Michael Th. Rassias
Springer New York
e druk, 2014
9781489981943
Problem-Solving and Selected Topics in Number Theory
In the Spirit of the Mathematical Olympiads
Specificaties
Paperback, blz.
|
Engels
Springer New York |
e druk, 2014
ISBN13: 9781489981943
Rubricering
Levertijd ongeveer 8 werkdagen
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
ISBN13:9781489981943
Taal:Engels
Bindwijze:paperback
Uitgever:Springer New York
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>