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Number theory is concerned with the properties of the natural numbers: 1, 2, 3 ... During the seventeenth and eighteenth centuries, number theory became established through the work of Fermat, Euler and Gauss. With the hand calculators and computers of today the results of extensive numerical work are instantly available and the road leading to their discoveries may be traversed with comparative care. Now in its second edition, this book consists of a sequence of exercises that will lead readers from quite simple number work to the point where they can prove algebraically the classical results of elementary number theory for themselves. A modern secondary school course in mathematics is sufficient background for the whole book which is designed to be used as an undergraduate course in number theory to be pursued by independent study without supporting lectures.

Number theory.

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Number theory

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Number theory. --- Duality theory (Mathematics)

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Number theory --- Forms, Quadratic --- Formes quadratiques --- Forms, Quadratic.

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Classically, higher logarithms appear as multivalued functions on the projective line. Today they can be interpreted as entries of the period matrix of a certain variation of Hodge structure, itself called the "polylogarithm". The aim of the book is to document the sheaf-theoretical foundations of the field of polylogarithms. Earlier, partly unpublished results and constructions of Beilinson, Deligne, and Levin on the classical and elliptic polylog are generalized to the context of Shimura varieties. The reader is expected to have a sound background in algebraic geometry. Large parts of the book are expository, and intended as a reference for the working mathematician. Where a self-contained exposition was not possible, the author gives references in order to make the material accessible for advanced graduate students.

Category theory. Homological algebra --- Logarithmic functions. --- Logarithmic functions --- Mathematical Theory --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Number theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra