Foundations of Analysis: The Arithmetic of Whole, Rational, Irrational and Complex Numbers

by Edmund Landau, F. Steinhardt

Why does $2 \times 2 = 4$? What are fractions? Imaginary numbers? Why do the laws of algebra hold? What are the properties of the numbers on which the Differential and Integral Calculus is based? In other words, What are numbers? And why do they have the properties we attribute to them? This work answers such questions.

Genres: Mathematics, Nonfiction, Academic, Textbooks

372 pages, Paperback

First published January 1, 1957

Reviews

[Rudy · Rating 4 out of 5]

The book at stake might be physically compact, it is nonetheless open and certainly unbounded, intellectually: Landau delineates herein the very basis of arithmetics as commonly used in more well-known fields of mathematics in a concise, almost military fashion. It took me five months to go through it, progressing a few pages at a time, as a companion to texts operating at a higher level, that is, relying on the results exposed hereby. As a practical tip: the best introduction to real analysis I know of. Highly recommended.

[Samuel · Rating 5 out of 5]

Clear, concise and reigious exposition of preliminaries for real analysis.

[Mi Lia · Rating 5 out of 5]

It's safe to say that after reading this book I've decided I wanted to become a mathematician.
The text was as well written, consistent and clean as if you read a source code in Scheme.
Absolutely fantastic read.