Michael Th. Rassias
Problem-Solving and Selected Topics in Number Theory
In the Spirit of the Mathematical Olympiads
Gebonden Engels 2010 2011e druk 9781441904942Levertijd ongeveer 9 werkdagen
Gratis verzonden
Samenvatting
The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).
Specificaties
ISBN13:9781441904942
Taal:Engels
Bindwijze:gebonden
Aantal pagina's:324
Uitgever:Springer New York
Druk:2011
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Inhoudsopgave
<P>- Introduction.- The Fundamental Theorem of Arithmetic.- Arithmetic functions.- Perfect numbers, Fermat numbers.- Basic theory of congruences.- Quadratic residues and the Law of Quadratic Reciprocity.- The functions p(x) and li(x).- The Riemann zeta function.- Dirichlet series.- Partitions of integers.- Generating functions.- Solved exercises and problems.- The harmonic series of prime numbers.- Lagrange four-square theorem.- Bertrand postulate.- An inequality for the function p(n).- An elementary proof of the Prime Number Theorem.- Historical remarks on Fermat’s Last Theorem.- Bibliography and Cited References.- Author index.- Subject index.</P>
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