P-adic Analysis compared with Real Course description: The aim of this course is to understand $p$-adic numbers from the point of view of number theory, topology and analysis. Syllabus: Concept of completion, Normed fields and their completion, The field of $p$-adic numbers (Q_p), Hensel’s Lemma and congruences, Ostrowski’s theorem, The topology of $Q_p$ vs the topology of R, Elementary analysis in $Q_p$, $p$- adic functions. References:
- p-adic analysis compared with real: Svetlana Katok, student mathematical library, volume 37
- Local Fields: J.W.S. Cassels, London Mathematical Society, Student Texts 3
- A course in Arithmetic, J-P.Serre, Graduate texts in Mathematics