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Incomplete Notes on Fraleigh's Abstract Algebra (4th ed.)
[PS (gzipped PS 168 KB)] [PDF 337 KB)] These are my notes on James B. Fraleigh's excellent book on abstract algebra, A First Course in Abstract Algebra. My notes are on the fourth edition, however (the latest being the 7th edition.) They are almost complete, and at 44 pages, quite extensive. |
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Converting Triangulations to Grids (A Proposal). June 1998
[PS (gzipped PS 47 KB)] [PDF 108 KB)] This is a proposal I wrote for a project as a graduate student. For various reasons, I didn't work on it. Others have worked on variants of this approach since then. |
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Survey of Results on Minimal Triangulations. May 1998
[PS (gzipped PS 49 KB)] [PDF 122 KB)] For any closed compact 2-manifold, there is a finite number of minimal (irreducible) triangulations. Therefore, we may obtain any triangulation of a surface by splitting vertices of a minimal triangulation of the surface. The number of vertices in these minimal triangulations is linear in the genus of the underlying surface. |
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Insolubility of the Problem of Homeomorphy by A. A. Markov. 1958
[PS (gzipped PS 42 KB)] [PDF 111 KB)] As far as I know, this is the only English translation of A. A. Markov's paper. I presented it as part of my qualification examination in theory. For additional information, as well as good references, see the following writeup: [PS (gzipped PS 25 KB)] [PDF 50 KB)] |
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The Monty Hall Problem. January 1998
[PS (gzipped PS 40 KB)] [PDF 78 KB)] This is a short report about the infamous ``Monty Hall Problem.'' The report contains two solutions to the problem: an analytic and a numerical one. The analytic solution uses probability theory and corresponds to a mathematician's point of view in solving problems. The numerical solution simulates the problem on a large scale to arrive at the solution and therefore corresponds to a computer scientist's point of view. |