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Number Theory and Its History
"A very valuable addition to any mathematical library." — School Science and Math
This book, written by a prominent mathematician and Sterling Professor of Mathematics at Yale, differs from most other books on number theory in two important first, it presents the principal ideas and methods of number theory within a historical and cultural framework, making the subject more tangible and easily grasped. Second, the material requires substantially less mathematical background than many comparable texts. Technical complications and mathematical requirements have been kept to a minimum in order to make the book as accessible as possible to readers with limited mathematical knowledge. For the majority of the book, a basic knowledge of algebra will suffice.
In developing the importance and meaning of number theory in the history of mathematics, Professor Ore documents the contributions of a host of history's greatest Diophantos, Euclid, Fibonacci, Euler, Fermat, Mersenne, Gauss, and many more, showing how these thinkers evolved the major outlines of number theory. Topics covered include counting and recording of numbers, the properties of numbers, prime numbers, the Aliquot parts, indeterminate problems, theory of linear indeterminate problems, Diophantine problems, congruences, analysis of congruences, Wilson's Theorem, Euler's Theorem, theory of decimal expansions, the converse of Fermat's Theorem, and the classical construction problems.
Based on a course the author gave for a number of years at Yale, this book covers the essentials of number theory with a clarity and avoidance of abstruse mathematics that make it an ideal resource for undergraduates or for amateur mathematicians. It has even been recommended for self-study by gifted high school students.
In short, Number Theory and Its History offers an unusually interesting and accessible presentation of one of the oldest and most fascinating provinces of mathematics. This inexpensive paperback edition will be a welcome addition to the libraries of students, mathematicians, and any math enthusiast.
This book, written by a prominent mathematician and Sterling Professor of Mathematics at Yale, differs from most other books on number theory in two important first, it presents the principal ideas and methods of number theory within a historical and cultural framework, making the subject more tangible and easily grasped. Second, the material requires substantially less mathematical background than many comparable texts. Technical complications and mathematical requirements have been kept to a minimum in order to make the book as accessible as possible to readers with limited mathematical knowledge. For the majority of the book, a basic knowledge of algebra will suffice.
In developing the importance and meaning of number theory in the history of mathematics, Professor Ore documents the contributions of a host of history's greatest Diophantos, Euclid, Fibonacci, Euler, Fermat, Mersenne, Gauss, and many more, showing how these thinkers evolved the major outlines of number theory. Topics covered include counting and recording of numbers, the properties of numbers, prime numbers, the Aliquot parts, indeterminate problems, theory of linear indeterminate problems, Diophantine problems, congruences, analysis of congruences, Wilson's Theorem, Euler's Theorem, theory of decimal expansions, the converse of Fermat's Theorem, and the classical construction problems.
Based on a course the author gave for a number of years at Yale, this book covers the essentials of number theory with a clarity and avoidance of abstruse mathematics that make it an ideal resource for undergraduates or for amateur mathematicians. It has even been recommended for self-study by gifted high school students.
In short, Number Theory and Its History offers an unusually interesting and accessible presentation of one of the oldest and most fascinating provinces of mathematics. This inexpensive paperback edition will be a welcome addition to the libraries of students, mathematicians, and any math enthusiast.
400 pages, Paperback
First published January 1, 1948
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Displaying 1 - 8 of 8 reviews
November 1, 2007
This was a very fun book to work through as my summer pleasure reading one year in high school. So... er... that probably says more about me than about the book.
Anyway, if you like reading math textbooks for fun, then you totally rock! If you also happen not to know lots of number theory yet, this is a good one to try.
Anyway, if you like reading math textbooks for fun, then you totally rock! If you also happen not to know lots of number theory yet, this is a good one to try.
April 13, 2018
Very fun read. The author’s enthusiasm and curiosity are infectious, and his proof expositions are lucid and elegant; with the one exception of the chapter on primitive roots, which took a couple tries to make sense of.
March 15, 2021
A superb introduction to basic number theory - rich in historical context.
It covers the basics you would expect - primes, aliquot parts (an old fashioned term for divisors), congruences, diophantine problems. There is an emphasis on computational methods with the charming (and also old fashioned) use of 'algorism' for 'algorithm'. There is not a whiff of emphasis on computational efficiency - something that grows vastly in importance in later, current, more anguished times. Which is refreshing. ( The author does note a few times the practical impossibility of methods because the amount of computation is too vast. but doesn't stress about it. ). There are a few spots where he delves quite deeply into the intricacies - out of all proportion to the rest of the book. And I must confess I skipped over a couple of these bits. Time is short in these more desperate times. Back then, long empty days ... for the privileged few.
The book was published in 1948. The author shares his anticipation that these new fangled calculating machines developed for war might soon be released for more peaceful pursuits. And looks forward to advances in number theory from a far more extensive ability to experiment numerically - far beyond what even giant historical figures such as Gauss could ever have done. And thus it did come to pass. For a while.
He notes that no odd perfect numbers are known and that there are no known Fermat primes ( beyond the first five). But there might be. It is fascinating to note that seventy years or so later we still don't know. Though we do know that if they exist they must be truly gargantuously large. Look it up!!
Great book. Fascinating read. Charming and delightful throughout.
It covers the basics you would expect - primes, aliquot parts (an old fashioned term for divisors), congruences, diophantine problems. There is an emphasis on computational methods with the charming (and also old fashioned) use of 'algorism' for 'algorithm'. There is not a whiff of emphasis on computational efficiency - something that grows vastly in importance in later, current, more anguished times. Which is refreshing. ( The author does note a few times the practical impossibility of methods because the amount of computation is too vast. but doesn't stress about it. ). There are a few spots where he delves quite deeply into the intricacies - out of all proportion to the rest of the book. And I must confess I skipped over a couple of these bits. Time is short in these more desperate times. Back then, long empty days ... for the privileged few.
The book was published in 1948. The author shares his anticipation that these new fangled calculating machines developed for war might soon be released for more peaceful pursuits. And looks forward to advances in number theory from a far more extensive ability to experiment numerically - far beyond what even giant historical figures such as Gauss could ever have done. And thus it did come to pass. For a while.
He notes that no odd perfect numbers are known and that there are no known Fermat primes ( beyond the first five). But there might be. It is fascinating to note that seventy years or so later we still don't know. Though we do know that if they exist they must be truly gargantuously large. Look it up!!
Great book. Fascinating read. Charming and delightful throughout.
June 30, 2008
Dated...but the history is fascinating. I would only recommend this book for folks that are into advanced mathematics.
January 24, 2024
It was fine. You really need to like math in order to follow this.
July 2, 2015
It's from 1948, so it's quite out-dated; a lot of the math is describes as difficult or time-consuming can easily be done on any modern calculator. But it still offers a nice blend of math history and regular, proof-driven math, so for any higher-level math student it's worth reading.
November 13, 2016
1. counting and recording of numbers
2. properties of numbers
3. Euclid's algorithm
4. prime numbers
5. aliquot parts
6. diophantine problems
7. congruences
8. analysis of congruences
9. wilson's theorm
10. euler's theorm
11. fermat's theorm
2. properties of numbers
3. Euclid's algorithm
4. prime numbers
5. aliquot parts
6. diophantine problems
7. congruences
8. analysis of congruences
9. wilson's theorm
10. euler's theorm
11. fermat's theorm
April 4, 2012
Fun introduction to number theory with history thrown in. Good examples and helps clear some confusion about some math concepts.
Displaying 1 - 8 of 8 reviews