PPT-1 Conjectures on

Cops and Robbers Games Played on Graphs Anthony Bonato Ryerson University Toronto Canada University of Iceland Mathematics Seminar Cops and Robbers Cops and Robbers Cops and Robbers 2. Hellerstein University of California Berkeley hellersteincsberkeleyedu ABSTRACT The rise of multicore processors and cloud computing is putting enormous pressure on the software community to 64257nd solu tions to the dif64257culty of parallel and di Stein Harv ard Univ ersit fcalemathharvardedu httpwwwmathharvardedufcale Harv ard Univ ersit wasmathharvardedu httpmodularfasharvardedu Abstract In this pap er study divisibilit of discriminan ts of Hec algebras asso ciated to spaces of cusp forms o 2 Informatik Saarland University German Research Ce nter for Arti64257cial Intelligence DFKI Saarbr57512ucken Germany email autexierdfkide Yale University New Haven USA email carstencsyaleedu Abstract For automatic theorem provers it is as important also guessing, his particular conjectures spun out almost voluptuously. Gavin imagined that one of the men had decided that this creature of alluring mystery was writing a long and painful letter to a Sir Karl Popper Overview Popper’s speech, given in 1953, addresses two major problems in the philosophy of science that were of interest to him during most of his career. The first of these Mathematical . Conjecture?. Arash. Rastegar. Sharif University of Technology. Advices to a problem solver. 1) Writing neat and clean. 2) Writing down the summary of arguments. 3) Clarifying the logical structure . began to feel dubious about their claims to scientific status. My problem perhaps first took the simple form, 'What is wrong with Marxism, Psycho-analysis, and individual psychology? Why are they so Daniel . Dadush. Centrum . Wiskunde. & . Informatica. (CWI). Oded. . Regev. New York University. . A Reverse . Minkowski. . Inequality & . its conjectured Strengthening. . . Strong Reverse . Introduction and Coordinated Effects. Adrian Majumdar. Adrian.Majumdar@rbbecon.com. Contributors. Adrian Majumdar. Benoît Durand. Chris Doyle. Alan Crawford.  . We are indebted to Greg Shaffer for his invaluable comments and contributions to Chapters 2 and 5 and to Glen Weyl for his detailed and insightful comments on Chapter 4.. on Cops and Robbers. Anthony Bonato. Ryerson University. Genus. (Aigner, . Fromme. , 84) . planar graphs (genus . 0. ) have cop number . ≤ 3.. (Clarke, 02) . outerplanar. graphs have cop number . Making conjectures. Proof. Adapted from . Thinking Mathematically . (Consider the table of Contents. ). One up and One Down:. Multiplication. Start with a 7 x 7 (square) array. One up and One Down:. Multiplication. Constructing. CONJECTURES. Generating. examples. Getting literature. Definition of 132-pattern. Let [n] = {1,2,…,n}. . p. = a. 1. a. 2. …a. n. is a permutation of [n].. Consider . a. i. , . a. Daniel . Dadush. Centrum . Wiskunde. & . Informatica. (CWI). Oded. . Regev. New York University. . A Reverse . Minkowski. . Inequality & . its conjectured Strengthening. . . Strong Reverse . To form conjectures through inductive reasoning. To disprove a conjecture with a counterexample. To avoid fallacies of inductive reasoning. Example 1. You’re at school eating lunch. You ingest some air while eating, which causes you to belch. Afterward, you notice a number of students staring at you with disgust. You burp again, and looks of distaste greet your natural bodily function. You have similar experiences over the course of the next couple of days. Finally, you conclude that belching in public is socially unacceptable. The process that lead you to this conclusion is called.