Transition to Analysis with Proof

Reviews / Votes

This book is designed for undergraduate students and provides an introduction to analysis including an introduction to proofs. Namely, it starts with basic logic along with set theory and suggests plenty of instructive examples on how to do a correct mathematical reasoning. Then, he moves to functions, sequences, basic topology, differentiation, and integration. The text ends with power series and elementary transcendental functions. Each section of the book has a clear and convenient structure. It opens with "Preliminary remarks", which in a few sentences explain what the following passage is about. Then, the main text follows in which every statement is equipped with an instructive proof. Examples and exercises help master the material of the topic. \A look back" blocks consist of a few simple questions (like "What is a monotone sequence?") and serve as a test if you understand the basics.

General remarks. The language of the book is quite vivid and lively, at the same time it is available for non-native students. The text has useful navigation tools like glossary, index, and the table of notations. The only disadvantage, in my opinion, is the lack of solutions and answers to the exercises.

Nikita Evseev (Novosibirsk)