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Critical Acclaim for Pi and the AGM:

"Fortunately we have the Borwein's beautiful book . . . explores in the first five chapters the glorious world so dear to Ramanujan . . . would be a marvelous text book for a graduate course."—Bulletin of the American Mathematical Society

"What am I to say about this quilt of a book? One is reminded of Debussy who, on being asked by his harmony teacher to explain what rules he was following as he improvised at the piano, replied, "Mon plaisir." The authors are cultured mathematicians. They have selected what has amused and intrigued them in the hope that it will do the same for us. Frankly, I cannot think of a more provocative and generous recipe for writing a book . . . (it) is cleanly, even beautifully written, and attractively printed and composed. The book is unique. I cannot think of any other book in print which contains more than a smidgen of the material these authors have included.—SIAM Review

"If this subject begins to sound more interesting than it did in the last newspaper article on 130 million digits of Pi, I have partly succeeded. To succeed completely I will have gotten you interested enough to read the delightful and important book by the Borweins."—American Mathematical Monthly

"The authors are to be commended for their careful presentation of much of the content of Ramanujan's famous paper, 'Modular Equations and Approximations to Pi'. This material has not heretofore appeared in book form. However, more importantly, Ramanujan provided no proofs for many of the claims that he made, and so the authors provided many of the missing details . . . The Borweins, indeed have helped us find the right roads."—Mathematics of Computation ... Read more

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Analyses the foundation of the San-kuo Wei Dynasty by Ts'ao P'I in 220 CE, using the main historical accounts, a wide range of religious and philosophical writings, epigraphical records, and above all, the records contained in the commentaries to Ch'en Shou's San-kuo chih by the fifth century writer P'ei Sung-chih. ... Read more

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This is a mathematics book written specifically for the enjoyment of non-mathematicians and those whohated math in school.The book is organized into two sections: (I) Beauty for the Eye (shallow water for the non-swimmer); and(II) A Feast for the Mind (slowly getting deeper for the more adventurous). ... Read more

Customer Reviews (3)

Excellent, greatly appreciated
Wow! What a great book.

If you have any interest in basic mathematic and would like to find out why pi, e and simple series are related, this is an excellent book to start with. It will give you part of the raw materials needed for your research.

I agree with another reviewer that many proof are not very elegant, but perhaps it is simply because they are none simpler. I don't know the definitive answer to that.

Nevertheless, the way the material is presented makes it very efficient and pleasant to browse.

I am not aware of any similar resource. It's a gem.

Thank you Mr Adrian

Interesting with faults
This book starts off with a collection of formulas that diverge to infinity, then formulas that converge, then formulas involving pi and e. A later section gives proofs of these.
The proofreading of this book must be called to question. On page 21 one of the values we use for pi is given as 335/113. The actual value should be 355/113. This simple mistake makes later information suspect.
The proofs need written explanation to go along with the mathematical explanation. It would have been better to see an explanation that in English says what the steps show.
Also on page 21 the radius is shown by R, rather than r, which is used throughout the United States.
On p.215, the explanation says to mulitply "out the RHS ..." I needed to do a google search to find out that RHS stands for Right Hand Side of the equation.
All in all, the book has some interesting formulas and some good proofs. But the errors that I found, and I am by no means even an amateur mathematician, means that this book has serious lacks.

A disaster: a useless collection of formulae
I was drawn by the title of this book, hoping to see interesting elementary methods applied to the proof and application of pi, e etc.

However, it turned out the author simply collected an almost useless collection of math formulae. The proofs are so flaky they look like a joke. The author states in the beginning that he hopes the book can be of use to high school students or any amateur that are interested in math, but the proofs actually involves derivatives found in analysis, no elegant elementary methods. What a shame!

... Read more

Product Description
Mobile systems, whose components communicate and change their structure, now pervade the informational world and the wider world of which it is a part. The science of mobile systems is as yet immature, however. This book presents the pi-calculus, a theory of mobile systems. The pi-calculus provides a conceptual framework for understanding mobility, and mathematical tools for expressing systems and reasoning about their behaviours. The book serves both as a reference for the theory and as an extended demonstration of how to use pi-calculus to describe systems and analyse their properties. It covers the basic theory of pi-calculus, typed pi-calculi, higher-order processes, the relationship between pi-calculus and lambda-calculus, and applications of pi-calculus to object-oriented design and programming. The book is written at the graduate level, assuming no prior acquaintance with the subject, and is intended for computer scientists interested in mobile systems. ... Read more

Customer Reviews (1)

Difficult reading but worth the effort
It is interesting that the pi-calculus, which on first inspection can be viewed as a highly abstract formalism somewhat removed from reality, has now found application in a variety of fields, such as business process modeling, computational biology, artificial intelligence, and network modeling. It is one of the many examples of process algebra that have appeared in the last two decades, and has been the subject of intense research. This book gives an overview of the formalism of pi-calculus, both in its original form as envisaged by its creator Robin Milner, and from the standpoint of its variations and extensions. For readers (such as this reviewer) who are relatively new to process algebra, the writing may be somewhat difficult to follow, this due mostly to the choice of notation. On the other hand, readers (such as this reviewer) who are familiar with the lambda calculus or functional programming will find familiar territory in the book, and will more fully appreciate the sixth part of the book, which deals with the interpretation of functions as processes. Those readers interested in applications will have to consult other books and papers.

Conceptually the pi-calculus is fairly easy to understand: it is a method of passing values that can respect the local scope. This ability distinguishes it from being merely a value-passing process algebra, which would be helpful in some contexts but not of much use in applications. The authors describe pi-calculus as being a theory of mobile systems, in that one can use it to understand mobility and to study the patterns executed by mobile systems. They distinguish between two kinds of 'mobility', one being that of 'links' that can move in an abstract space of 'linked processes', while the other deals with 'processes' that can move in an abstract space of linked processes. The (first-order) pi-calculus deals with the first kind of mobility, and does this via the manipulation of 'names' and 'processes.' A 'name' in the pi-calculus is the name of a link, and a process can interact with another one via the names that they share. When a particular process receives a name, it can then interact with processes that were unknown to it. The authors do treat the second kind of mobility in the book in the guise of 'higher-order' pi-calculus.

Of particular importance to the pi-calculus is in the binding of names in a process. Remembering the same concepts in mathematical logic, particularly in the lambda calculus, one speaks of the occurrence of name in a process as 'bound' if it lies within the scope of a binding of occurrence of the name; it is 'free' if it is not bound. The interaction of two processes via a name can only occur if that name occurs freely in both of them. But the pi-calculus also has the notion of 'scope extrusion', wherein the scope of a restricted name is extended to include only the process that receives the name. Therefore in the pi-calculus a restricted name can move as long as it is renamed. The ability of the pi-calculus to do scope extrusion has been one of its major selling points.

Processes no matter how they look syntactically may have essentially the same behavior. The pi-calculus has a few notions of behavioural equivalence and these are discussed in great detail by the authors. A process can be classified according to its 'internal' behavior as well as how it is 'observed' to behave. The authors describe, and then reject, the notions of 'reduction bisimilarity'of two processes, for two processes can be related if they have no internal actions. To mend this triviality, the authors introduce a notion of the 'observable' of a process. The observables of a process are viewed as the collection of names that it can use for sending and for receiving. Using the construction of an 'observability predicate', the reduction bisimilarity relation is modified to that of the 'strong barbed bisimilarity' between two processes. The observability predicate is a kind of measure as to whether a process can perform an input or output action. Two processes are 'strong barbed bisimilar' if they have the same observables and to each internal transition of one there is an internal transition of the other to a process that is strong barbed bisimilar. Using an example as motivation, the authors go on to reject strong barbed bisimilarity as being a satisfactory notion of equivalence of processes. This leads them to the notion of 'strong barbed congruence', where two processes are strong barbed congruent if they are strong barbed bisimilar in all contexts.

For this reviewer, who prefers to view all processes as applications of functions, the most interesting part of the book was Part 6, which deals with the relation between the pi-calclulus and the lambda-calculus, the latter of which has resulted in many successful (functional) programming languages. The authors study how functions in the lambda-calculus can be represented as processes in the pi-calculus. Their discussion is very interesting, in that it sheds light on to what extent the lambda-calculus can be used to model concurrency. The lambda-calculus is traditionally been viewed as one that involves only sequential operations, so this discussion may point the way in using it to deal with concurrent processes. One should not expect that both of these calculi are the same in terms of their semantics, and this is born out in the authors' proof that the semantics of the pi-calculus is strictly finer than the operational semantics of the lambda-calculus. The encoding of the lambda-calculus into the pi-calculus also involves some rather interesting mathematical constructions, such as the Levy-Longo and Bohm trees. The authors use these trees to show that the equality induced by the pi-calculus is the same as that induced by certain models of the lambda-calculus. Functions are therefore processes. ... Read more

Product Description
The Pi-Water system is based on harmony with nature. The essence of this technology does not just have biological and hormonic functions. The Pi-Water system also causes changes and reactions in the levels of molecules and atoms, which are the very origin of all substances. These changes indicate that there may be a new scientific technology system represented by Pi-Water opposed to the existing vast scientific technology systm of modern science. ... Read more

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A resource encyclopedia for Researchers, PI's, Spies, andGenerally Nosy People. The ultimate guide for finding information andintelligence on anything. ... Read more

Customer Reviews (5)

About half out of date
The advent of widespread digital devices has rendered much of the information here obsolete. Needs a new revision.

Out of date
Definitely out of date
Published in 1995
Ten pages on the internet today is useless.
Almost all the equipment is out of date.
Did get a couple of usefull ideas thus the 2 star rating

Definitive spy source book
After reading this book, I have no doubt Lee Lapin has the drop on the information gathering business.For those in the business, it is a well rounded guide for data access and equipment useage in conducting investigations.For the novice, it provides great insight and a useful tool for individuals doing their own investigations.A fun to read book cover to cover.I was very pleased with A1 books who sold the used book through the marketplace.The book was in great shape for used and looked brand new!

Interesting stuff. Unfortunately becoming quickly outdated
This book is full of information for those interested in spying, PI'ing and privacy issue buffs. Unfortunately, some if not most, of it's information is over eight years old and in dire need of an update.
The public information gathering section still has relevence. And it is written in a tongue in cheek manner which I enjoyed. There are also quite a few typographical errors in this edition which lend a bit of humor themselves.

A thoroughly enjoyable look at spies and their toys
An articulate, at times irreverent but always fascinating look into the world of spies, gadgets, and gizmos.Mr. Lapin offers, in plain, friendly language, a straightforward look into the many aspects of spying, from bugs to people.He includes numerous sources to find more information, enough to make the reader's head whirl.Who KNEW there was this much information available and how to get it?Mr. Lapin, that's who, and he wanted everyone to be able to know about it.He even mentions material that is not open to the general public, but the point is, we now know it exists."A Resource Encyclopedia for Researchers, PIs, Spies, and Generally Nosy People," is the subheading and the book more than lives up to it. ... Read more

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New in Stock and ready to ship!! ... Read more

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This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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Artwork by Roni Horn. ... Read more

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Mathematik ist eine äußerst vielseitige, lebendige Wissenschaft. Von ihren großen Themen wie Zahlen, Unendlichkeiten, Dimensionen und Wahrscheinlichkeiten spannen die Autoren einen Bogen bis hin zu aktuellen Anwendungen in der Logistik, der Finanzwelt, der Kryptographie, der Medizin und anderen Gebieten.

Breit gefächert wie die Mathematik ist auch das Spektrum der Beiträge. Leicht verständliche, unterhaltsame Texte finden sich ebenso wie anspruchsvollere mathematische Herausforderungen.

Das Buch ist also eine Einladung an jeden, seinen eigenen Zugang zu dieser spannenden und abenteurreichen Wissenschaft zu finden.