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Imaginary Numbers, Unsolvable Equations, and Newton's Method (Abstract)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Diller, Jeffrey Alan |
| Copyright Year | 2011 |
| Abstract | You might have been led to believe that math is all about solving equations. Sadly, however, most equations can't actually be solved. The best one can do is to try to approximate their solutions. Newton's method, usually taught in calculus, is one of the oldest and best methods for accomplishing this. The weakness to the method is that it depends on already having a reasonable guess at where the solution lies. In this talk, we look at what happens when you apply Newton's method with no clue about the solution and even allow yourself to do ridiculous things like use imaginary numbers as starting guesses. Despite the unpromising premise, this story has a happy ending and some nice pictures. About the speaker: Jeff Diller is a professor of mathematics at the University of Notre Dame. He was a math major at the University of Dayton, graduating in 1988. With several minutes notice, he could probably still deliver one of the several talks that he was "persuaded" to give during his undergraduate days. He got his PhD at the University of Michigan in 1993 and held postdoctoral positions at Indiana University and Cornell University before arriving at Notre Dame in 1998. He is married with three boys, one of whom recently taught him to do cartwheels. 2011 Conference Page Math Events Page |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://ecommons.udayton.edu/cgi/viewcontent.cgi?article=1016&context=mth_kcs |
| Alternate Webpage(s) | http://math.nd.edu/assets/156051/m4e_diller_2_19_15.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
