Chapter 1. Introduction.- Chapter 2. Starting at the beginning: the natural numbers.- Chapter 3. Set theory.- Chapter 4. Integers and rationals.- Chapter 5. The real numbers.- Chapter 6. Limits of sequences.- Chapter 7. Series.- Chapter 8. Infinite sets.- Chapter 9. Continuous functions on R.- Chapter 10. Differentiation of functions.- Chapter 11. The Riemann integral.
Terence "Terry" Chi-Shen Tao, FAA FRS, is an Australian mathematician. His areas of interests are in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Professor Tao is a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. He maintains a personal mathematics blog, which has been described by Timothy Gowers as "the undisputed king of all mathematics blogs".