Limits, Limits Everywhere: The Tools of Mathematical Analysis
“Limits, limits everywhere” is not a usual popular book on Mathematics nor a traditional analysis textbook of definitions, theorems and proofs. The author is able to mix both styles relating informal language to mathematical language and giving proofs that are deep but easy to read and follow.
The book focuses on the explanation of one of the most fundamental concepts of mathematical analysis, the concept of limits. The book's first part deals with the concepts of integer, prime, rational and real numbers, inequalities, limits, bounded sequences, and infinity series. The second part explains the special numbers e, π, and γ, infinite products, continued fractions, Cantor's different types of infinities, and the constructions of the real numbers. Throughout the book, there are some brief history remarks that explain why and for what these mathematical tools are necessary.
This is a well-written book with a style that is easy to read and follow, which can be recommended for undergraduate students interested in finding out more about Mathematics.