Katok Svetlana. p-adic Analysis Compared with Real

American Mathematica Society, 2007. — 170 p.Arithmetic of the p-adic Numbers
From Q to R; the concept of completion
Normed fields
Construction of the completion of a normed field
The field of p-adic numbers Qp
Arithmetical operations in Qp
The p-adic expansion of rational numbers
Hensel's Lemma and congruences
Algebraic properties of p-adic integers
Metrics and norms on the rational numbers. Ostrowski's Theorem
A digression: what about Qg if g is not a prime?
The Topology of Qp vs. the Topology of R
Elementary topological properties
Cantor sets
Euclidean models of Zp
Elementary Analysis in Qp
Sequences and series
p-adic power series
Can a p-adic power series be analytically continued?
Some elementary functions
Further properties of p-adic exponential and logarithm
Zeros of p-adic power series
p-adic Functions
Locally constant functions
Continuous and uniformly continuous functions
Points of discontinuity and the Baire Category Theorem
Differentiability of p-adic functions
Isometries of Qp
Interpolation
Answers, Hints, and Solutions for Selected Exercises