Synopsis
A concise and well-motivated introduction to algebraic number theory, following the evolution of unique prime factorization through history.
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About the Author
John Stillwell is the author of many books on mathematics; among the best known are Mathematics and its History, Naive Lie Theory, and Elements of Mathematics. He is a member of the inaugural class of Fellows of the American Mathematical Society and winner of the Chauvenet Prize for mathematical exposition.
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Algebraic Number Theory for Beginners : Following a Path from Euclid to Noether
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ALGEBRAIC NUMBER THEORY FOR BEGINNERS
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Algebraic Number Theory for Beginners
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ALGEBRAIC NUMBER THEORY FOR BEGINNERS
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Algebraic Number Theory for Beginners
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Paperback. Condition: New. This book introduces algebraic number theory through the problem of generalizing 'unique prime factorization' from ordinary integers to more general domains. Solving polynomial equations in integers leads naturally to these domains, but unique prime factorization may be lost in the process. To restore it, we need Dedekind's concept of ideals. However, one still needs the supporting concepts of algebraic number field and algebraic integer, and the supporting theory of rings, vector spaces, and modules. It was left to Emmy Noether to encapsulate the properties of rings that make unique prime factorization possible, in what we now call Dedekind rings. The book develops the theory of these concepts, following their history, motivating each conceptual step by pointing to its origins, and focusing on the goal of unique prime factorization with a minimum of distraction or prerequisites. This makes a self-contained easy-to-read book, short enough for a one-semester course. Seller Inventory # LU-9781009001922
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ALGEBRAIC NUMBER THEORY FOR BEGINNERS
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Algebraic Number Theory for Beginners: Following a Path From Euclid to Noether
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Algebraic Number Theory for Beginners (Paperback)
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Paperback. Condition: new. Paperback. This book introduces algebraic number theory through the problem of generalizing 'unique prime factorization' from ordinary integers to more general domains. Solving polynomial equations in integers leads naturally to these domains, but unique prime factorization may be lost in the process. To restore it, we need Dedekind's concept of ideals. However, one still needs the supporting concepts of algebraic number field and algebraic integer, and the supporting theory of rings, vector spaces, and modules. It was left to Emmy Noether to encapsulate the properties of rings that make unique prime factorization possible, in what we now call Dedekind rings. The book develops the theory of these concepts, following their history, motivating each conceptual step by pointing to its origins, and focusing on the goal of unique prime factorization with a minimum of distraction or prerequisites. This makes a self-contained easy-to-read book, short enough for a one-semester course. This book, meant for undergraduate mathematics students and teachers, introduces algebraic number theory through problems from ordinary number theory that can be solved with the help of algebraic numbers, using a suitable generalization of unique prime factorization. The material is motivated by weaving historical information throughout. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781009001922