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Mathematical Mountaintops: The Five Most Famous Problems of All Time
Libro usado en buenas condiciones, por su antiguedad podria contener señales normales de uso
- GenresMathematicsNonfiction
177 pages, Hardcover
First published January 1, 2001
2 people are currently reading
37 people want to read
About the author
John L. Casti
60 books22 followersJohn L. Casti (born 1943) is an author, mathematician, and entrepreneur.
As a mathematician and researcher, Casti received his Ph.D. under Richard Bellman at the University of Southern California. He worked at the RAND Corporation in Santa Monica, CA, and served on the faculties of the University of Arizona, New York University and Princeton University, before moving to Vienna in 1973 to become one of the first members of the research staff at the International Institute for Applied Systems Analysis (IIASA) in Laxenburg, Austria. In 1986, he left IIASA to take up a position as a Professor of Operations Research and System Theory at the Technical University of Vienna. He also served as a member of the External Faculty of the Santa Fe Institute in Santa Fe, New Mexico, USA, from 1992-2002, where he worked extensively on the application of biological metaphors to the mathematical modeling of problems in economics, finance and road-traffic networks, as well as on large-scale computer simulations for the study of such networks.
His primary research interests have shifted somewhat in recent years from the natural sciences to the exploration of questions in the social and behavioral realm. One thread has been exploration of the relationship between the social "mood" of a population its biasing effect on actions and behaviors. In this direction, his 2010 book, Mood Matters: From Rising Skirt Lengths to the Collapse of World Powers, published by Copernicus Books, NY, addresses the directions and patterns of social causation and their implications for future trends and collective social events, such as styles in popular culture, the outcome of political processes, and even the rise and fall of civilizations. His most recent book is X-EVENTS: The Collapse of Everything, which addresses the underlying cause of extreme events generated by human inattention, misunderstanding, error, stupidity and/or malevolent intent. The English original edition was published in June 2012 by HarperCollins/Morrow, New York. The book now exists in 15 foreign editions, as well, including German, Japanese, Russian, Dutch, Korean and Portuguese.
As an entrepreneur, Casti formed two companies in Santa Fe and London in 2000, Qforma, Inc. and SimWorld, Ltd, respectively, devoted to the employment of tools and concepts from modern system theory for the solution of problems in business and finance, as well as health care. Qforma merged with SkilaMederi in June 2013. In early 2005 he returned to Vienna where he co-founded The Kenos Circle, a professional society that aims to make use of complexity science in order to gain a deeper insight into the future than that offered by more conventional statistical tools.
For several years, Professor Casti was a Senior Research Scholar at the International Institute for Applied Systems Analysis in Laxenburg, Austria, where he created an initiative for the study on Extreme Events in Human Society. In January 2012 he left IIASA to form a new research institute in Vienna, The X-Center, devoted to the study of human-caused extreme events. The X-Center has now expanded to a network of affiliated X-Centers in Helsinki, Tokyo, Seoul, New York and Singapore. Since early 2013, Dr. Casti has been serving as a Senior Research Fellow at the Center for Complex Systems and Enterprises at the Stevens Institute of Technology in the USA.
As an author, Casti has written more than 120 scientific articles and seven technical monographs and textbooks on mathematical modeling. In addition, he was formerly editor of the journals Applied Mathematics & Computation (Elsevier, New York) and Complexity (Wiley, New York). In 1989 his text/reference works Alternate Realities: Mathematical Models of Nature and Man (Wiley, 1989) was awarded a prize by the Association of American Publishers in a competition among all scholarly books published in mathematics and the natural sciences. In 1992, he also published Reality Rules (Wiley, New York), a t
As a mathematician and researcher, Casti received his Ph.D. under Richard Bellman at the University of Southern California. He worked at the RAND Corporation in Santa Monica, CA, and served on the faculties of the University of Arizona, New York University and Princeton University, before moving to Vienna in 1973 to become one of the first members of the research staff at the International Institute for Applied Systems Analysis (IIASA) in Laxenburg, Austria. In 1986, he left IIASA to take up a position as a Professor of Operations Research and System Theory at the Technical University of Vienna. He also served as a member of the External Faculty of the Santa Fe Institute in Santa Fe, New Mexico, USA, from 1992-2002, where he worked extensively on the application of biological metaphors to the mathematical modeling of problems in economics, finance and road-traffic networks, as well as on large-scale computer simulations for the study of such networks.
His primary research interests have shifted somewhat in recent years from the natural sciences to the exploration of questions in the social and behavioral realm. One thread has been exploration of the relationship between the social "mood" of a population its biasing effect on actions and behaviors. In this direction, his 2010 book, Mood Matters: From Rising Skirt Lengths to the Collapse of World Powers, published by Copernicus Books, NY, addresses the directions and patterns of social causation and their implications for future trends and collective social events, such as styles in popular culture, the outcome of political processes, and even the rise and fall of civilizations. His most recent book is X-EVENTS: The Collapse of Everything, which addresses the underlying cause of extreme events generated by human inattention, misunderstanding, error, stupidity and/or malevolent intent. The English original edition was published in June 2012 by HarperCollins/Morrow, New York. The book now exists in 15 foreign editions, as well, including German, Japanese, Russian, Dutch, Korean and Portuguese.
As an entrepreneur, Casti formed two companies in Santa Fe and London in 2000, Qforma, Inc. and SimWorld, Ltd, respectively, devoted to the employment of tools and concepts from modern system theory for the solution of problems in business and finance, as well as health care. Qforma merged with SkilaMederi in June 2013. In early 2005 he returned to Vienna where he co-founded The Kenos Circle, a professional society that aims to make use of complexity science in order to gain a deeper insight into the future than that offered by more conventional statistical tools.
For several years, Professor Casti was a Senior Research Scholar at the International Institute for Applied Systems Analysis in Laxenburg, Austria, where he created an initiative for the study on Extreme Events in Human Society. In January 2012 he left IIASA to form a new research institute in Vienna, The X-Center, devoted to the study of human-caused extreme events. The X-Center has now expanded to a network of affiliated X-Centers in Helsinki, Tokyo, Seoul, New York and Singapore. Since early 2013, Dr. Casti has been serving as a Senior Research Fellow at the Center for Complex Systems and Enterprises at the Stevens Institute of Technology in the USA.
As an author, Casti has written more than 120 scientific articles and seven technical monographs and textbooks on mathematical modeling. In addition, he was formerly editor of the journals Applied Mathematics & Computation (Elsevier, New York) and Complexity (Wiley, New York). In 1989 his text/reference works Alternate Realities: Mathematical Models of Nature and Man (Wiley, 1989) was awarded a prize by the Association of American Publishers in a competition among all scholarly books published in mathematics and the natural sciences. In 1992, he also published Reality Rules (Wiley, New York), a t
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Displaying 1 - 3 of 3 reviews
April 26, 2016
While relatively short and well written, this attempt at describing progress in several key problems in mathematics is still a difficult slog at points. However, the effort is rewarding.
The work deals with "the five most famous problems of all time." In order, they are:
-Hilbert's Tenth Problem, on solutions to Diophantine equations
-The Four Color Theorem
- The Continuum Hypothesis- is there an infinity "between" the cardinality of the natural numbers and of the real numbers?
-The Kepler Conjecture on the best method to pack equal sized spheres.
- Fermat's Last Theorem, probably the most famous of the lot.
The author also covers seven additional problems under investigation in an epilogue, and provides an annotated bibliography useful for follow on reading.
There were some passages that were difficult to comprehend, but perhaps this was due to shortcomings in the reader's mathematical background. There were some typos and errors in graphics (e.g., Figure 4.3 has D mislabeled as A', and the equation on p143 has an extra +).
The work deals with "the five most famous problems of all time." In order, they are:
-Hilbert's Tenth Problem, on solutions to Diophantine equations
-The Four Color Theorem
- The Continuum Hypothesis- is there an infinity "between" the cardinality of the natural numbers and of the real numbers?
-The Kepler Conjecture on the best method to pack equal sized spheres.
- Fermat's Last Theorem, probably the most famous of the lot.
The author also covers seven additional problems under investigation in an epilogue, and provides an annotated bibliography useful for follow on reading.
There were some passages that were difficult to comprehend, but perhaps this was due to shortcomings in the reader's mathematical background. There were some typos and errors in graphics (e.g., Figure 4.3 has D mislabeled as A', and the equation on p143 has an extra +).
July 21, 2011
didn't read all of this
February 5, 2017
Very well choosen collection of problems illustrating philosophical concerns as much as innovative solution methodologies.
JC does an excellent job in motivating the problems, and even manages a reasonable description of techniques in proofs that span hundreds of pages without too much hand waving.
JC does an excellent job in motivating the problems, and even manages a reasonable description of techniques in proofs that span hundreds of pages without too much hand waving.
Displaying 1 - 3 of 3 reviews