathematics or in the "real" world.While he has very few "formal" proofs compared to most number theory texts, Dr. Silverman thoroughly works through numerous numerical examples to give the reader a "feel" for what is going on.Read more

Subjects:  1. Advanced    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Textbooks    6. Theory Of Numbers    7. Mathematics / Advanced   

Subjects:  1. General    2. Geometry - Algebraic    3. Mathematical Physics    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. Mathematics / Geometry / Algebraic    8. Mathematics and Science   

Reviews (2)

Basic reference on partitions and q-series
This is *the* classic and most essential reference on the theory ofpartitions and related q-series written by the leading authority on thesubject. It requires almost no technical prerequisites, starts fromscratch, and proceeds in a very clear and orderly manner towards some ofthe more elaborate aspects of the subject. If you (plan to) work on thissubject, buy it. A Classic
This is the bible for the theory of partitions ... Read more

Subjects:  1. Algebra - General    2. Combinatorial Analysis    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Theory Of Numbers    7. Analytic number theory    8. Mathematics / Probability   

Subjects:  1. Mathematics    2. Probabilities    3. Probability & Statistics - General    4. Science/Mathematics    5. Mathematics / Number Theory    6. Probability & statistics   

Reviews (1)

The book on lattice
This book is devoted to the subject of lattice packings. It is an outstanding book with all pages interesting. It acts as a reference on the subjects of lattices. What you will find:Read more

Subjects:  1. Algebra - General    2. Combinatorics    3. Finite groups    4. Lattice Theory    5. Mathematics    6. Number Theory    7. Science/Mathematics    8. Sphere packings    9. Chemistry    10. Combinatorics & graph theory    11. Mathematics / Group Theory    12. Mathematics for scientists & engineers   

Reviews (1)

Number Theory
There has never been in any time a book in any language that can put on a par with Hasse's monumental refrence Number theory . It is a text as well as a great refrence, and it is sad that those people at springer verlag not just printed on a low quality papers, they put it altogether out of print. ... Read more

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Theory Of Numbers    5. Mathematics / Number Theory    6. arithmetic    7. quadratic forms    8. valuation theory   

Reviews (1)

Desparte For a Good Explanation
As a lazy undergraduate studying Number Theory, I found this book to come up with not just solutionsbut good ideas and easy to understand explanations.Worth buying! ... Read more

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

Subjects:  1. Algebra - Linear    2. Computer Books: General    3. Computer Science    4. Computers    5. Mathematical Analysis    6. Mathematics    7. Number Theory    8. Mathematics / Number Theory   

Subjects:  1. Geometry - General    2. Intersection homology theory    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Algebraic topology    7. Mathematics / Geometry / General   

Subjects:  1. Combinatorics    2. Graph Theory    3. Graphic Methods    4. Group Theory    5. Mathematics    6. Number Theory    7. Science/Mathematics    8. Theory Of Numbers    9. Combinatorics & graph theory    10. Groups & group theory    11. Mathematics / Number Theory   

Reviews (5)

gives an appreciation of key contributors
A book that gives you historical perspective on several key mathematicians. It shows the development of number theory, and its intersection with other branches of maths. For example, Gauss made discoveries about the composition of forms. It predates by about a century the understanding of groups. Yet the text shows that Gauss clearly had many of the concepts understood, and with this, he was able to greatly expand algebraic number theory.
A skillful blend of history and solid number theory
A clearly written book that covers number theory at a graduate or advanced undergraduate level. Covers much of the material in Gauss's Disquisitiones, but without all the detail. The book covers elementary number theory, binary quadratic forms, cyclotomy, Gaussian integers, quadratic fields, ideals, algebraic curves, rational points on elliptic curves, geometry of numbers, and introduces p-adic numbers. Only a slight bit of analytic number theory is covered. A good book in my opinion to start learning algebraic number theory. Wonderfully fills the otherwise troublesome gap between undergraduate number theory and overly abstract graduate level algebraic number theory. A superbly presented work of impressive scholarship
The Queen Of Mathematics: A Historically Motivated Guide To Number Theory by Jay R. Goldman (School of Mathematics, University of Minnesota) is a college-level mathematical text that scrutinizes number theory as it was developed through the 17th, 18th, and 19th centuries. The notable contributions of Fermat, Euler, Lagrange, Legendre, Hilbert are meticulously examined are studied and dissected in a pedagogical manner, along with an especial emphasis on the work by Gauss. A superb combination historical narrative and introductory mathematic text, The Queen Of Mathematics is a superbly presented work of impressive scholarship as well as a seminal contribution to the history of the Science of Mathematics academic reference collections and reading lists. ... Read more

Subjects:  1. History & Philosophy    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Theory Of Numbers    6. Algebra    7. History of science   

Subjects:  1. Applied    2. Approximation theory    3. Mathematics    4. Number Theory    5. Numerical analysis    6. Science/Mathematics    7. Algebra    8. Mathematics / Mathematical Analysis   

Reviews (12)

Pleasant introduction to cryptography
Chapters 1 and 2 give some elementary background material on number theory and finite fields. Chapter 3 discusses some old and naive cryptosystems. Chapter 4 discusses public key cryptosystems. In the RSA system, the receiver chooses two large primes p,q and makes public their product pq=n and some integer e relatively prime to phi(n). The sender then sends his message to the power e reduced mod n. To invert this operation one must know phi(n), i.e. one must know the factorisation n=pq. Since factoring big numbers is hard, only the intended receiver will be able to decipher the message instantly. RSA thus uses the fact that multiplying is easy but inverting it is hard; similarly, one can employ other such "trapdoor functions", such as exponentiation in Z/nZ, to create other public key cryptosystems. In chapter 5 we look at various algorithms and tricks for factorisation and primality testing. As for the cryptosystems, classical number theory that is hundreds of years old still provides the best tools (modulo arithmetic, quadratic residues, continued fractions, etc.), and in chapter 6 we see how another classical theory--elliptic curves--also proves to be fruitful in cryptography. The points of an elliptic curve over a finite field form a finite group, which we can use as the basis for new cryptosystems, analogous to how we made cryptosystems out of Z/nZ for instance. And starting with an integer and constructing corresponding finite field elliptic curves we can employ these groups and elliptic curve techniques to give improved algorithms for primality testing and factorisation.

Outstanding presentations
This book is an outstanding introduction to cryptographic techniques and algorithms Although it's labelled as a "graduate text in mathematics", most of it should be accessible to anyone who knows a little linear algebra. For readers just interested in the how-to of the algorithms, not even that is needed. Koblitz does a thorough job of leading up to each algorithm and proving its formal properties. He also presents the algorithms themselves, unencumbered by denser material of interest to mathematicians. Excellent book for self study
This is an excellent book fot those, who are interested in the theoretical background of cryptography. It was also my first book in number theory, and I had no trouble following most of the text ( except the chapter on Elliptic curves, which -as I realize now- IS difficult)Read more

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

Subjects:  1. Exponential sums    2. Forms, Modular    3. General    4. Integrals    5. Mathematics    6. Number Theory    7. Science/Mathematics    8. Technology    9. Mathematics / Number Theory    10. Mathematics and Science    11. Technology, Engineering, Agriculture, Veterinary Science   

Subjects:  1. Algebra    2. Functions, Zeta    3. Mathematical Analysis    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. p-adic analysis    8. p-adic numbers    9. Algebraic number theory    10. Analysis    11. Functions    12. Mathematics / Number Theory    13. Mathematics-Mathematical Analysis    14. Numbers    15. Zetafunktion    16. p-adische Analysis    17. p-adische Zahl   

Reviews (1)

definitive book on number theory - now in English
For mathematicians who specialise in number theory, there is one universally recognised benchmark. Landau's monumental Elementare Zahlentheorie. Written decades ago, it is still regarded as the definitive text. The only problem is that it is in German. So if you do not know German, you're out of luck.
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Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics   

Reviews (5)

Declaration of love for numbers
The least you can say about Number 9 is that it is a remarkable book for many reasons. Not a lot of non-fiction books have the guts to address mathematics in such a personal way. The author Cecil Balmond even creates the character of Enjil to accompany the reader during his search for the truth behind the number 9. The claim of the author that it reads as detective story is certainly true for the first half the book. But be warned, you will not get a definite answer to the questions posed. Although more than once the author claims that the riddles have been solved, she does not seem to be aware that her so called solution is actually a redefinition of the same questions. But then again, you can ask yourself if a real solution would have fitted together with the magical atmosphere nourished by this book. How to read this book
I would just like to respond to Flavio's review. As a physicist, I drew the same kinds of mathematical conclusions he did when he read the book. I do not, however, feel that this is the point. Whether 9 comes out in the decimal system or 7 comes out in the octal system is irrelevant. "No 9" remains a beautifully written piece of literature that expresses author's fascination with numbers and geometry. Sure, you can find rigourous mathematical proofs why '9' must come out. I have worked it out myself, and I don't disagree. However, there are many scientific phenomena (rainbows, fractals etc.) that are no less beautiful despite being taken apart, analysed, and understood. Brilliant
It captured the spiritual as well as the mathematical. A wonderful little read - for those who have an interest in what lies beyond numbers. A most unusual, charming book.Would certainly recommend it. ... Read more

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Theory Of Numbers    5. Applied mathematics    6. Architecture    7. Philosophy of mathematics    8. Structural engineering    9. Numerology    10. Philosophy   

Subjects:  1. Advanced    2. Algebra - Abstract    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Theory Of Numbers    7. Algebraic number theory    8. Mathematics / Advanced   

Reviews (4)

If you actually like number theory...
...stay away from this book.This book was required for an upper-division number theory course I took, and the teacher used it for one of our eight assignments.I assume he did this because there are few worthwhile problems in the book.The author spends too much time explaining the history behind the theorems and too little time discussing applications.He proves the theorems but the proofs make no sense to someone learning just from the book.The teacher for my course explained all of the theorems in ways that actually made sense and were easily reproducable.When studying I never looked at this book and instead used Nathanson's GTM for number theory.If you only care about the history of number theory, this book has some redeeming quality.Otherwise, stay away.Dover math books tend to be inferior to texts like UTMs and GTMs, as evidenced by the latter costing literally ten times as much sometimes.

Good for self teaching
I am currently working through this book, and I really like the format, which is usually a small, digestible chapter followed by a set of exercises (usually 10 or so).Quite a wide variety of topics are covered including congruences, primitive roots, analysis of the number theoretic functions (e.g., the number of primes below x), and a little on diophantine approximations and continued fractions.Nothing post-calculus is used in the book except for some algebraic structures such as fields and rings, however, they are fully explained at the beginning of the book.(And some previous acquaintance with these would probably be good.)The exercises are especially good, being not too easy and not too hard.In response to the review below, to actually understand math like this you must be willing to do some work yourself.If you are looking to sit back in your easy chair and be entertained, then you should buy a book on the history of number theory, not a textbook.

Deceptive Title
No concept is beyond the reach of an intelligent mind, so long as that concept is brilliantly explained.If there were a race for explanatory brilliance, this book would fall somewhere short of the starting line.Forexample, an appendix lists 58 mathematical symbols, (most of which youwon't encounter in high school).These symbols are blithely usedthroughout the text, yet none is adequately explained.If you don't havecalculus, statistics, trigonometry and a few other disciplines alreadyfirmly under your belt, forget this text.Of interest to all readers maybe the occasional insets giving concise biographies of importantmathematicians. ... Read more

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