Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate, including: (1) divisibility, (2) congruences, (3) theRiemann zeta function, (4) Diophantine equations and Fermat’s conjecture, (5)the theory of partitions. Comprehensive in nature, Topics from the Theory of Numbers is an ideal text for advanced undergraduates and graduate students alike. Motivates the subject with historical background and notes Problems and examples illustrate the ideas of the text Touches upon many of the most famous ideas and proofs in number theory 178 well-chosen problems INDICE: Preface.- Preface to the First Edition.- Part One. Introduction, Historical Background, and Notations.- Introduction and Historical Background.-Introductory Remarks and Notations.- Part Two. Elementary Number Theory.- Divisibility.- Congruences.- Quadratic Residues.- Arithmetical Functions.- The Theory of Partitions.- Part Three. Topics from Analytic and Algebraic Number Theory.- The Distribution of Primes and the Riemann Zeta Function.- The Prime Number Theorem.- The Arithmetic of Number Fields.- Ideal Theory.- Primes in Arithmetic Professions.- Diophantine Equations.- Fermat’s Equation.- Answers to Selected Problems.- Subject Index.- Name Index.- Index of Functions.
- ISBN: 978-0-8176-4837-4
- Editorial: Birkhaüser
- Encuadernacion: Rústica
- Páginas: 360
- Fecha Publicación: 01/12/2008
- Nº Volúmenes: 1
- Idioma: Inglés