"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 ways: 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 mathematicians: 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.