Foundations of Analysis

by Edmund Landau

Why does $2 \times 2 = 4$? What are fractions? Imaginary numbers? Why do the laws of algebra hold? And how do we prove these laws? 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? Thanks to the genius of Dedekind, Cantor, Peano, Frege and Russell, such questions can now be given a satisfactory answer. This English translation of Landau's famous Grundlagen der Analysis-also available from the AMS-answers these important questions.

Genres: Mathematics, Nonfiction, Academic, Textbooks

136 pages, Hardcover

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.

[Ahmet Kasabalı · Rating 4 out of 5]

Helpful and relevant book about the construction of real numbers. Just to be sure you read all of the theorems...

[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.