Rassias Problem-Solving and Selected Topics in Number Theory

In the Spirit of the Mathematical Olympiads
Erscheinungsjahr 2010
ISBN: 978-1-4419-0495-9
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 324 Seiten, Web PDF

Reihe: Mathematics and Statistics (R0)

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).

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Rassias, Michael Th.

Inhaltsverzeichnis

- 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.- Author index.- Subject index.- Bibliography and Cited References.

Über Autor(innen)

Michael Th. Rassias has received several awards in mathematical problem solving competitions including two gold medals at the Pan-Hellenic Mathematical Competitions of 2002 and 2003 held in Athens, a silver medal at the Balkan Mathematical Olympiad of 2002 held in Targu Mures, Romania and a silver medal at the 44th International Mathematical Olympiad of 2003 held in Tokyo, Japan.