From Numbers to Analysis

Starting with the Zermelo-Fraenhel axiomatic set theory, this is a self-contained, step-by-step construction of real and complex numbers. The basic properties of real and complex numbers are developed, including a proof of the Fundamental Theorem of Algebra. Historical notes outline the evolution of the number systems and alert readers to the fact that polished mathematical concepts, as presented in lectures and books, are the culmination of the efforts of great minds over the years. The text also includes short life sketches of some of the contributing mathematicians. It provides the logical foundation of analysis and gives a basis to abstract algebra. It aims to complement those books on real analysis which begin with axiomatic definitions of real numbers.