The Mathematics of Coordinated Inference

A Study of Generalized Hat Problems

Nonfiction, Science & Nature, Mathematics, Topology, Logic
Cover of the book The Mathematics of Coordinated Inference by Christopher S. Hardin, Alan D. Taylor, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Christopher S. Hardin, Alan D. Taylor ISBN: 9783319013336
Publisher: Springer International Publishing Publication: October 17, 2013
Imprint: Springer Language: English
Author: Christopher S. Hardin, Alan D. Taylor
ISBN: 9783319013336
Publisher: Springer International Publishing
Publication: October 17, 2013
Imprint: Springer
Language: English

Two prisoners are told that they will be brought to a room and seated so that each can see the other. Hats will be placed on their heads; each hat is either red or green. The two prisoners must simultaneously submit a guess of their own hat color, and they both go free if at least one of them guesses correctly. While no communication is allowed once the hats have been placed, they will, however, be allowed to have a strategy session before being brought to the room. Is there a strategy ensuring their release? The answer turns out to be yes, and this is the simplest non-trivial example of a “hat problem.”

This book deals with the question of how successfully one can predict the value of an arbitrary function at one or more points of its domain based on some knowledge of its values at other points. Topics range from hat problems that are accessible to everyone willing to think hard, to some advanced topics in set theory and infinitary combinatorics. For example, there is a method of predicting the value f(a) of a function f mapping the reals to the reals, based only on knowledge of f's values on the open interval (a – 1, a), and for every such function the prediction is incorrect only on a countable set that is nowhere dense.

The monograph progresses from topics requiring fewer prerequisites to those requiring more, with most of the text being accessible to any graduate student in mathematics. The broad range of readership includes researchers, postdocs, and graduate students in the fields of set theory, mathematical logic, and combinatorics. The hope is that this book will bring together mathematicians from different areas to think about set theory via a very broad array of coordinated inference problems.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Two prisoners are told that they will be brought to a room and seated so that each can see the other. Hats will be placed on their heads; each hat is either red or green. The two prisoners must simultaneously submit a guess of their own hat color, and they both go free if at least one of them guesses correctly. While no communication is allowed once the hats have been placed, they will, however, be allowed to have a strategy session before being brought to the room. Is there a strategy ensuring their release? The answer turns out to be yes, and this is the simplest non-trivial example of a “hat problem.”

This book deals with the question of how successfully one can predict the value of an arbitrary function at one or more points of its domain based on some knowledge of its values at other points. Topics range from hat problems that are accessible to everyone willing to think hard, to some advanced topics in set theory and infinitary combinatorics. For example, there is a method of predicting the value f(a) of a function f mapping the reals to the reals, based only on knowledge of f's values on the open interval (a – 1, a), and for every such function the prediction is incorrect only on a countable set that is nowhere dense.

The monograph progresses from topics requiring fewer prerequisites to those requiring more, with most of the text being accessible to any graduate student in mathematics. The broad range of readership includes researchers, postdocs, and graduate students in the fields of set theory, mathematical logic, and combinatorics. The hope is that this book will bring together mathematicians from different areas to think about set theory via a very broad array of coordinated inference problems.

More books from Springer International Publishing

Cover of the book Nutrition and Health in a Developing World by Christopher S. Hardin, Alan D. Taylor
Cover of the book Food Security and Sustainability by Christopher S. Hardin, Alan D. Taylor
Cover of the book Engineering Graphics by Christopher S. Hardin, Alan D. Taylor
Cover of the book Web Engineering by Christopher S. Hardin, Alan D. Taylor
Cover of the book LQG for the Bewildered by Christopher S. Hardin, Alan D. Taylor
Cover of the book In Memory Data Management and Analysis by Christopher S. Hardin, Alan D. Taylor
Cover of the book Carbon Markets by Christopher S. Hardin, Alan D. Taylor
Cover of the book Genetic Programming by Christopher S. Hardin, Alan D. Taylor
Cover of the book Digital Subsampling Phase Lock Techniques for Frequency Synthesis and Polar Transmission by Christopher S. Hardin, Alan D. Taylor
Cover of the book Formal and Analytic Solutions of Diff. Equations by Christopher S. Hardin, Alan D. Taylor
Cover of the book A Project-Based Introduction to Computational Statics by Christopher S. Hardin, Alan D. Taylor
Cover of the book Host Defense Peptides and Their Potential as Therapeutic Agents by Christopher S. Hardin, Alan D. Taylor
Cover of the book Behavior Engineering and Applications by Christopher S. Hardin, Alan D. Taylor
Cover of the book (En)Gendering Taiwan by Christopher S. Hardin, Alan D. Taylor
Cover of the book Equity and Quality Dimensions in Educational Effectiveness by Christopher S. Hardin, Alan D. Taylor
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy