Subjects:  1. Algebra - General    2. Algebra, Homological    3. Algebraic Number Theory    4. Galois theory    5. Geometry - Algebraic    6. Homology Theory    7. Mathematics    8. Number Theory    9. Science/Mathematics    10. Algebra    11. Analytic number theory    12. Mathematics / Algebra / General    13. algebraic geometry    14. group theory   

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

Subjects:  1. Arithmetic    2. General    3. History & Philosophy    4. Logic    5. Mathematics    6. Number concept    7. Philosophy    8. Science/Mathematics    9. Mathematics / Number Theory    10. Mathematics-History & Philosophy    11. Number theory    12. Philosophy / Logic   

Reviews (2)

"No"-cohomology number theory par excellence
This is a truly original book by a giant of mathematics.
A warning to beginners
Experts find this a very good book, and I rate it on their advice. But others need to understand that Weil is making a bit of a joke with the title. This book is "basic" in the sense that it proves the theorems that Weil feels organize and clarify all of number theory--the "basic" theorems in that sense. It is an introduction to class field theory. Read more

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Class field theory    5. Mathematics / Number Theory   

Subjects:  1. Algebra - General    2. Finite Groups    3. Group Theory    4. Homology Theory    5. Mathematics    6. Number Theory    7. Science/Mathematics    8. Topology - General    9. Algebraic topology    10. Mathematics / Algebra / General    11. Representations of groups   

Editorial Review

The seemingly impossible Zen task--writing a book about nothing--has a loophole: people have been chatting, learning, and even fighting about nothing for millennia. Read more

Reviews (102)

The universe begins and ends with zero
Zero: The Biography of a Dangerous Idea is a tour of the historical advances that were made in mathematics and science due to the use or misuse of the dual ocncepts of Zero and Infinity. The author tours throught the ages as he traces the path that humankind has taken with this concept and its implications.
Eye-opening and fun
This was a great book.I took it on a trip, and it provided sufficient reading for a couple plane trips and a couple boring nights.Though written by a mathematician, it's appropriate for nearly any audience, and I've had no trouble passing it off to friends who aren't engineers.
Zero and I
Zero is the most interesting book I have ever read. It ponders the existence of infinitely small amounts of everything as well as infinitely large amounts. Everything can be divided into an infinite amount of pieces, but although the size of the pieces decreases as the amount of pieces increases, the sizes will always approach zero, but never hit it. How can zero exist as a number then? Zero began as a place holder in Babylonian and Mayan societies. It was accepted as a place holder in some societies, while rejected in others. Zero does not conform to the laws of mathematics, and therefore became a difficult concept to accept. Since it did not fit in with laws, it could destroy all logic. Charles Seife wrote this "biography" as a result of his love of math and science, and his desire to inflict logic upon others. While this book provides for interesting intellectual insight into the history of math and the importance of logic, it also offers the reader a feeling of relative size, both massive and miniscule, in comparison to the rest of the world. ... Read more

Subjects:  1. Arithmetic    2. History & Philosophy    3. Mathematics    4. Number Theory    5. Philosophy & Social Aspects    6. Science/Mathematics    7. Theory Of Numbers    8. Zero (The number)    9. History / General    10. Popular science   

Reviews (4)

Searching for the book vs. the disk?
The Encyclopedia of Integer Sequences is available in three formats.Sellers often incorrectly match the ISBN to the format.It may be helpful to know the ISBN, rather than to rely on the results of a search by Title/Author. This is a data disk, not the book
This product is not the Encyclopedia of Integer Sequences as it is portrayed here on Amazon; it is instead an almost useless data disk.The integer sequences are there all right, in lexicograhic order;but they are completely unidentified (except for a code number keyed to the book)!In other words, without the book this very expensive diskette is useless. My God!
Since combinatorics is my major, this book fulfills my dream. It contains over 5000 sequences, from famous Fibonacci to notorious 1,3,6,11,17,25,... (Perfect ruler,general term still unknown ), to nonsense1,11,21,1211,111221,..(every term describe the former term). Nearly everyimportant integer sequence in mathematics get a line here, with references.This is a dream book for combinatorics specialists, a must for high-schoolteachers while doing some short essays with gifted students, a fun book formathematics fans, especially those like mathematical games. ... Read more

Subjects:  1. Algebraic Number Theory    2. Computer Science    3. Differential Equations    4. Mathematics    5. Number Systems    6. Number Theory    7. Numbers, Natural    8. Science/Mathematics    9. Sequences (Mathematics)    10. Applied mathematics    11. Mathematics / Differential Equations    12. Probability & statistics    13. Reference works   

Subjects:  1. Mathematics    2. Mathematics / Number Theory   

Reviews (2)

An excursion into the labyrinths carved by numbers
Number theory is the most enigmatic of disciplines, in that the problems are so easy to state and understand and yet so hard to resolve. Furthermore, when solved, the proofs are sometimes surprisingly easy. Inthis collection, Guy has put together a truly fascinating survey of what iscurrently (un)known about numbers. Outstanding source of intersting problems in number theory
Another of my 10 favorite books.A constant source of inspiration ... Read more

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

Subjects:  1. Mathematics    2. Number Theory   

Subjects:  1. Calculus    2. Congresses    3. Differential Equations    4. Ergodic theory    5. Geometric group theory    6. Geometry    7. Geometry - General    8. Integral Calculus    9. Mathematics    10. Number Theory    11. Rigidity (Geometry)    12. Science/Mathematics    13. Mathematics / Geometry / General    14. Rigidity theory    15. dynamical systems   

Reviews (4)

The unity of math!
The popular press leaves us with the impression that math is Makes the others Look bad
I got this book as a gift from a long time friend. He had trouble with reading it. It is only for that reason I give it only 4 stars. These authors make others that I have read on this range of subjects look bad: Fields Medalists included! A lot of it is that they just bother to give you the real mathematics with examples. I think the initial miss definition of the Riemann surface gives a false impression, because the explanations of ramified covers and toral elliptic lattices is just wonderful. Reading this book makes Dr. Singerman'spapers look so much better! I was disappointed in the treatment of triangle groups, but the treatment of modular functions and gamma1 and gamma2 makes up for that. It is a masterful work... the best I have seen by a modern author.It reminds me of books by Ulam or Russell. Sawyer's little book is not as good!

long on content, short on abstract nonsense
This is a great book because it presents some of the neatest topics in mathematics, without the usual discouraging layers of abstraction and notation.It attacks the topics historically so you get some idea of the motivation and steps followed, instead of a compendium of the most general results and their most elegant proofs.Read more

Subjects:  1. Functional Analysis    2. Geometry - Algebraic    3. History & Philosophy    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. Algebraic geometry    8. Calculus & mathematical analysis    9. Curves, Elliptic    10. Mathematics / Applied   

Subjects:  1. Algebra - General    2. Group Theory    3. Homology Theory    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. Theory Of Groups    8. Topology - General    9. Algebra    10. Algebraic topology    11. Mathematics / Algebra / General   

Reviews (24)

Comment
great to have new view of the world we live in - very refreshing. Author does blow his own trumpet a lot, but then it looks like he has good reason to. Now if I could only find a practical application of this knowledge in my every day life.... I guess I'll just have to be satisfied with feeling and knowing there is a cosmic order to everything.

No Science but Fiction
The book is written by a scientist (that's at least what Peter Plichta claims), but the contents have nothing to do with science. Plichta presents an explanation of phenomena in nature (especially in physics and chemistry, for instance the remarkable absence of stable isotopes of the elements 43 and 61), but he does not prove his theories. On the contrary, his theories appear to be forced together like pieces of a jigsaw that do not really fit. The "fantastic discovery" of the prime-number-cross by Plichta is not worth the attention it gets. The beams of the cross consist of the numbers (6*n + 1) and (6*n + 5). It is easy to see that numbers not divisible by 2 and 3 are of the form (6*n + 1) or (6*n + 5), since (6*n) is divisible by 2 and 3, (6*n + 2) and (6*n + 4) are divisible by 2 and (6*n + 3) is divisible by 3. What remains is (6*n + 1) and (6*n + 5). Since there are primes not of the form (6*n + 1) or (6*n + 5), namely 2 and 3, and since there are numbers (6*n + 1) and (6*n + 5) that are not prime, namely 25 and 35 (and many more...), there is obviously only a weak relation between prime numbers and the numbers (6*n + 1) and (6*n + 5). The prime-number-cross in fact makes non-divisibility by 2 and 3 the most important property of prime numbers, which is a serious misjudgement of the prime number concept. Also the fact that squares of primes are always of the form (24*n + 1) is in reality a property of numbers (6*n + 1) and (6*n + 5), as can be seen easily by writing out the products (6*n + 1)*(6*n + 1) and (6*n + 5)*(6*n + 5). It will be no surprise that 2*2 and 3*3 are not of the form (24*n + 1).
Peter Plitchta is a rare mind of the highest order!
Other reviews did not mention he discovered 2 elements previously unknown on the periodic table! Also he has a patent on a type of fuel created from a gas from one of the unknown elements! This is revolutionary enough, anyone who can discover things like this is worth listening to, there is no question Peter Plicha is a genius and is far above most scientists and mathematicians. ... Read more

Subjects:  1. General    2. New Age / Parapsychology    3. Philosophy & Social Aspects    4. Science    5. Science/Mathematics    6. Cosmology & the universe    7. Number theory   

Reviews (2)

Good Introduction to Key Topics and Proofs of Number Theory
William J. LeVeque's short book (120 pages), Elementary Theory of Numbers, is quite satisfactory as a self-tutorial text. It should appeal to math majors new to number theory as well as others that enjoy studying mathematics.
Contents of this Book
1. Introduction 2. The Euclidean Algorithm and Its Consequences 3. Congruences 4. The Powers of an Integer Modulo "m" 5. Continued fractions 6. The Gaussian Integers 7. Diophantine EquationsRead more

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

Reviews (1)

Gauss and then some
Dirichlet is all about quadratic forms. But first there are three preliminary chapters on the tools we will need: unique factorisation, modulo arithmetic, quadratic reciprocity. Then in chapter 4 we get to the quadratic forms, ax^2+2bxy+cy^2. "The whole theory originates in the problem of deciding whether a given number is representable by a given form" (p. 92). (Remember, for example, that Fermat solved the case a=1, b=0, c=1 -- which integers are sums of two squares?) "The number b^2-ac, on which the properties of the form mainly depend, is called the determinant of the form", and two forms are equivalent (represent the same numbers) when one results from the other by applying a variable transformation matrix of determinant 1. And now the problem above reduces to "the two main problems in the theory of equivalence: I. To decide whether two given forms of the same determinant are equivalent. II. To find all substitutions that send one of two equivalent form to the other." (p. 100). We spend the rest of the chapter solving there two problems for any determinant D, and we work out the applications in the cases D=-1,-2,-3,-5 (which includes the theorem of Fermat above). In the cases D=-3,-5 representations are not generally unique (which we secretly think of as the manifestation of the loss of unique factorisation in Z[sqrt(-3)] and Z[sqrt(-5)]) and this goes hand in hand with the fact that the number of equivalence classes (the "class number") of forms in those cases is 2, not 1. Such matters are the motivation for Dirichlet's great contribution: the determination of the class number for any D (chapter 5). Apart from this motivation of measuring "how far quadratic integers deviate from unique prime factorisation", as Stillwell puts it (p. xvii), Dirichlet also assigns his solution of the class number problem great intrinsic beauty: "This problem is the last and most important solved in this book, and is connected with the most beautiful algebraic and analytic investigations of this century" (p. 100).
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Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Theory Of Numbers   

Reviews (1)

a rare book
The book get a very clear view about the trigonometrical sums in number theory and it's not so easy to find a work like this in the specialized literature.By the way it is a work of "first hand" that means that the author is one of the most important theorist in this field and much of the topics are originals.Last but not least the price is very very good. ... Read more

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

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

Reviews (1)

A first class job, just as in the first volume
The author continues his excellent overview of computational number theory in this book. And, as in the first volume, the writing is first-rate and gives the reader a comprehensive overview of the more advanced algorithms in the subject. Contrary to the first volume, I have not used many of the algorithms in this book and cannot attest to their quality, but the author gives the detailed background on each of them, enhancing their credibility. I read this book mostly to gain more insight into algebraic geometry and its connection with coding theory and cryptography. The following algorithms were ones that I found helpful and interesting but only a few of which I coded myself: (1) The algorithm for generating a random element from an ideal. (2) The compositum of two number fields (3) Valuation of a prime ideal. (4)Ideal factorization. (5)Smith normal form for finite groups. (6) Quotient of groups. (7) Group extensions. (8) Right four-term exact sequences. (9) Image and inverse image of a subgroup. (10)Subgroups with prime index. (11) Solving linear systems in integers. (12) Algorithms involving p-adic logarithms. (13) Computation of the Dedekind eta-function. (14) Unramified Abelian extensions using complex multiplication. (15) Computation of quasi-periods for elliptic functions. (16) Computation of the sigma-function for an elliptic curve. ... Read more

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

Subjects:  1. Geometry - Differential    2. Group Theory    3. Harmonic analysis    4. Lie groups    5. Linear topological spaces    6. Mathematical Analysis    7. Mathematics    8. Number Theory    9. Science/Mathematics    10. Symmetric spaces    11. Linear algebra    12. Mathematics / Group Theory