Counterexamples in Probability

Last updated

Counterexamples in Probability is a mathematics book by Jordan M. Stoyanov. Intended to serve as a supplemental text for classes on probability theory and related topics, it covers cases where a mathematical proposition might seem to be true but actually turns out to be false.

Contents

First published in 1987, the book received a second edition in 1997 and a third in 2013.

Reception

Robert W. Hayden, reviewing the book for the Mathematical Association of America, found it unsuitable for reading cover-to-cover, while recommending it as a reference for "graduate students and probabilists...the small audience whose needs match the title and level." [1] Similarly, Geoffrey Grimmett called the book an "excellent browse" that, despite being a "serious work of scholarship" would not be suitable as a course textbook. [2] R. W. Hammett wrote that it "should become a classic supplement" for those students who wish to go above and beyond their ordinary course requirements, and that "it should also become essential to those who plan to work in the field." [3] D. R. Grey gave it a positive evaluation as a reference text while noting that the counterexamples it includes range "from those accessible to first-year undergraduates ... to those only comprehensible to specialists in stochastic processes". [4]

Richard Durrett gave a more negative review, saying that "Most readers will learn a few interesting things" but regarding most of the counterexamples to be well-known or redundant. While Durrett appreciated the illustrations by A. T. Fomenko, [5] the more positive review by F. W. Steutel did not, calling them a "rather unhappy cross" between Dalí and Escher. [6]

Publication history

The book was also issued in Russian editions in 1999 and 2012.

See also

Related Research Articles

<span class="mw-page-title-main">Persi Diaconis</span> American mathematician and statistician

Persi Warren Diaconis is an American mathematician of Greek descent and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University.

<span class="mw-page-title-main">Ronald Graham</span> American mathematician (1935–2020)

Ronald Lewis Graham was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He was president of both the American Mathematical Society and the Mathematical Association of America, and his honors included the Leroy P. Steele Prize for lifetime achievement and election to the National Academy of Sciences.

<span class="mw-page-title-main">Joe Harris (mathematician)</span> American mathematician

Joseph Daniel Harris is a mathematician at Harvard University working in the field of algebraic geometry. After earning an AB from Harvard College, where he took Math 55, he continued at Harvard to study for a PhD under Phillip Griffiths.

<span class="mw-page-title-main">Constance Reid</span> American writer

Constance Bowman Reid was the author of several biographies of mathematicians and popular books about mathematics. She received several awards for mathematical exposition. She was not a mathematician but came from a mathematical family—one of her sisters was Julia Robinson, and her brother-in-law was Raphael M. Robinson.

<span class="mw-page-title-main">Yuval Peres</span>

Yuval Peres is a mathematician known for his research in probability theory, ergodic theory, mathematical analysis, theoretical computer science, and in particular for topics such as fractals and Hausdorff measure, random walks, Brownian motion, percolation and Markov chain mixing times. He was born in Israel and obtained his Ph.D. at the Hebrew University of Jerusalem in 1990 under the supervision of Hillel Furstenberg. He was a faculty member at the Hebrew University and the University of California at Berkeley, and a Principal Researcher at Microsoft Research in Redmond, Washington. Peres has been accused of sexual harassment by several female scientists.

Raymond H. Thompson is a Canadian scholar of medieval literature specializing in King Arthur and the Matter of Britain, and in the reinterpretation of this material in modern literature. He is a professor emeritus in the Department of English at Acadia University in Canada.

Priscilla E. (Cindy) Greenwood is a Canadian mathematician who is a professor emeritus of mathematics at the University of British Columbia. She is known for her research in probability theory.

<span class="mw-page-title-main">Michael Woodroofe</span> American probabilist and statistician (1940–2022)

Michael Barrett Woodroofe was an American probabilist and statistician. He was a professor of statistics and of mathematics at the University of Michigan, where he was the Leonard J. Savage Professor until his retirement. He was noted for his work in sequential analysis and nonlinear renewal theory, in central limit theory, and in nonparametric inference with shape constraints.

Jana Jurečková is a Czech statistician, known for her work on rankings, robust statistics, outliers and tails, asymptotic theory, and the behavior of statistical estimates for finite sample sizes.

Sherman Kopald Stein is an American mathematician and an author of mathematics textbooks. He is a professor emeritus at the University of California, Davis. His writings have won the Lester R. Ford Award and the Beckenbach Book Prize.

Hazel Perfect was a British mathematician specialising in combinatorics.

E. Joyce Snell is a British statistician who taught in the mathematics department at Imperial College London. She is known for her work on residuals and ordered categorical data, and for her books on statistics.

Lynn Gamwell is an American nonfiction author and art curator known for her books on art history, the history of mathematics, the history of science, and their connections.

Thomas Shelburne Ferguson is an American mathematician and statistician. He is a professor emeritus of mathematics and statistics at the University of California, Los Angeles.

Judith Veronica Field is a British historian of science with interests in mathematics and the impact of science in art, an honorary visiting research fellow in the Department of History of Art of Birkbeck, University of London, former president of the British Society for the History of Mathematics, and president of the Leonardo da Vinci Society.

Ruma Falk was an Israeli psychologist and philosopher of mathematics known for her work on probability theory and human understanding of probability and statistics.

Robert Anthony Hyman (1928–2011) was a British historian of computing.

Nils Donald Ylvisaker, often known as Don Ylvisaker, was an American mathematical statistician.

Counterexamples in Probability and Statistics is a mathematics book by Joseph P. Romano and Andrew F. Siegel. It began as Romano's senior thesis at Princeton University under Siegel's supervision, and was intended for use as a supplemental work to augment standard textbooks on statistics and probability theory.

References

  1. Hayden, Robert W. (2014-10-27). "Counterexamples in Probability". MAA Reviews . Mathematical Association of America . Retrieved 2024-04-17.
  2. Grimmett, Geoffrey (1989). Journal of the Royal Statistical Society, Series A . 152 (1): 135–136. doi:10.2307/2982850.{{cite journal}}: CS1 maint: untitled periodical (link)
  3. Hammond, R. W. (1990). Journal of the American Statistical Association . 85 (410): 592. doi:10.2307/2289807.{{cite journal}}: CS1 maint: untitled periodical (link)
  4. Grey, D. R. (1989). The Statistician . 38 (1): 79–80. doi:10.2307/2349025.{{cite journal}}: CS1 maint: untitled periodical (link)
  5. Durrett, Richard (1989). American Scientist . 77 (4): 405. JSTOR   27855910.{{cite journal}}: CS1 maint: untitled periodical (link)
  6. Steutel, F. W. (1989). Bulletin of the London Mathematical Society . 21 (3): 300–301. doi:10.1112/blms/21.3.300.{{cite journal}}: CS1 maint: untitled periodical (link)