Analysis I/ Terence Tao

Includes index

Introduction -- Starting at the beginning: the natural numbers -- Set theory -- Integers and rationals -- The real numbers -- Limits of sequences -- Series -- Infinite sets -- Continuous unctions on R -- Differentiation of functions -- The Riemann integral -- A: Appendix: the basics of mathematical logic -- B Appendix: the decimal system

Part one of a two-volume introduction to real analysis. The emphasis is on rigour and on foundations. The material starts at the very beginning - the construction of the number systems and set theory - then goes on to the basics of analysis, through to power series, variable calculus and Fourier analysis, and finally to the Lebesgue integral.