This self-contained handbook providing broad coverage on the foundations of mathematical analysis, is intended as a study guide for advanced undergraduates and beginning graduate students in mathematics and is a reference for more advanced mathematicians. It provides an introduction to a wide range of topics including set theory and mathematical logic; algebra; toplogy; normed spaces; integration theory; toplogical vector spaces; and differential equations. The author demonstrates the relationships between these topics and includes a few chapters on set theory and logic (...) to explain the lack of examples in the presentation of classical pathological objects through nonconstructive proofs. (shrink)

In Decision Space: Multidimensional Utility Analysis, first published in 2001, Paul Weirich increases the power and versatility of utility analysis and in the process advances decision theory. Combining traditional and novel methods of option evaluation into one systematic method of analysis, multidimensional utility analysis is a valuable tool. It provides formulations of important decision principles, such as the principle to maximize expected utility; enriches decision theory in solving recalcitrant decision problems; and provides in particular for the cases in which an (...) expert must make a decision for a group of people. The multiple dimensions of this analysis create a decision space broad enough to accommodate all factors affecting an option's utility. The book will be of interest to advanced students and professionals working in the subject of decision theory, as well as to economists and other social scientists. (shrink)