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Graph Theory, Part 2 - Princeton University

GraphTheory, Part27 ColoringSupposethatyouareresponsiblefors chedulingtimesforlecturesin a University . Youwantto make surethatany two lectureswitha commonstudent occurat di erent timesto avoidacon couldputthevariouslecturesona chartandmarkwithan\X"any pairthathasstudents in common:LectureACGHILMPSA stronomyXXXXC hemistryXXGreekXXXXXH istoryXXXXI talianXXXL atinXXXXXXM usicXXXXP hilosophyXXSpanishXXXXA moreconvenient representationof thisinformationis a graphwithonevertexforeach lectureandin which two verticesarejoinedif thereis a con ictbetweenthem:GMLIAPSCHNow, we cannotscheduletwo lecturesat thesametimeif thereis a con ict,butwe wouldliketo useas fewseparatetimesas possible,subjectto thisconstraint. How many di erent timesarenecessary?

Graph Theory, Part 2 7 Coloring Suppose that you are responsible for scheduling times for lectures in a university. You want ... De nition 16 (Chromatic Number). The chromatic number of a graph is the minimum number of colors in a proper coloring of that graph.

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Graph Theory, Part 2 - Princeton University

web.math.princeton.edu

Graph Theory, Part 2 7 Coloring ... We color G with color 5 (light blue), because it cannot be colored with any of the four other colors. G M I L A S H P C color 1 color 2 color 3 color 4 color 5 So we see that the quality of our coloring (with fewer colors being considered better) from the

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Stochastic Calculus, Filtering, and Stochastic Control

web.math.princeton.edu

Introduction This course is about stochastic calculus and some of its applications. As the name suggests, stochastic calculus provides a mathematical foundation for the treatment of equations that involve noise. The various problems which we will be dealing with,

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LECTURE NOTES IN ANALYSIS (2011) Sergiu Klainerman

web.math.princeton.edu

LECTURE NOTES IN ANALYSIS (2011) Sergiu Klainerman Department of Mathematics, Princeton University, Princeton NJ 08544 E-mail address: seri@math.princeton.edu. Part 1 INTRODUCTION TO PDE. 1. The world of PDE To start with partial di erential equations, just like ordinary di erential or integral

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Analysis of Multiscale Methods for Stochastic Di erential ...

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Analysis of Multiscale Methods for Stochastic Di erential Equations WEINAN E ... ERIC VANDEN-EIJNDEN Courant Institute Abstract We analyze a class of numerical schemes proposed in [25] for stochastic di erential equations with multiple time-scales. Both advective and di usive time-scales are con- ... in the limit of " ! 0 is a stochastic di ...

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Lecture Notes on General Relativity Columbia University

web.math.princeton.edu

what is now known as special relativity. 1.2 The Birth of Special Relativity In 1905 Einstein published a paper titled \On the electrodynamics of moving bodies", where he described algebraic relations governing the motion of uniform observers so that Maxwell equations have the same form regardless of the observer’s frame. In order to achieve his

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Probabilityand RandomProcesses - Math

web.math.princeton.edu

0 Introduction 0.1Whatisprobability? Most simply stated, probability is the study of randomness. Randomness is ofcourseeverywherearoundus ...

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Ramon van Handel - Princeton University

web.math.princeton.edu

dimension" refers to the presence of many distinct but interacting random variables; in others, the problems arise in high-dimensional spaces and prob-abilistic methods enter the picture indirectly. It would be out of the question to cover all of these topics in a single course.

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