Basic Information on the Lecture Course overview. Attempts to prove Fermat’s Last Theorem long ago were hugely in u-ential in the development of algebraic number theory by Dedekind, Hilbert, Kummer, Kronecker, and others. For general algebraic background, see author's online text "Abstract Algebra: The Basic Graduate Year". This course is intended to give its participants a more profound knowledge of both algebra and number theory, and to supply the foundations of further independent scientific study in this direction. It seems that Serge Lang's Algebraic Number Theory is one of the standard introductory texts (correct me if this is an inaccurate assessment). One could compile a shelf of graduate-level expositions of algebraic number theory, and another shelf of undergraduate general number theory texts that culminate with a first exposure to it. Ressources en bibliothèque . Assume as prerequisite a standard graduate course in algebra, but cover integral extensions and localization before beginning algebraic number theory. This is a text I have taught from before, but it is unfortunately very expensive. Take addition for instance, doesnt require much knowledge but as when its applications become complicated higher knowledge is required. Take addition for instance, doesnt require much knowledge but as when its applications become complicated higher knowledge is required. Samuel, algebraic number theory. The answer is, it depends. cryptography. An introduction to algebraic number theory. Translated from the German by Norbert Schappacher. Newest algebraic-number-theory questions feed Subscribe to RSS The abstract algebra material is referred to in this text as TBGY. Berlin, Germany; New York, NY: Springer, c1999. An algebraic number field is a finite extension of Q; an algebraic number is an element of an algebraic number field. Théorie algébrique des nombres / Samuel; Prerequisite for . I would recommend Stewart and Tall's Algebraic Number Theory and Fermat's Last Theorem for an introduction with minimal prerequisites. These numbers lie in algebraic structures with many similar properties to those of the integers. From number theory to physics. $\begingroup$ Pierre Samuel's "Algebraic Theory of Numbers" gives a very elegant introduction to algebraic number theory. Solving the Birch-Swinnerton-Dyer conjecture and win one of the Millenium Prizes (1M USD) from the Clay Mathematics Institute. Assume as prerequisite a standard graduate course in algebra, but cover integral extensions and localization before beginning algebraic number theory. (Algebraic Number Theory). Applications of number theory: eg. Algebraic number theory studies the arithmetic of algebraic number fields — the ring of integers in the number field, the ideals and units in the ring of integers, the extent to which unique factorization holds, and so on.