p-adic Numbers (3^rd Ed., 3rd ed. 2020) An Introduction Universitext Series

1 Apéritif.- 2 Foundations.- 3 The p-adic Numbers.- 4 Exploring ℚ_p.- 5 Elementary Analysis in ℚ_p.- 6 Vector Spaces and Field Extensions.- 7 Analysis in ℂ_p.- 8 Fun With Your New Head.- A Sage and GP: A (Very) Quick Introduction.- B Hints and Comments on the Problems.- C A Brief Glance at the Literature.- Bibliography.- Index.

Fernando Q. Gouvêa is a number theorist and historian of mathematics. In number theory he has been interested in the connection between p-adic modular forms and deformations of Galois representations. As a historian his main focus is on the early history of algebraic number theory, but he has also written on other historical topics. He enjoys books and has written many book reviews for a wide range of publications. For many years he served as editor of MAA Focus and of MAA Reviews. His current project is a forthcoming book on the history of p-adic numbers and p-adic analysis in the first decades of the twentieth century. Gouvêa’s other books include Arithmetic of p-adic Modular Forms, A Guide to Groups, Rings, and Fields, and (with William P. Berlinghoff) Math through the Ages: A Gentle History for Teachers and Others.