# Algebraic number theory

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Algebraic Number Theory

Algebraic Number Theory

The Theory of Algebraic Numbers by Harry Pollard An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class...

Julius Wilhelm Richard Dedekind was a German mathematician who made important contributions to abstract algebra (particularly ring theory), algebraic number theory and the foundations of the real numbers.

Algebraic Theory of Numbers by Pierre Samuel Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics—algebraic geometry, in...

Advanced Number Theory by Harvey Cohn 'A very stimulating book ... in a class by itself.' — American Mathematical MonthlyAdvanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the...

Algebraic Extensions of Fields by Paul J. McCarthy '...clear, unsophisticated and direct...' — MathThis textbook is intended to prepare graduate students for the further study of fields, especially algebraic number theory and class field theory. It presumes some familiarity with topology and a solid background in abstract algebra. Chapter 1 contains the basic results concerning algebraic extensions. In addition to separable and...

Kenneth Ribet : Serre's Modularity Conjecture http://fora.tv/2007/10/25/Kenneth_Ribet_Serre_s_Modularity_Conjecture

Algebraic Number Theory by Edwin Weiss Careful organization and clear, detailed proofs make this book ideal either for classroom use or as a stimulating series of exercises for mathematically-minded individuals. Modern abstract techniques focus on introducing elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.

Mathematical Conversations by E. B. Dynkin Combining three books into a single volume, this text comprises Multicolor Problems, dealing with several of the classical map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; and Random Walks, addressing basic problems in probability theory.The book's primary aim is not so much to impart new information as to teach an active, creative attitude toward...

Mathematician Ken Ono describes how an inspiring mentor helped him redefine his relationship with numbers in this excerpt from his new book, written with mathematics writer Amir Aczel

Formula sheet - Geometry

Math = Love Make a set of nesting boxes to illustrate the number systems and have students place the index cards in the correct box(es)

Mathematics of the 19th Century: Mathematical Logic, Algebra, Number Theory, Probability Theory

★♥★ #Maths - #Symbols used in #Algebra ★♥★