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Mathematics: From the Birth of Numbers, by Jan Gullberg
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- Sales Rank: #426905 in Books
- Published on: 1997
- Binding: Hardcover
- 1093 pages
Most helpful customer reviews
3 of 3 people found the following review helpful.
Excellent math resource
By Little Old Granny
In the last few years I decided to learn more about mathematics. I think I may have had "math anxiety" early in my schooling. Either that or my brain isn't mathematically inclined.
I ordered this book hoping it would partially overcome my difficulty in learning math. I would say it does. The book is way too big and long to sit down and read as one would other types of books. However, it is a tremendous resource, well written and relatively easy to understand (that depends somewhat on one's math expertise). The title "Mathematics From the Birth of Numbers" describes the book exactly. It starts with, literally, the birth of numbers in "ancient" times and goes through all of the kinds of mathematics, such as number theory, calculus, geometry, etc. I recommend this book more as a reference than as a textbook or a book to read from cover to cover. For example, if you want to know something about number theory, go to that section of the book and read what you want to know. Same with other topics. Illustrations and equations are plentiful and answers to the exercises are in the back.
My only criticism which really isn't a criticism; the book is too heavy for me to sit comfortably in my recliner and read. It couldn't be any lighter in weight, though.
If you want a good history of mathematics plus explanations of most of the various mathematical disciplines, I would recommend this book.
7 of 7 people found the following review helpful.
Broad coverage of high school topics
By William A. Huber
This book is a wonderful supplement to the standard high school curriculum, beginning with algebra and extending through Euclidean geometry, analytic geometry, to differential and integral calculus, and including brief introductions to other "back of the book" topics like probability, determinants, and so on. It is full of hard-to-find details left behind by most texts, such as explicit solutions to third- and fourth- degree polynomials in one variable. It's fun to browse this book in search of such tidbits to fill in your mathematical knowledge.
"Mathematics..." is written at a level just right for someone who has progressed as far as calculus or college engineering math but no further. It is also nice that the myriad (albeit brief) historical references help connect the material with its initial development. Unfortunately, the lack of any contextual information (brief biographies would be welcome) make these references rather dry and unrevealing: authors, dates, and titles of publications is frequently all we get.
I have to agree, too, with the Willingboro reviewer: although this text covers a wide variety of traditional high school and early college topics, at the same time it clearly exhausts its author's knowledge of the subject and therefore cannot provide a foundation for proceeding further. It is akin to a travelogue that directs the reader along completed, well-worn paths, visiting all the conventional landmarks, without pointing out the existence of other paths, other points of interest, or taking the readers to lookout points and vistas suggesting territory remaining to be explored.
Almost all the topics covered are ancient, rarely extending beyond what was known by the middle of the 19th century. (A chapter on fractals is the only exception.) Many important and modern subjects are barely mentioned and certainly not developed beyond the limited introduction available in most high school texts: graph theory, number theory, complex analysis, algebraic geometry, functional analysis, group theory, Galois theory, differential geometry, category theory, ..., the list can go on and on. (For example, topology--a vast subject--gets less than three pages, whereas eight pages are devoted to illustrating the routine mechanics of solving euclidean triangles using trigonometry.) This is a shame, because the wealth of topics nevertheless discussed by this book provides an amazing foundation for introducing these modern ideas and pointing out their deeper implications and ramifications. As a result, mathematics comes out looking like a kind of beautiful fossil rather than an organic, evolving creature.
62 of 64 people found the following review helpful.
A Desert Island book for math lovers
By Stan Vernooy
How did this guy do it? He wasn't even a mathematician - he was a doctor. And he wrote a book that's fascinating for both mathematicians and non-mathematicians. The book goes all the way from the incention of numbers and the most elementary arithmetic, all the way through elemetary calculus. Along the way he manages to give at least an introduction to fractals, combinatorics, non-Euclidean geometry, harmonic analysis, and probability - all topics which the typical American student would probably miss on her or his way through the standard sequence of material leading up through calculus.
But Gullberg does much more than just present the material. He includes the history of how - and WHY - each major mathematical innovation was developed, placing the entire subject in a human and historical context that is missing from almost any other book on any of these many topics.
I don't care how much math you know - there are almost certainly historical facts in here that you haven't encountered before. And I don't care how LITTLE math you know - you'll find this book accessible and fascinating.
The only thing I didn't care for was the silly little limericks and cartoons scattered throughout the book. Most of them weren't funny, and served only to distract the reader from the fascinating material.
This book should be read thoroughly from page 1 through page 1039, and then read over and over again, as you dip randomly into whatever chapters happen to strike your fancy at any particular time, for the rest of your life. I originally bought a paperback copy, but I soon realized that I had to have a hardcover version that will stay on my shelf until the day I die - except when it's in my lap or on my desk.
Unparalleled and irreplaceable.
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