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Er geht auf die Wahrscheinlichkeitskonzeption der Subjektivisten und der Objektivisten ein.
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Quadratic and Hermitian Forms. For a long time - at least from Fermat to Minkowski - the theory of quadratic forms was a part of number theory. Much of the best work of the great number theorists of the eighteenth and nineteenth century was concerned with problems about quadratic forms.
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Parallel to this development the ideas of abstract algebra and abstract linear algebra introduced by Dedekind, Frobenius, E. Noether and Artin led to today's structural mathematics with its emphasis on classification problems and general structure theorems. On the basis of both - the number theory of quadratic forms and the ideas of modern algebra - Witt opened, in , a new chapter in the theory of quadratic forms. His most fruitful idea was to consider not single "individual" quadratic forms but rather the entity of all forms over a fixed ground field and to construct from this an algebra ic object.
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This object - the Witt ring - then became the principal object of the entire theory. Thirty years later Pfister demonstrated the significance of this approach by his celebrated structure theorems. From Fermat to Minkowski: 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. Two examples might illustrate our objectives.
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Nov 19, Gregory rated it it was amazing. I could not put this down and highly recommend it to anyone with some mathematics background really, calculus , some complex analysis and the elements of abstract algebra is enough who wants to make some sense of the bewildering array of seemingly unrelated techniques used in modern number theory.
The author ostensibly takes a historical approach, but if there is an overriding theme to this book it is showing how the various pieces of the puzzle fit together logically, and not simply historica I could not put this down and highly recommend it to anyone with some mathematics background really, calculus , some complex analysis and the elements of abstract algebra is enough who wants to make some sense of the bewildering array of seemingly unrelated techniques used in modern number theory. The author ostensibly takes a historical approach, but if there is an overriding theme to this book it is showing how the various pieces of the puzzle fit together logically, and not simply historically.
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