Reviews (2)

Good textbook for graduate and advanced undergraduate course
I read the book and is almost self contained. No knowledge in Number Theory is assumed. Has a great combination of text and math. Last few chapters could have been better.

Assistant Researcher
An excellent book.I am a beginning cryptographer with some statistics, discrete math, user level crypto and programming under my belt - crossing over from another field.This book is an excellent read with proper amounts of examples and theorems.It is easy to follow and would make a good reference. ... Read more

Subjects:  1. Applied    2. Computer security    3. Cryptography    4. Cryptography/Access Control    5. Mathematics    6. Number Theory    7. Science    8. Science/Mathematics    9. Security - General    10. System Theory    11. Theory Of Numbers    12. Calculus & mathematical analysis    13. Data security & data encryption    14. Mathematical foundations    15. Mathematics / Combinatorics   

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

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

Subjects:  1. General    2. Group Theory    3. Mathematics    4. Number Theory    5. Profinite groups    6. Science/Mathematics    7. Theory Of Groups    8. Algebraic number theory    9. Groups & group theory    10. Mathematics / Algebra / General    11. Mathematics | Pure Mathematics   

Subjects:  1. Algebraic Geometry    2. Functional Analysis    3. Geometry - Algebraic    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. Theory Of Functions    8. Mathematics / Number Theory   

Reviews (7)

a really neat book
Everyone has that smart-alex relation who ruins Thanksgiving dinner by proving to every four year old inthe room that they know more about math than they do. There are several waysto deal with such a pain in the posterior but the least likely to involve violence and police intervention is this book. No recreational mathematician should be without it
In the foreword to G.H. Hardy's book A Mathematician's Apology, C.P. Snow tells an anecdote about Hardy and his collaborator Srinavasa Ramanujan. Hardy, perhaps the greatest number theorist of 20th century, took a taxi from London to the hospital at Putney where Ramanujan was dying of tuberculosis, Hardy noticed its number, 1729. Always inept about introducing a conversation, he entered the room where Ramanujan was lying in bed and, with scarcely a hello, blurted out his opinion about the taxi-cab number. It was, he declared, "rather a dull number," adding that he hoped that wasn't a bad omen. "No, Hardy!No, Hardy," said Ramanujan, "it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways." Great for Middle and High School Students
A great supplemental tool for teachers! I had terrific fun with my 6th grade math studentswhen reading them certain passages in this book. Many of the topics covered, such as factorials, hexidecimals, triangularnumbers, pi, primes, etc. are not generally covered in the middle schoolvery well or at all, and this book serves as a great launching tool fordiscussions that kids enjoy and think about long after class is over. Also, many topics go in depth and will challenge even the best high schoolmath students and take them in many directions that traditional matheducation does not. ... Read more

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

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

Reviews (2)

The definitive book on the subject
This book is not absolutely perfect, but it is so much better than any other one on the subject that it deserves a 5-star rating. The majority of books on Fibonacci numbers and the golden ratio fall into three categories: (1) Books for children, (2) Mystical mumbo-jumbo, and (3) Books claiming you can use Fibonacci numbers to win in the stock market (!). Even Mario Livio's book, which is better than most, uses so much of its space to _debunk_ some of the mystical mumbo-jumbo that it de-emphasizes the wonderful patterns that can be found in the Fibonacci sequence, which is beautiful enough in its mathematical properties that one doesn't need to make such digressions. Dunlap's book, by contrast, _does_ emphasize those patterns. And when it's not directly addressing the Fibonacci sequence's properties, it's discussing things like the golden ratio and Penrose tilings, which are completely within the category of mathematics related to the topic.
It's the Beauty of Mathematics
Well, I have studied these numbers and other fascinating phenomena in mathematics, and I never found it enough. So, every book I read about this stuff I found a new set of new things, or at least a new view/review of the old things I knew. After my short study (7 years now) in the field of Number theory and Related topics, I dare say, that this book was another addition to my knowledge that -thanks GOD- I didn't waste. ... Read more

Subjects:  1. Applied Mathematics    2. Fibonacci numbers    3. Geometry    4. Geometry - General    5. Golden section    6. Mathematics    7. Number Theory    8. Science/Mathematics   

Reviews (2)

Charming book, but serious errors
This is a charming book with lots of information (see other reviews) presented in the form of a clever teacher/student dialog. However there are serious mathematical and typographical errors. For example, pi is defined to be "the ratio of the circumference of a circle to its diagonal." Flannery meant diameter; circles don't have diagonals. In another place he interchanges the numbers 48 and 84 to get the incorrect result that 36/48 = 3/7. The problem with these errors is that people read this book to get information, and the information needs to be correct.

Deals much more with mathematical reasoning than the actual number
There have been plenty of mathematics books written about specific numbers, like pi, zero, e, the golden ratio, etc.All of these books typically go into a detailed the history of the number, give examples of where the number shows up, and how work with the number has affected the world.I bought this book because I was expecting it to show the square root of 2 along those same lines.Unfortunately, that wasn't the case at all.
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Subjects:  1. General    2. Mathematics    3. Number Theory    4. Reference    5. Science/Mathematics    6. Science / General   

Reviews (1)

A glorious book
This book is a must have for anybody interested in number theory.It contains a treasure trove of solved and unsolved problems in number theory and records related to them and is highly entertaining. ... Read more

Subjects:  1. Mathematics    2. Number Theory    3. Numbers, Prime    4. Science/Mathematics    5. Theory Of Numbers    6. Combinatorics & graph theory    7. Mathematics / Number Theory   

Reviews (1)

THE BOOK OF PROBLEMS
Polya and Szego's 1923 two volumes of mathematics problems are still the best collections ofproblems for people who want to learn advanced undergraduate and graduate level mathematics.When I want to know something about zeros of polynomials, about inequalities for polynomials ortrigonometric polynomials, or determinants and quadratic forms, the firstplace I look is volume 2 of Polya and Szego.It is a great source ofproblems to give to students if you are a teacher, and the best set ofproblems to work through if you are learning mathematics at the advancedundergraduate level or higher. Volume 2 contains long chapters on complexvariables and number theory and some problems in geometry.Both volumesbelong on a shelf close to the desk of anyone who teaches college levelmathematics.They are also very useful for those who use mathematics.These two volumes are gems, and would be rated above 5 stars if possible. The German original is available here in a nice English translation. Somenew material was added when the translation was first published. ... Read more

Subjects:  1. Calculus    2. Mathematical Analysis    3. Mathematics    4. Problems, exercises, etc    5. Science/Mathematics    6. Calculus & mathematical analysis    7. Geometry    8. Mathematics / Mathematical Analysis    9. Number theory    10. Topology   

Subjects:  1. Algebraic Geometry    2. Fermat numbers    3. General    4. Geometry - Algebraic    5. Geometry - General    6. Mathematics    7. Number Theory    8. Science/Mathematics    9. Theory Of Numbers    10. Algebraic number theory    11. Fermat    12. History of Mathematics    13. Mathematics / Number Theory   

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

Subjects:  1. Calculus    2. Functional Analysis    3. Functions, Zeta    4. Mathematical Analysis    5. Mathematics    6. Number Theory    7. Science/Mathematics    8. Series    9. Theory Of Functions    10. Mathematics / Calculus    11. Mathematics / Number Theory    12. Mathematics-Mathematical Analysis    13. Mathematics-Number Theory   

Reviews (2)

Plain but solid account of all things binomial
Pascal's triangle flirts with the Greek theme of "figurate numbers": the third row are the triangular numbers, the forth row are the pyramidal numbers, and so on for the higher dimensional analogs (chapter 1). But the entries of the triangle, i.e. the binomial coefficients, turn up more naturally in "n choose k"-type combinatorics, ignored by the Greeks but picked up by everyone else: the Indians, the Arabs, the Chinese, and the Renaissance Italians (chapters 2-5). The binomial coefficients have an inherent desire to be tabulated triangularly, and we see several charming variants of this reproduced from original sources. Pascal then put the triangle in its definite form, and provided neat inductive proofs of its marvellous properties (chapters 6-7). The most exciting twist of the story is Newton's discovery of the general binomial expansion, i.e. the expansion of (a+b)^n also for non-integer exponent (chapter 8). Such infinite series are powerful tools in the calculus; indeed, Wallis had already used similar tricks to integrate (1-x^2)^(1/2), yielding his infinite product formula for pi. Meanwhile, the binomial coefficients kept up their combinatorial life (chapters 9-10), especially in the fields favoured by Pascal himself--probability theory and gambling--culminating with Bernoulli's famous Ars Conjectandi.

A world history of the origin of Pascal's triangle
Pascal's famous triangle is much like the Fibonacci numbers, in that there always seems to be room for more properties and uses. With all these possibilities, it is easy to become overwhelmed by all the information about them. In this book, the emphasis is on the original discovery of the triangle rather than the mathematical properties that it has, even though the two are inseparable. Read more

Subjects:  1. Advanced    2. Mathematics    3. Number Theory    4. Pascal's triangle    5. Science/Mathematics    6. History of mathematics    7. Philosophy of mathematics   

Subjects:  1. Advanced    2. Algebra - General    3. Calculus    4. Mathematical Analysis    5. Mathematics    6. Number Theory    7. Representation Of Groups    8. Science/Mathematics    9. Theory Of Functions    10. Automorphic forms    11. Functional analysis    12. Mathematics / Number Theory   

Subjects:  1. Applied    2. Computer science    3. Logic    4. Logic, Symbolic and mathematic    5. Logic, Symbolic and mathematical    6. Mathematical And Symbolic Logic    7. Mathematics    8. Number Theory    9. Science/Mathematics    10. Set Theory    11. Mathematical logic    12. Mathematics / Logic   

Reviews (8)

Full of info
...but poorly written.It's very interesting in a historical sense.For instance, Table 9 shows composite Mersenne's numbers up to n=251, most of them with question marks when a factor wasn't known to be composite or prime, and C when it was known to be composite but the factors weren't known.For instance, 2^101-1 was known to have at least 4 prime factors, but no factors were known.At the time (1964-1966), ENIAC was being used to compute such things.Yesterday, on my lowly Pentium 4, using Mathematica's built-in functions, I factored all the numbers completely in less than 45 minutes of computation time.One of them (2^251-1) took 34 minutes and 7 seconds and another took 5 minutes 10 seconds -- all the rest were very fast.It's amazing how much better the algorithms and computers are, today.

Full of info, but poorly written.
And NOT written in a recreational style, by any means.

Recreational Mathematics Is NotA Contradiction In Terms
If you are curious about numbers (as I am), this is one of several books you need to have in your library. It is informative, entertaining, comprehensive and easy to read, even if you are not blessed with a mathematics degree from an institution of higher learning.Read more

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

Reviews (1)

Don't be foled by the small size of this book
This book, though less than two hundred pages, requires tremendoous knowledge of complex anlysis, number theory, calculus, don't think that this book serve as an introduction to prime number theorem!!!! It is not!!! ... Read more

Subjects:  1. Functions, Zeta    2. Mathematics    3. Number Theory    4. Numbers, Prime    5. Science/Mathematics    6. Theory Of Numbers    7. Analytic number theory    8. Mathematics / Number Theory   

Subjects:  1. Fourier Analysis    2. Mathematical Analysis    3. Mathematics    4. Number Theory    5. Reciprocity theorems    6. Science/Mathematics    7. Theory Of Numbers    8. Algebraic number theory    9. Mathematics / Number Theory