Reviews (6)

A well defended postion, but perhaps a bit too defensive
I was at one time a research scientist, but not a physicist. I took a year of Quantum Mechanics, but certainly don't regard myself as very knowledgeable in this area or mathematics. Therefore, this review is coming from a space of being an educated layperson with a broad background and open mind. I think this is important to know before you read more of my review.
not trivial, not definitive
First some background.I am not a physicist or involved in this field in any way so my review is aimed at the amateur who wants to know about the state of affairs in physics and specifically string theory.
A timely and honest critique
I've been following the arguments made by Peter Woit against String Theory for quite some time, and it's a pleasure to be able to have them all in a single volume. His arguments are very persuasive, and his writing clear and to the point. This, however, is not a book that the general audience will find easy to follow. The earlier chapters recount the canonical story of the success of the particlephysics in the 20th century, and if you are familiar with that story you can safely skip these chapters. The later chapters are the really interesting ones, but unless you have at least some familiarity with theoretical particle physics and the modern mathematics, you might find yourself lost. Even with that caveat it is still possible to appreciate the central theme of this book: theoretical particle physics took a wrong turn somewhere in the late 70s and the early 80s, and has never been able to recover from this. Woit is appealing in this book to the practitioners in the field to be more honest with their assessments of the direction in which the theoretical particle physics is headed, and the lack of any meaningful progress.
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Subjects:  1. General    2. Mathematics    3. Number Theory    4. Physics    5. Pop Arts / Pop Culture    6. Popular Culture - General    7. Quantum Theory    8. Science    9. Science/Mathematics    10. String models    11. Supersymmetry    12. Symmetry (Physics)    13. Particle & high-energy physics    14. Popular science   

Editorial Review

This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity. The authors present the theory in a concise and straightforward manner, with an eye out for the practical applications. Exercises at the end of each chapter, including some that have been solved, help readers confirm and enhance their understanding of the material. This book is appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments. ... Read more

Reviews (31)

Need some challenge? Come here!
I started to learn this course at the beginning of this semester and I just brought this book from Amazon in August.
first edition is a classic, the second one unremarkable
The first edition is one of the best book in its field. A classic. A reference for many advanced courses in computer theory. Excellent introductory text, but has several weaknesses
This was my textbook for an introductory course on Finite Automata and Languages - I enjoyed it a lot and I think that the chapters until the Turing Machines are covered very well, along with good examples. As one previous reviewer has already mentioned, the exercises can get very hard as compared to what's actually presented - this I found not too good.Read more

Subjects:  1. Computational complexity    2. Computer Science    3. Formal languages    4. Logic    5. Machine theory    6. Mathematics    7. Number Theory    8. Science/Mathematics    9. Artificial intelligence    10. Computers / Computer Science    11. General Theory of Computing    12. Programming languages   

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

Reviews (2)

Another fabulous book from Paul Nahin
Here is a book that is a delight to read.It is well-written and the text flows marvelously between each page and around the many formulas that are so carefully presented and worked out.I rate this book as 5-stars for presenting ever more mathematics relating to complex numbers in a clear and detailed manner.
Sequel to An Imaginary Tale
The reviews of An Imaginary Tale capture much of what will be said of Dr. Euler's Fabulous Formula. I happen to like Paul Nahin's books very much ever since reading The Science of Radio, one of my favorite books of all time. If you didn't like Imaginary, you won't like Dr. Euler's . If you like the earlier book, this one is a must.
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Subjects:  1. Euler's numbers    2. History    3. History & Philosophy    4. Mathematical Analysis    5. Mathematics    6. Number Theory    7. Numbers, Complex    8. Science/Mathematics    9. History of Science and Medicine, Philosophy of Science    10. History of mathematics    11. Mathematics / History    12. Popular science   

Reviews (10)

Proofs from the Book
The famous eccentric mathematician had a theory that God (who he liked to call the SF-Supreme Fascist) had a book with every mathematical theorem and that the book had the most beautiful and elegant proofs for the theorems.
belong's on any math lover's bookshelf
It is a pleasure to explore these polished gems, some prettier than others but all worth looking at. I find it worth having within reach and reading a theorem and proof now and again for the sheer joy of (re)discovery.

A unique compendium of sublime results.
The book presents its proofs clearly. What is contained in this book is so sublime that you'll keep on returning to it.
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Subjects:  1. Advanced    2. General    3. Mathematical Analysis    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. Mathematics / General    8. analysis    9. combinatorics    10. geometry    11. proofs   

Subjects:  1. Computer Science    2. General    3. Mathematics    4. Number Theory    5. Numerical Analysis    6. Science/Mathematics    7. Computers / Computer Science   

Reviews (2)

Excellent book for beginning courses
This book is ideal for an undergraduate course in number theory. The combination of theory, problems and biographical sketches of the principals who made it what it is today is an excellent pedagogical technique. It allows an instructor to show how number theory began very early in mathematical history and how it has progressed over the centuries. Number theory holds the distinction as being the reservoir of most of the easily stated yet difficult problems. As Paul Erd�s said, "If it is a simply stated problem that has remained unsolved for centuries, it is almost certainly one in number theory." In this book, you learn the reasons for this situation. The best Elementary Number Theory textbook for students
I recommend it for all College and University students taking number theory classes.Read more

Subjects:  1. Applied    2. General    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Mathematical theory of computation    7. Mathematics / Number Theory   

Reviews (7)

Excellent introduction to a vast, fascinating subject
This book is awesome. Tons of material covered, but at a decent pace and with good examples. All the reader needs is a good working knowledge of how to read and construct proofs, and the time and patience to get through the material. The exercises range from the computational to the theoretical, from the routine to the extremely challenging. Many of the examples and exercises are intriguing, well-known results. The author touches on a large amount of subject matter and has many references for those interested in further reading. He makes no use of any of the methods that come from the main branches of Mathematics, namely Algebra, Analysis, etc. (though he mentions a few famous results), but he also mentions that he will not be using these methods in the beginning. It starts off a bit easy but gets moderately challenging. This book will never leave my shelf, and has sparked an interest inside of me that shows no signs of burning out. Again, an excellent book.

Good foundational text for Cryptography
I bought this book as a supplemental study guide - my course was a mix of Number Theory, Abstact Algebra, Finite Fields and Probablility (pre-requisites for Cryptography study).The professor used lectures with hand-written supplements as primary study media.
Very helpful resource
I'm currently taking a Discrete Mathematics class that is a stew of number theory, abstract algebra and probability.
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Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Mathematics / Advanced   

Reviews (7)

Short and to the point
This book is excellent! It chapters are broken down into short sections and the content in each section is to the point! I also bought the book Proofs and Fundamentals by Ethan D. Bloch but found it to be long and drawn out. If you liked The Nuts and Bolts of Proofs by Antonella Cupillari then this book is for you!

Very well written book
I have a mathematics degree. Like most math majors, I struggled with proofs all through college. This book really has help me understand the art of writing proofs. The book is very well written and easy to read. This is just an awesome book!!!

Now I know how beautiful proofs can be
This book provides a nice introduction to mathematical reasoning and proofs. My intention on purchasing this book was to learn how to perform mathematical proofs. I believe it has achieved that purpose. The text is easy to follow and the author presents the work clearly. ... Read more

Subjects:  1. Logic    2. Mathematics    3. Number Systems    4. Number Theory    5. Proof theory    6. Science/Mathematics    7. Set Theory    8. Mathematical foundations    9. Mathematics / Combinatorics   

Reviews (4)

Superb
In both the physics and mathematics community something very exciting is happening. Highly competent physicists and mathematicians have for the last six or seven years been writing books that give deep insight into the concepts and intuition behind their specialties. A voluminous literature of course exists that is written for the specialist in the field of relevance, and these are written in a high-level, formal style, and no motivation, either historically or technically is given. Those interested in entering the field will have to rely on getting verbal explanations from the researchers themselves, which may be difficult if they are not close to them in a geographical sense. This is also another reminder that there is definitely an oral tradition in mathematics, and experts it seems are reluctant to explain themselves to newcomers. Physicists in particular are particularly sensitive to this state of affairs. They need to not only understand a large amount of material in physics, but they require deep insight into the mathematical tools that must be used to formulate their theories, and this insight must be obtained rather quickly. They do not have time to wait until the mathematical concepts "come to them."
A good solid book
This is exactly the kind of book which introduces enough mathematics in order to present a good overview for a start but which does not overload you with too many details.

Very highly recommended
This is one of the finest books that lucidly and simply explain very complex concepts and terms in number theory, group theory and abstract algebra to anyone with reasonable mathematical maturity -- Easy to read, self contained and all topics are developed in simple illustrative manner without requiring dry proofs without sacrificing rigor.
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Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. History of Science and Medicine, Philosophy of Science    5. Mathematics / Number Theory    6. Physics    7. Popular science   

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

Editorial Review

At the very beginning of his book on Read more

Reviews (36)

packed with math andworth the effort
There is a lot to be learned from An Imaginary Tale.However, it will take some effort on part of the reader.Overall, I think it is a worthwhile read, but I do have the following criticisms.
the complex clarified
I really enjoyed this book even though it was quite a bit of work for me.I found for a book of this scope, this one takes three to four times longer to read.This is no fault of the author.The text is clear, interesting and very informative.Equations are typeset in a format suited to algebraic equations in contrast to some similar books where equations are embedded in sentences.The reason for the long read time is the amount of material presented in a condensed format.Literature teachers would appreciate the economy of it all.The intermediate steps left out of some proofs are to be either trusted or calculated by the reader.To truly experience this history and gain an appreciation of the math skills, one should work through these steps.
Good Work!
I just finished reading this book. The writer has used a very gripping approach to explain the evolution of the idea of complex numbers. However, at some points, the book does get involved too much into mathematicas and loses its historical touch. I would say it is 70-% history and 30% Maths.
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Subjects:  1. History & Philosophy    2. Mathematical Analysis    3. Mathematics    4. Number Theory    5. Numbers, Complex    6. Science/Mathematics    7. Theory Of Numbers    8. Applied mathematics    9. History of Science and Medicine, Philosophy of Science    10. History of science    11. Mathematics / History   

Reviews (4)

good book
This book (5th edition) cover the topics of undergraduate number theory well. The chapters are - Comprehensive
This is a fantastic book on number theory. It covers far more ground than most introductory text (comparable to Hardy and Wright in depth with much less concern for the big O). It covers material usually only available in separate texts: Rational points on elliptic curves, the partition function, and Dirchlet series.Quite readable chapters, well motivated theoretically, although the historic motivation for the subject matter comes largely in the end-of-the-chapter notes.It's an excellent refresher and reference for non-specialist who find themselves using an algorithm or formula they've forgotten(number theory now playing a role in physics and CS, like never before). It is well cross-referenced with regards to methods of proofs the can be accomplished in different section by different methods - this again making it an excellent reference. The best intro to the subject!
I have started my studies in Number Theory reading this book from thepreface to the last word. It is amazing! I think it is a betterintroduction to the subject than the classical Hardy and Wright...it is"more objective" and almost 100% elementary...a good high schoolreader could do well with it. The chapter of diophantine equations has somedivine proofs, very clever and very beautiful. And there is an easy proofof the irracionality of Pi. The only negative point is the existence ofsome points where the authors could be less concise and a bit clearer,stating the theorems before giving the demonstrations, instead of saying atthe end of the paragraph "we then have proved the theorem of..."Its a good book for self-study. It has many exercises. ... Read more

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

Reviews (48)

A review of history by a modern day barbarian
I give this book 4 stars because it does give a very good review of the history of Pi from which one can gain an appreciation of the difficulties of the long and sustained effort of man to understand the nature of Pi and its occurance in so many aspects of science and architecture.Mr. Beckmann's frequent side comments on the debilitating effect of Christianity on the development of science and civilization is, however, disturbing to me.It is my belief that that the church Our Lord founded, the Catholic Church, is the fountainhead of civilization.
A History of Pi
I found this book to be estremely interesting.It really opened my eyes to how elusive pi is.Additionally, I found Beckmann's opinions to be very interesting to and hold some real value.I had never thought about the Roman's in the manner that he talked.Upon thinking about it, I believe he has a strong argument.I felt I got a good history of pi and how it has been calculated to more and more decimal places over the centuries.I definitey want to read more on Euler.

Not what I expected
In a book called A History of Pi, I was, perhpas at fault, to expect more than simply a history lesson.As a graduate student in science I was interested in more of a discussion of how pi arises so much in all areas of mathetmatics, especially in areas that seem to have nothing to do with circular geometry.What I did get was a history of mathematics, often biased, especially against the Romans.While interesting, this book was unsatisfying and reminds me of the boring, yet worthwhile history lessons I recieved in high school. ... Read more

Subjects:  1. Algebra    2. History & Philosophy    3. Mathematics    4. Science/Mathematics    5. History of science   

Subjects:  1. Algebra - Linear    2. Diophantine approximation    3. General    4. Linear Algebra    5. Linear algebraic groups    6. Mathematics    7. Number Theory    8. Science/Mathematics    9. Theory Of Numbers    10. Exponential Functions    11. Groups & group theory    12. Mathematics / Number Theory    13. Measures of Independence    14. Simultaneous Diophantine Approximation    15. Trancendental Numbers   

Reviews (10)

The one and only
Typically, a paper which defines a new field of science is not the best introduction to new researchers in the field. This is not the case with The Mathematical Theory of Communication. If you are interested in information theory, this is the one and only place to start.

6 stars. A gem.
This book is the best technical book i've ever read. It's clear, concise and logic. It explains all the fundamentals of communication theory, a basic for telecom and electronic engineers. All technical universities of everywhere must explain their communication theory subject following exactly this text. Above any other technical book. A gem.

The foundation for developments in electronics, telecommunications and computing
The origin of this book lies in the Bell Telephone Laboratories initiative in researching how wireless and telecommunications can be improved. The problem it deals with is a classic one for electronics, telecommunications and computing - noise vs. fidelity of data transmitted. The solution it propounds is simple and yet so revolutionary that it charted the course of these fields since it was published.
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Subjects:  1. Mathematical physics    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Telecommunication    6. Applied mathematics   

Reviews (6)

Introduction to Analytic Number Theory
The reason I bought this book was to understand an elementary proof of the prime number theorem. Actually, it contains only an outline of an elementary proof. But the book introduces methods for the proof with awesome clarity. It must have been much greater if we could see the detailed elementary proof of the prime number theorem written by Apostol. He gives a reference to An Introduction to the Theory of Numbers by G.H. Hardy and E.M. Wright for the detailed proof, but the reader may be required to do unnecessary guessing (which is believed to be good in learning math, but seems to be nothing but trouble for me) to go through it.
Amazing
This book is absolutely incredible.The topics covered range from some very elementary topics on the theory of certain basic arithmetic functions, to much more advanced topics such as the theory of Dirichlet L-Functions.I have never seen a clearer explanation of the characters associated with finite Abelian groups, and the L-functions associated with Dirichlet Characters, than that provided by this book.Apostol makes even the most difficult concepts seem clear and simple.As an added bonus, the end-of-chapter exercises range from moderately difficult to almost excruciatingly so (but still very fun to work on) and give the reader excellent experience in solving problems in this field.With all this said, it should be pointed out that, as another reviewer stated, this book should not be read until the reader has already had a good deal of previous exposure to number theory.I myself would recommend the book of Hardy and Wright.As a second text on number theory, and an introduction to the aspects of number theory related to function theory and analysis, I believe that Apostol's book is the best that anyone could possibly hope for.

Exceptional readability
You normally dont talk so much about readability of a book on Math, but of all the other books on number theory that I've seen, this isquite a page turner. Strikes just the right ballance between theory, proofs and examples. As mentioned somewhere in the book, one of the aims of the author is to arouse reader's interest in number theory..which this book will certainly do..especially since its main emphasis is on prime numbers. ... Read more

Subjects:  1. Arithmetic functions    2. Mathematics    3. Number Theory    4. Numbers, Prime    5. Science/Mathematics    6. Analytic number theory    7. Analytische Zahlentheorie    8. Mathematics / Number Theory   

Reviews (2)

A Human Story
The striking facts about Danzig's book are :
Postmodern mathematics?
Einstein called this "the most interesting book on the evolution of mathematics which has ever fallen into my hands."
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Subjects:  1. Arithmetic    2. General    3. History    4. History & Philosophy    5. History Of Mathematics    6. Mathematics    7. Number Theory    8. Number concept    9. Science    10. Science/Mathematics    11. Theory Of Numbers    12. Mathematics / Number Theory    13. Science / General   

Subjects:  1. Communication    2. Mathematics    3. Methodology    4. Number Theory    5. Reference    6. Research    7. Science/Mathematics    8. Sociology    9. Social Science / Research   

Subjects:  1. Logic    2. Mathematical Analysis    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Mathematics / Number Theory    7. Mathematics and Science