Ebook Mathematical Fallacies and Paradoxes (Dover Books on Mathematics), by Bryan Bunch
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Mathematical Fallacies and Paradoxes (Dover Books on Mathematics), by Bryan Bunch
Ebook Mathematical Fallacies and Paradoxes (Dover Books on Mathematics), by Bryan Bunch
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From ancient Greek mathematics to 20th-century quantum theory, paradoxes, fallacies and other intellectual inconsistencies have long puzzled and intrigued the mind of man. This stimulating, thought-provoking compilation collects and analyzes the most interesting paradoxes and fallacies from mathematics, logic, physics and language.
While focusing primarily on mathematical issues of the 20th century (notably Godel's theorem of 1931 and decision problems in general), the work takes a look as well at the mind-bending formulations of such brilliant men as Galileo, Leibniz, Georg Cantor and Lewis Carroll ― and describes them in readily accessible detail. Readers will find themselves engrossed in delightful elucidations of methods for misunderstanding the real world by experiment (Aristotle's Circle paradox), being led astray by algebra (De Morgan's paradox), failing to comprehend real events through logic (the Swedish Civil Defense Exercise paradox), mistaking infinity (Euler's paradox), understanding how chance ceases to work in the real world (the Petersburg paradox) and other puzzling problems. Some high school algebra and geometry is assumed; any other math needed is developed in the text. Entertaining and mind-expanding, this volume will appeal to anyone looking for challenging mental exercises.
- Sales Rank: #535786 in Books
- Published on: 1997-07-01
- Released on: 1997-07-01
- Original language: English
- Number of items: 1
- Dimensions: 8.47" h x .46" w x 5.40" l, .54 pounds
- Binding: Paperback
- 240 pages
About the Author
Marcia Ascher is Professor Emerita of Mathematics at Ithaca College. She is the coauthor of "Code of the Quipu: A Study in Media, Mathematics, and Culture" and the author of "Ethnomathematics: A Multicultural View of Mathematical Ideas."
Most helpful customer reviews
38 of 39 people found the following review helpful.
Intriguing
By mcgalaxy
Being a physicist who has always had an interest in math, I've found this book a good way to learn about aspects of mathematics usually saved for metamathematical philosophy courses. The book is not a textbook but it has enough depth for you to understand why paradoxes like Godel's, Grelling's and Russell arise and what their implications are. Each chapter gets more interesting and more complicated than the previous. Even though the book does not have a completely polished feel, I recommend it to any recreational mathematician.
21 of 21 people found the following review helpful.
This is a Great Book for Math Fans
By A Customer
This is a great book for people who love mathematics, including: recreational math enthusiasts, math teachers, professors and other university level math instructors, curious and self-motivated students, etc. This book provides numerous examples of how seemingly logical steps can lead to mathematically fallacious results. The level of math ranges from advanced high school to college level math, but the level is not really important ... what is important is the insights one can get from looking at common mathematical mistakes.
This book may also be of interest to neuroscientists, cognitive scientists, and psychologists who are interested in how human beings learn and apply mathematics. On a somewhat related note, I have noticed that (for some strange reason) this book has attracted a set of rather bizarre reviewers (see below). Please ignore them and buy this inexpensive and insightful book on math.
13 of 14 people found the following review helpful.
Informal and engaging
By Skymariner
This is a great informal treatment of some of the more notable paradoxes and fallacies of mathematics and mathematical reasoning, old and new. Bunch's prose style is clear and unencumbered and his presentation of each topic - from his easily resolved fallacies and paradoxes of basic algebra and geometry to the deeper and unresolved paradoxes of logic and analysis - is always clean, well-illustrated and engaging.
At a glance, he treats:
The Liar paradox and Godel's Incompleteness theorems
Zeno's and the Sorites paradoxes and the conceptual difficulties associated with the continuum
The existence of irrational magnitudes and some basic philosophical issues associated with existence proofs
The Petersburg paradox
The paradoxes of Infinity and the Formalist and Intuitionist responses to them
The set theoretic paradoxes of Cantor, Russell, and Burali-Forti
The paradoxes of the axiom of choice including the Cantor diagonilisation, Skolem, Hausdorff and Tarski-Banach parodoxes
and a range of thought experiments which highlight the difficulties that may be asociated with applying abstract reasoning to the real world - notably those of the Thompson lamp experiment and Tarski-Banach golden sphere manufacturing plant.
If you want a good popular treatment of the subject matter with a detailed and informal emphasis on the key themes mathematical logic, then this is the book for you. The informal description Godel's first Incompleteness theorem is excellent, as is the discussion of the paradoxes of self reference as they appear in set theory and logic. As such, I would recommend it as excellent recreational reading for anyone with a budding interest in mathematical logic, whether they be math graduates or high-school students.
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