Book Description

Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar. Following closely behind is g, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery.

In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics.

Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . .. But unlike its more celebrated colleagues p and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction.

Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!).

Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.

Customer Reviews (22)

Good but demanding
Target:

Despite what the author says in the introduction, the book is addressing people with a firm grip on high-school (=real) calculus; not only does Havil go into difficult topics, his proofs are rather succinct and often require some thinking on the reader's part. However, a good high-school student should be able to follow most of the book, even the last chapter that deals with complex analysis as Havil does a great job explaining it.


Pluses:

I think this book is ideal for high-school students and undergrads who want to know more mathematics in general and gamma and real analysis in particular.
It's one of the best popular books i've read. Havil presents difficult issues with great ease, leaving tiny bits of proofs for the reader to fill in, but which shouldn't be a problem for anyone who was able to understand what he did up to that point (as i have said, high-school calculus should be enough).
Something i appreciated is Havil states and proves a LOT of exciting results like the probability that two numbers should be co-prime is 6/pi*2, Euler's product formula, etc. The writing is good, clear and direct, Havil delivers on every promise he makes and doesn't do a lot of hand-waving like most other popular math books do; however, in chapter 12, he writes 12 formulas that link gamma with pi, e, log(2), pi*2, the floor function, etc. and leaves 10 of them for the reader to prove.
The are cases when the author deliberatelychose a longer proof to illustrate how incredibly close some mathematical expressions are (for ex. he shows that 1+1/2+...+1/n -log(n+1) is bounded by zeta(2)=pi*2/6).
Havil makes use of a lot of historical information on the mathematical concepts involved, as well as the people who developed them, and he does it in the same thorough manner in which he wrote the book. Great info here as well.


Minuses:

I have found about 20 typos throughout the book, including 4 in formulas used in proofs, although nothing that can not be corrected by simply checking the next line for continuity.
The book is not all about gamma; as Havil says, gamma is deeply connected to the harmonic series and to the logarithms so a closer look at these and their other functions is necessary; however, in some cases, i felt the author had strayed a bit too much.

An excellent read!
Evidently some "reviewers" should be reviewing books involving simpler mathematics; they clearly didn't get what this book is about!!

Havil's book is not really for the person in the street despite his introductory comments.You must have sufficient background to stand up to some lengthy derivations and the willingness to work through them in detail.If you lack these, I don't think you'll get much out of the book.

All in all, a very nice piece of mathematical writing!

Though I've found only a few errors in the entire book, a complete errata list would be nice.

Needs to read Bill Dunham
This had such promise...but never materialized.Havil is obviously enchanted with Euler--who wouldn't be?--but he fails to explain the material, and seems to have failed to proofread his book.

In Dunham's Journey Through Genius, the explanations are clear and step-wise.I read it with a thick pad of paper and a pen--I don't really trust anyone--but it was all workable.Havil states things unclearly, so it's far from obvious just what he's trying to show.The discussions are unfollowable, at least to me.

Reading as much of this as I was able to stand is a lot like finding out that there's no Santa Claus.

woah!
I'm an aspiring theoretical math major entering college in the fall, and I must say that this is one of the most fasinating books I've ever laid hands on.If you've had a fair deal of calculus and you're willing to dig through a couple of hefty proofs, this book will take you to some really wild places.In short... buy it!!

A tough (but rewarding) read for an inconsistent audience
Per the foreword, this book is "aimed at students of mathematics, be they eager high school students or undergraduates". As a summa cum laude graduate math major (of some years ago) I expected to enjoy an romp thru some beautiful mathematical ideas. Well, the ideas are there, and Havil is to be commended for gathering some unusual and interesting topics. And much of the extensive mathematical notation is supported with nice numeric examples. However, much of it is not. All too often there are pages of integrals, sums, and products that go happily on without a clue to some of the beautiful things that are happening. The most frustrating example is the "proof" of Euler's zeta function formula, one of the prettiest pieces of mathematics. I still cannot understand Havil's presentation. (It was thrilling to read the same proof in "Prime Obsession" by Derbyshire so I know it can be explained with simple algebra.) Also, "Gamma" appears to be intended to be read in one sitting since it is rarely possible to begin at an advanced chapter. It is assumed that you remember definitions and notations which have appeared long before. To the author's credit, there are occasional backward references by page number, but then, about half of these are frustratingly wrong. Finally, it would be nice to see a copy of the errata for this book. I hope this book appears in a 2nd edition where the level of its presentation is made much more consistent. ... Read more

Product Description
In this program, geometry is combined with approximation to solve relatively complex problems involving shooting an arrow and landing an airplane on the deck of an aircraft carrier. Emphasizing the value of sketching as a visualization tool, the program also explains how the solution of the archery problem, through geometric inversion, can help solve the problem of a plane landing. (59 minutes) ... Read more

Product Description
This program shows that a single mathematical model can describe the take-off of a wide variety of aircraft, running the gamut from a single-engine trainer to the Concorde. Because the search for approximations is somewhat complex, graphical notation is employed to reveal the interaction and variation of the forces involved. (26 minutes) ... Read more

Book Description
This digital document is an article from IFR, published by Thomson Gale on June 1, 2007. The length of the article is 1110 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Computing your CADP: any approach plate is a soup of acronyms and abbreviations. Here's the math behind one you've seen but never spoken.(APPROACH CLINIC)(Constant Angle Descent Point)
Author: John Clark
Publication: IFR (Magazine/Journal)
Date: June 1, 2007
Publisher: Thomson Gale
Volume: 23Issue: 6Page: 18(2)

Distributed by Thomson Gale ... Read more

Book Description
Written in a straightforward manner, this laboratory manual for a two-semester organic chemistry course provides only the essential background material, laboratory set-ups, and procedures for each exercise. The exercises have been carefully written to minimize set-up time and eliminate the need for elaborate and expensive laboratory equipment. Laboratory techniques are emphasized rather than theoretical understanding. ... Read more

Customer Reviews (2)

Organic Chem Lab Manual
Perfect/new condition with VERY fast shipping. Cheapest price I could find, and was significantly cheaper than elsewhere. I had the first lab, and ordered the manual that night assuming that it would not arrive before my next lab, but it did! I was very pleasantly surprised. Thanks!

an inexpensive yet effective lab book for undergraduate orga
An inexpensive, yet effective lab manual for undergraduate organic chemistry.The students do not have to buy a hard cover text, full of colors.The reagents used are cheap and, generally, available at low cost.There is great variety of experiments- some are standard syntheses, some are kinetcis, but above all there is a great qualitative analysis chapter.The techniques illustrated in the first few chapters are essential in running high yield syntheses.An excellent set of appendices with subjects like % yield, how to make solutions and how to balance a redox equation.This is a book where one learns how to do expts. without necessarily running a very expensive lab. ... Read more