In this new introduction to undergradute real analysis the author takes a different approach from past studies of the subject by introducing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman.

The exposition is informal and relaxed, with many helpful asides, and examples Contains an excellent selection of more than 500 exercises Ideal for self-study

Autorentext

Zusammenfassung
Berkeley, California, USA CHARLES CHAPMAN PUGH Contents 1 Real Numbers 1 1 Preliminaries 1 2 Cuts . 40 2 A Taste of Topology 51 1 Metric Space Concepts 51 2 Compactness 76 3 Connectedness 82 4 Coverings . 179 3 Exercises 186 4 Function Spaces 201 1 Uniform Convergence and CO[a, b] 201 2 Power Series .

Inhalt
1 Real Numbers.- 2 A Taste of Topology.- 3 Functions of a Real Variable.- 4 Function Spaces.- 5 Multivariable Calculus.- 6 Lebesgue Theory.