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Mathematics: From the Birth of Numbers 精装
- 语言 : 英语
- 精装 : 1093页
- ISBN : 039304002X
- 尺寸 : 19.05 x 5.59 x 26.16 cm
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First, it is partly a history of mathematics. Beginning with the first chapter, the author discusses the origin of numbers themselves (albeit briefly) and guides the reader through an increasingly well-developed mathematical landscape culminating with a treatment of differential equations. Is it a complete history? Not at all. It is developed well enough to give the reader a taste of how mathematics occurred throughout the past centuries, but it would not serve as a primary text for a course in the history of mathematics. What it lacks in depth, however--as I'll say repeatedly--it makes up for in breadth. Few textbooks on the history of mathematics could cover as many subjects as are handled by this book, making it a perfect supplementary text.
Second, it is partly a course in mathematics. Again, the breadth requires a certain lack of depth. Ostensibly the reader without much mathematical experience *could* learn mathematics from this book. However, the development of ideas is more rapid than most students would be able to keep up with. Readers wishing to actually learn mathematics would be better served buying several textbooks: one or two each on their topics of interest. However, it again makes a wonderful supplementary text because it collects the bare bones of all of those sub-disciplines between the same two covers. Additionally, it provides the beginning student of mathematics with a truly marvelous and extensive survey of the field. The student who doesn't know whether s/he wants to read a book next on probability theory, combinatorics, or differential equations would be extraordinarily well-served by this book's tantalizing overviews.
Third, it is a remarkable reference. Once more, while such a broad book cannot be encyclopedic on any one topic, it does make for a good book to keep on hand whenever one needs to refresh one's memory of the basics of any number of mathematical topics. Because it's both a course and a history, furthermore, I found it contained some information that most other books on mathematics omit. When I (yes, even in the twenty-first century) wanted to learn how to perform more advanced operations than mere counting on my abacus, this book was my first reference. Similarly, students who grew up in the age of computers might be interested, if for no other reason than historical curiosity, to read the section explaining the correct operation of a slide rule. Regarding the use of this book as a reference, the reader should be aware that, while the vast majority of the notation is fairly standard, I did notice a few instances in which the author uses different notation from that to which I'm accustomed from my own mathematical education.
Mostly, we can consider this book a single portrait of what one might consider to be elementary (meaning high-school and early undergraduate) mathematics. No, it doesn't contain as many proofs as I would like and no, it doesn't have the exercises that would make it a more effective (if twice as long) pedagogical tool. But it is still a remarkable book because it manages to collect all of that content into a *single* portrait. In so doing, the author helps the reader to observe the connections between the various disciplines of mathematics and for that reason, this book deserves our attention and respect.
The reader with absolutely no mathematical experience will probably find this to be a difficult read, but if you have even a little bit of background in mathematics, I think you will (as I did) find it to be a delightful and entertaining book well worth keeping in your personal or professional library.
It has been said that if you are to own one math book, then this should be it. I think that this is true but not for all people. If you should own one reference book about material which is not very advanced, then yes, this is the book. However, if you want a book ABOUT math, then I think 'The World of Mathematics' by Newman is the one you should own. Personally, if I were to own just one math book it would definitely be Hardy's 'A course of pure mathematics'. But why own just one math book? Buy all of them!
It should be on every math major's bookshelf, and within arm's reach of every math aficionado.
The author's obcession/love of mathematics is evident in its rigorous detail.
It would be a fabulous gift for any math major or history major...even for a budding anthropologist.