tag:blogger.com,1999:blog-264226589944705290.post3620424287957049141..comments2023-11-05T03:45:25.001-08:00Comments on God Plays Dice: Counterexamples in XMichael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-264226589944705290.post-60233776036366972162010-08-11T09:03:23.025-07:002010-08-11T09:03:23.025-07:00And more:
Michael Capobianco, John C. Molluzzo: E...And more:<br /><br />Michael Capobianco, John C. Molluzzo: Examples and Counterexamples in Graph Theory<br /><br />P. Lounesto: Counterexamples in Clifford algebras. Advances in Applied Clifford Algebras 6 (1996), 69-104.<br />(see also the link)<br />http://users.tkk.fi/ppuska/mirror/Lounesto/counterexamples.htm<br /><br />A.B. Kharazishvili: Strange Functions in Real Analysis, Second Edition, 410p.<br /><br />J. Stoyanov: Counterexamples in Probability. John Wiley, Chichester, 1987, 1997.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-82030369144566175872010-08-11T08:39:29.045-07:002010-08-11T08:39:29.045-07:00More for the collection:
Fornaess J., Stensones B...More for the collection:<br /><br />Fornaess J., Stensones B. Lectures on Counterexamples in Several Complex Variables (Princeton, 1987)(252p)<br /><br />Khaleelulla S. Counterexamples in Topological Vector Spaces (LNM0936, Springer, 1982)(ISBN 354011565X)(199p)<br /><br />Two (not so convincing) lists of counterexamples in Algebra:<br /><br />http://mathoverflow.net/questions/29006/counterexamples-in-algebra<br /><br />http://ncatlab.org/nlab/show/counterexamples+in+algebraAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-15966711632369754562010-06-24T08:43:53.597-07:002010-06-24T08:43:53.597-07:00Um, Mitch, every PID is a UFD. You probably meant ...Um, Mitch, every PID <i>is</i> a UFD. You probably meant the other way, like Z[x].<br /><br />I've been collecting counterexamples for properties of integral domains like these for a while. Not likely ever to make them public, though--I'm no mathematician.lettermanhttps://www.blogger.com/profile/06584147571485976479noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-90751254875314000682009-09-28T16:39:40.730-07:002009-09-28T16:39:40.730-07:00Let me help you write Counterexamples in Combinato...Let me help you write <b>Counterexamples in Combinatorics</b>.<br /><br /><i>Chapter 1: Graphs</i><br />Section 1.1: Petersen's graph<br />Section 1.2: The random G(n,p) graph.Unknownhttps://www.blogger.com/profile/04752384695446260553noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-44655807851833235352009-09-24T21:19:09.561-07:002009-09-24T21:19:09.561-07:00Laymen have "intuition" in analysis? So...Laymen have "intuition" in analysis? Sounds like someone's never taught a calculus class.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-1538218844714064882009-09-24T21:03:28.283-07:002009-09-24T21:03:28.283-07:00It has something with layman intuition one can try...It has something with layman intuition one can try to apply in topology, analysis, and probability, but not so in algebra and NT. In the latter one tends to operate in a more rigorous fashion, just as there is little else to do...Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-18194166489820982032009-09-22T09:27:57.780-07:002009-09-22T09:27:57.780-07:00Mitch,
that's a good explanation. The need fo...Mitch,<br /><br />that's a good explanation. The need for these books might have to do with the way that textbooks are written, then; for some reason authors of algebra textbooks are more likely to include the counterexamples than authors of analysis textbooks.Michael Lugohttps://www.blogger.com/profile/01950197848369071260noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-91503738005284768162009-09-22T06:32:48.522-07:002009-09-22T06:32:48.522-07:00- "snowman"? "seahorse"? That&...- "snowman"? "seahorse"? That's some metaphor. It took me a while but I see what you're saying now.<br /><br />- One explanation (of the lack of algebra/combbinatorics examples) could be because (from what I see) those fields tend to have all the counterexamples right there as motivators for structure. For example, the chain of inclusion of integral domain, UFD, PID, Euclidean domain, and field. These are usual presented almost immediately after their definitions with the counterexample (a PID that's not a UFD, etc).<br /><br />Or it could be just no one's got around to it.Mitchhttps://www.blogger.com/profile/06352106235527027461noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-76405081924321462612009-09-21T11:53:04.543-07:002009-09-21T11:53:04.543-07:00The subject matter is the same vein but unfortunat...The subject matter is the same vein but unfortunately the price is not. Oh how I love Dover books.Tom LaGattahttps://www.blogger.com/profile/04734947352183054259noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-12311542878723888452009-09-21T10:40:57.885-07:002009-09-21T10:40:57.885-07:00I think it also has something to do with the fact ...I think it also has something to do with the fact that results in algebra are relatively robust. They have a lot to do with the general contours of mathematics rather than niggling about the borders to see the fine structure there. In a <i>very</i> loose analogy, algebra is the snowman in the Mandelbrot set while analysis is the seahorse valley.Anonymousnoreply@blogger.com