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Listed in: Mathematics and Statistics, as MATH-359
Harris B. Daniels (Section 01)
The p-adic numbers were first introduced by Kurt Hensel near the end of the nineteenth century. Since their introduction they have become a central object in modern number theory, algebraic geometry, and algebraic topology. These numbers give a new set of fields (one for each prime p) that contain the rational numbers and behave in some ways like the real numbers. While these fields are similar to the real numbers in some respects, they also possess some unique and unexpected properties. The main objective of this course will be to rigorously construct the p-adic numbers and explore some of the algebraic, analytic, and topological properties that make them interesting.
Requisite: Math 350 or consent of the instructor. Limited to 32 students. Spring semester. Professor Daniels.
If Overenrolled: Preference will be given to pre-registered students, math majors, and juniors and seniors.