Graduate Programs      Graduate Home Ph D Programs Masters Degree Ph D Program Requirements Course Descriptions Current Courses Admissions Current Graduate Students Graduate Student Seminar SIAM Chapter Seminar Recent Graduates Incoming Students Graduate Seminar Zilin Jiang Carnegie Mellon University Title: An Expedition to the World of $p$-adic Numbers Abstract: The foundation of Real Analysis is based on the field of real numbers, the extension of the rationals under its canonical norm, the absolute value. However, for any prime $p$, the rationals can be extended by an alternative norm, and the product is the $p$-adic number system.In this talk, we will start with Ostrowski theorem, which lists all possible (nonequivalent) norms on the rationals. This will be followed by the definition of $p$-adic numbers and some of its properties. A classical application of $p$-adic numbers, Monsky's Theorem, will be presented at the end of the talk.Date: Thursday, January 15, 2015Time: 5:30 pmLocation: Wean Hall 8220Submitted by:  Zilin Jiang