Real Analysis for Graduate Students: Measure and Integration Theory
by Richard F. Bass
Publisher: CreateSpace 2011
Number of pages: 206
Nearly every Ph.D. student in mathematics needs to take a preliminary or qualifying examination in real analysis. This book provides the necessary tools to pass such an examination. Every effort was made to present the material in as clear a fashion as possible.
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by Marcel B. Finan - Arkansas Tech University
The text is designed for an introductory course in real analysis suitable to upper sophomore or junior level students who already had the calculus sequel and a course in discrete mathematics. The content is considered a moderate level of difficulty.
by Lee Larson - University of Louisville
From the table of contents: Basic Ideas (Sets, Functions and Relations, Cardinality); The Real Numbers; Sequences; Series; The Topology of R; Limits of Functions; Differentiation; Integration; Sequences of Functions; Fourier Series.
by Bruce K. Driver - University of California, San Diego
Contents: Natural, integer, and rational Numbers; Fields; Real Numbers; Complex Numbers; Set Operations, Functions, and Counting; Metric Spaces; Series and Sums in Banach Spaces; Topological Considerations; Differential Calculus in One Real Variable.
by Jiri Lebl - Lulu.com
This is a free online textbook for a first course in mathematical analysis. The text covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, and sequences of functions.