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This book arose from a course of lectures given by the first author
during the winter term 1977/1978 at the University of Munster (West
Germany). The course was primarily addressed to future high school
teachers of mathematics; it was not meant as a systematic
introduction to number theory but rather as a historically
motivated invitation to the subject, designed to interest the
audience in number-theoretical questions and developments. This is
also the objective of this book, which is certainly not meant to
replace any of the existing excellent texts in number theory. Our
selection of topics and examples tries to show how, in the
historical development, the investigation of obvious or natural
questions has led to more and more comprehensive and profound
theories, how again and again, surprising connections between
seemingly unrelated problems were discovered, and how the
introduction of new methods and concepts led to the solution of
hitherto unassailable questions. All this means that we do not
present the student with polished proofs (which in turn are the
fruit of a long historical development); rather, we try to show how
these theorems are the necessary consequences of natural questions.
Two examples might illustrate our objectives."
This book arose from a course of lectures given by the first author
during the winter term 1977/1978 at the University of Munster (West
Germany). The course was primarily addressed to future high school
teachers of mathematics; it was not meant as a systematic
introduction to number theory but rather as a historically
motivated invitation to the subject, designed to interest the
audience in number-theoretical questions and developments. This is
also the objective of this book, which is certainly not meant to
replace any of the existing excellent texts in number theory. Our
selection of topics and examples tries to show how, in the
historical development, the investigation of obvious or natural
questions has led to more and more comprehensive and profound
theories, how again and again, surprising connections between
seemingly unrelated problems were discovered, and how the
introduction of new methods and concepts led to the solution of
hitherto unassailable questions. All this means that we do not
present the student with polished proofs (which in turn are the
fruit of a long historical development); rather, we try to show how
these theorems are the necessary consequences of natural questions.
Two examples might illustrate our objectives."
Procreare iucundum, sed parturire molestum. (Gauss, sec.
Eisenstein) The plan of this book was first conceived eight years
ago. The manuscript developed slowly through several versions until
it attained its present form in 1979. It would be inappropriate to
list the names of all the friends and advisors with whom I
discussed my various drafts but I should like to mention the name
of Mr. Gary Cornell who, besides discussing with me numerous
details of the manuscript, revised it stylistically. There is much
interest among mathematicians to know more about Gauss's life, and
the generous help I received has certainly more to do with this
than with any individual, positive or negative, aspect of my
manuscript. Any mistakes, errors of judgement, or other
inadequacies are, of course, the author's responsi bility. The most
incisive and, in a way, easiest decisions I had to make were those
of personal taste in the choice and treatment of topics. Much had
to be omitted or could only be discussed in a cursory way."
Procreare iucundum, sed parturire molestum. (Gauss, sec.
Eisenstein) The plan of this book was first conceived eight years
ago. The manuscript developed slowly through several versions until
it attained its present form in 1979. It would be inappropriate to
list the names of all the friends and advisors with whom I
discussed my various drafts but I should like to mention the name
of Mr. Gary Cornell who, besides discussing with me numerous
details of the manuscript, revised it stylistically. There is much
interest among mathematicians to know more about Gauss's life, and
the generous help I received has certainly more to do with this
than with any individual, positive or negative, aspect of my
manuscript. Any mistakes, errors of judgement, or other
inadequacies are, of course, the author's responsi bility. The most
incisive and, in a way, easiest decisions I had to make were those
of personal taste in the choice and treatment of topics. Much had
to be omitted or could only be discussed in a cursory way."
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