Alain M. Robert

Kurt Hensel (1861-1941) discovered the p-adic numbers around the turn of the century. These exotic numbers (or so they appeared at first) are now well-established in the mathematical world and used more and more by physicists as well. This book offers a self-contained presentation of basic p-adic analysis. The author is especially interested in the analytical topics in this field. Some of the features which are not treated in other introductory p-adic analysis texts are topological models of p-adic spaces inside Euclidean space, a construction of spherically complete fields, a p-adic mean value theorem and some consequences, a special case of Hazewinkel's functional equation lemma, a remainder formula for the Mahler expansion, and most importantly a treatment of analytic elements.

This short but rigorous book approaches the main ideas of linear algebra through carefully selected examples and relevant applications. It is intended for students with various interests in mathematics, as well as established scientists seeking to refresh their basic mathematical culture.The book is also a good introduction to functional analysis and quantum theory since it discusses the general principles of linear algebra without finiteness assumptions.

This short but rigorous book approaches the main ideas of linear algebra through carefully selected examples and relevant applications. It is intended for students with various interests in mathematics, as well as established scientists seeking to refresh their basic mathematical culture.The book is also a good introduction to functional analysis and quantum theory since it discusses the general principles of linear algebra without finiteness assumptions.

Kurt Hensel (1861-1941) discovered the p-adic numbers around the turn of the century. These exotic numbers (or so they appeared at first) are now well-established in the mathematical world and used more and more by physicists as well. This book offers a self-contained presentation of basic p-adic analysis. The author is especially interested in the analytical topics in this field. Some of the features which are not treated in other introductory p-adic analysis texts are topological models of p-adic spaces inside Euclidean space, a construction of spherically complete fields, a p-adic mean value theorem and some consequences, a special case of Hazewinkel's functional equation lemma, a remainder formula for the Mahler expansion, and most importantly a treatment of analytic elements.