Advanced Number Theory - Harvey Cohn

Name of Book :- Advanced Number Theory .

Writer :- Harvey Cohn .

Pages :- 283

Publishers :- Dover Publications, Inc. , New York .

Edition :- 1962 .
-----------------------------------------------------------------------------------
This is a very good book. So please seed after download completes .
-----------------------------------------------------------------------------------
Preface :-

The prerequisites for this book are the ΓÇ£standardΓÇ¥ first-semester course
in number theory (with incidental elementary algebra) and elementary
calculus. There is no lack of suitable texts for these prerequisites (for
example, An Introduction to the Theory of Numbers, by 1. Niven and H. S.
Zuckerman, John Wiley and Sons, 1960, can be cited as a book that intro-
duces the necessary algebra as part of number theory). Usually, very little else can be managed in that first semester beyond the transition from
improvised combinatorial amusements of antiquity to the coherently
organized background for quadratic reciprocity, which was achieved in
the eighteenth Century.
The present text constitutes slightly more than enough for a second-
semester course, carrying the student on to the twentieth Century by
motivating some heroic nineteenth-Century developments in algebra and
analysis. The relation of this textbook to the great treatises Will necessarily
be like that of a historical novel to chronicles. We hope that once the
student knows what to seek he will find chronicles to be as exciting as a
historical novel.
The problems in the text play a significant role and are intended to
stimulate the spirit of experimentation which has traditionally ruled
number theory and which has indeed become resurgent with the realization
of the modern computer. A student completing this course should acquire
an appreciation for the historical origins of linear algebra, for the zeta-
function tradition, for ideal class structure, and for genus theory. These ideas, although relatively old, still make their influence felt on the frontiers
of modern mathematics. Fermat's last theorem and complex multiplication
are unfortunate omissions, but the motive was not to depress he degree
of difficulty SO much as it was to make the most efficient usage of one
semester.
My acknowledgments are many and are difficult to list. I enjoyed the .
benefits of courses under Bennington P. Gill at City College and Saunders
MacLane at Harvard. The book profited directly from suggestions by my
students and from the incidental advice of many readers, particularly
Burton W. Jones and Louis J. Mordell. 1 owe a special debt to Herbert S.
Zuckerman for a careful reading, to Gordon Pal1f or major improvements,
and to the staff of John Wiley and Sons for their cooperation.