Mathematics - Finding books in the library: Number theory

נמצא בספרייה גם באנגלית
Translation of: Elementary Number Theory / David M. Burton
הבעיות בתורת המספרים מתאפיינות ביופי ובפשטות של הצגתן, אך גם, לעתים, בתחכום ובמאמץ הרב הדרושים לפתרונן. ספר זה מציג נושאים בסיסיים בתורת המספרים, בדרך אלמנטרית, ללא שימוש בידע מתקדם במתמטיקה. הנושאים המוצגים בספר:תורת ההתחלקות של השלמים, משפט פרמה, פונקציות אריתמטיות , שורשים פרימיטיביים ואינדקסים, כלל ההדדיות הריבועית, מספרים משוכללים, מספר פיבונאצ'י, שברים משולבים ועוד.

The Fifth Edition of one of the standard works on number theory, written by internationally-recognized mathematicians.

"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."---MATHEMATICAL REVIEWS

First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.

These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006. Generally speaking, the prerequisites do not go beyond basic mathematical material and are accessible to many undergraduates. The contents mainly concern diophantine problems on affine curves, in practice describing the integer solutions of equations in two variables. This case historically suggested some major ideas for more general problems. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's celebrated results are proved in full detail.