TY  - BOOK
AU  - Berberian,Sterling K
TI  - A first course in real analysis
T2  - Undergraduate texts in mathematics
SN  - 9781493991044
U1  - 515 
PY  - 1994///
CY  - New York
PB  -  Springer-Verlag
KW  - Mathematical Analysis
KW  - Numbers-
KW  - Real
KW  - Mathematics
N1  - Includes bibliographical refernces and Index
N2  - The book offers an initiation into mathematical reasoning, and into the mathematician's mind-set and reflexes. Specifically, the fundamental operations of calculus--differentiation and integration of functions and the summation of infinite series--are built, with logical continuity (i.e., "rigor"), starting from the real number system. The first chapter sets down precise axioms for the real number system, from which all else is derived using the logical tools summarized in an Appendix. The discussion of the "fundamental theorem of calculus," the focal point of the book, especially thorough. The concluding chapter establishes a significant beachhead in the theory of the Lebesgue integral by elementary means.
ER  -