MATH 419
Algebraic Number Theory Fall 2017 Division III; Quantative/Formal Reasoning;
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We all know that integers can be factored into prime numbers and that this factorization is essentially unique. In more general settings, it often still makes sense to factor numbers into “primes,” but the factorization is not necessarily unique! This surprising fact was the downfall of Lamé’s attempted proof of Fermat’s Last Theorem in 1847. Although a valid proof was not discovered until over 150 years later, this error gave rise to a new branch of mathematics: algebraic number theory. In this course, we will study factorization and other number-theoretic notions in more abstract algebraic settings, and we will see a beautiful interplay between groups, rings, and fields.
The Class: Type: lecture/seminar
Limit: 40
Expected: 20
Class#: 1731
Requirements/Evaluation: evaluation will be based primarily on homework assignments and exams
Prerequisites: MATH 355, or permission of instructor
Distributions: Division III; Quantative/Formal Reasoning;

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