Published April 1998
by Walter de Gruyter .
Written in English
|Contributions||Kalman Gyory (Editor), Attila Petho (Editor), Vera T. Sos (Editor)|
|The Physical Object|
|Number of Pages||595|
Citation Information. Number Theory. Diophantine, Computational and Algebraic Aspects. Proceedings of the International Conference held in Eger, Hungary, July August 2, Diophantine approximation and quadratic fields. Number Theory: Diophantine, Computational and Algebraic Aspects. Proceedings of the International Conference held in Eger, Hungary, July August 2, (pp. 55–94). Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued mathematician Carl Friedrich Gauss (–) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics.". This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than exercises and the text is largely self-contained.
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their -theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function properties, such as whether a ring admits. Number Theory Books, P-adic Numbers, p-adic Analysis and Zeta-Functions, (2nd edn.)N. Koblitz, Graduate T Springer Algorithmic Number Theory, Vol. 1, E. Bach and J. Shallit, MIT Press, August ; Automorphic Forms and Representations, D. Bump, CUP ; Notes on Fermat's Last Theorem, A.J. van der Poorten, Canadian Mathematical Society Series of Monographs . Requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and interesting engineering applications. It first builds the foundation of computational number theory by covering the arithmetic of integers and polynomials at a very basic level. In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, continued fractions, etc.) which in recent years have proven to be extremely useful for applications to cryptography and coding theory. Both cryptography and codes have crucial applications in our daily lives, and they 1/5(1).
Number Theory: Volume I: Tools and Diophantine Equations (Graduate Texts in Mathematics Book ) - Kindle edition by Cohen, Henri. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Number Theory: Volume I: Tools and Diophantine Equations (Graduate Texts in Mathematics Book Reviews: 1. The book deals with algorithmic problems related to binary quadratic forms. It uniquely focuses on the algorithmic aspects of the theory. The book introduces the reader to important areas of number theory such as diophantine equations, reduction theory of quadratic forms, geometry of numbers and algebraic number theory. In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical gh computer algebra could be considered a subfield of scientific computing, they are generally considered as. Algebra (from Arabic: الجبر al-jabr, meaning "reunion of broken parts" and "bonesetting") is one of the broad parts of mathematics, together with number theory, geometry and its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.