Elementary Decision Theory [EPUB]
07 February 2016, 15:10
1986 | EPUB | 15.4MB
This well-known and highly respected introduction to decision theory was developed at Stanford University. It furnishes a simple and clear-cut method of exhibiting the fundamental aspects of statistical problems. Beginners will find this treatment a motivating introduction to important mathematical notions such as set, function, and convexity.
The Arrow Impossibility Theorem [EPUB]
05 February 2016, 21:52
2015 | EPUB | 14.95MB
Kenneth Arrow's pathbreaking "impossibility theorem" was a watershed in the history of welfare economics, voting theory, and collective choice, demonstrating that there is no voting rule that satisfies the four desirable axioms of decisiveness, consensus, nondictatorship, and independence.
In this book, Amartya Sen and Eric Maskin explore the implications of Arrow's theorem. Sen considers its ongoing utility, exploring the theorem's value and limitations in relation to recent research on social reasoning, while Maskin discusses how to design a voting rule that gets us closer to the ideal – given that achieving the ideal is impossible. The volume also contains a contextual introduction by social choice scholar Prasanta K. Pattanaik and commentaries from Joseph E. Stiglitz and Kenneth Arrow himself, as well as essays by Sen and Maskin outlining the mathematical proof and framework behind their assertions.
A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours [EPUB]
29 January 2016, 08:22
2015 | EPUB | 1.01MB
Employing intuitive ideas from mathematics, this quirky "meta-memoir" raises questions about our lives that most of us don't think to ask, but arguably should: What part of memory is reliable fact, what part creative embellishment? Which favorite presuppositions are unfounded, which statistically biased? By conjoining two opposing mindsets--the suspension of disbelief required in storytelling and the skepticism inherent in the scientific method--bestselling mathematician John Allen Paulos has created an unusual hybrid, a composite of personal memories and mathematical approaches to re-evaluating them.
Entertaining vignettes from Paulos's biography abound--ranging from a bullying math teacher and a fabulous collection of baseball cards to romantic crushes, a grandmother’s petty larceny, and his quite unintended role in getting George Bush elected president in 2000. These vignettes serve as springboards to many telling perspectives: simple arithmetic puts life-long habits in a dubious new light; higher dimensional geometry helps us see that we're all rather peculiar; nonlinear dynamics explains the narcissism of small differences cascading into very different siblings; logarithms and exponentials yield insight on why we tend to become bored and jaded as we age; and there are tricks and jokes, probability and coincidences, and much more.
For fans of Paulos or newcomers to his work, this witty commentary on his life--and yours--is fascinating reading.