<?xml version="1.0" encoding="utf-8"?>
<lom:lom xsi:schemaLocation="http://ocw.mit.edu/xmlns/LOM http://ocw.mit.edu/xsd/LOM/lomv1.0/lomv1.0.xsd http://ocw.mit.edu/xmlns/ocwLOM http://ocw.mit.edu/xsd/ocwLOM/ocwlomv1.0/ocwlomv1.0.xsd" xmlns="http://ocw.mit.edu/xmlns/LOM" xmlns:lom="http://ocw.mit.edu/xmlns/LOM" xmlns:ocwlom="http://ocw.mit.edu/xmlns/ocwLOM" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
  <!--************************************************************ This LOM
			record was produced by an automatic transformation to IEEE LOM, from
			OpenCourseWare's (OCW) initial version of Learning Object Metadata (LOM). (The
			initial version was based on IMS Global Consortium's LOM.)
			********************************************************--><!--***************************--><!--**** GENERAL ****--><!--***************************--><lom:general uniqueElementName="general"><lom:title uniqueElementName="title"><lom:string language="en">Counting III</lom:string></lom:title><lom:description><lom:string language="en">This resource explains the Bookkeeper rule, Binomial theorem, Poker hands, magic trick, and combinatorial proof.</lom:string></lom:description><lom:language>en</lom:language><lom:aggregationLevel uniqueElementName="aggregationLevel"><lom:source uniqueElementName="source">LOMv1.0</lom:source><lom:value uniqueElementName="value">2</lom:value></lom:aggregationLevel></lom:general><!--***************************--><!--**** LIFECYCLE ****--><!--***************************--><lom:lifeCycle uniqueElementName="lifeCycle"><lom:version uniqueElementName="version"><lom:string language="en">Spring 2005</lom:string></lom:version><lom:contribute><lom:role><lom:source uniqueElementName="source">OCW_LOMv1.0</lom:source><lom:value uniqueElementName="value">Author</lom:value></lom:role><lom:entity>Devadas, Srinivas</lom:entity><lom:date uniqueElementName="date"><lom:dateTime uniqueElementName="dateTime">2006-07-11</lom:dateTime></lom:date></lom:contribute><lom:contribute><lom:role><lom:source uniqueElementName="source">OCW_LOMv1.0</lom:source><lom:value uniqueElementName="value">Contributor</lom:value></lom:role><lom:entity>Lehman, Eric</lom:entity><lom:date uniqueElementName="date"><lom:dateTime uniqueElementName="dateTime">2006-07-11</lom:dateTime></lom:date></lom:contribute><lom:contribute><lom:role><lom:source uniqueElementName="source">OCW_LOMv1.0</lom:source><lom:value uniqueElementName="value">Contributor</lom:value></lom:role><lom:entity>Meyer, Albert</lom:entity><lom:date uniqueElementName="date"><lom:dateTime uniqueElementName="dateTime">2005-09-07</lom:dateTime></lom:date></lom:contribute><lom:contribute><lom:role><lom:source uniqueElementName="source">OCW_LOMv1.0</lom:source><lom:value uniqueElementName="value">Contributor</lom:value></lom:role><lom:entity>Leiserson, Charles</lom:entity><lom:date uniqueElementName="date"><lom:dateTime uniqueElementName="dateTime">2005-09-07</lom:dateTime></lom:date></lom:contribute></lom:lifeCycle><!--***************************--><!--**** TECHNICAL ****--><!--***************************--><lom:technical uniqueElementName="technical"><lom:location>/NR/rdonlyres/22005A39-5E6D-47C3-8E65-199E702E7B62/0/l15_counting3.pdf</lom:location><lom:format>application/pdf</lom:format><lom:otherPlatformRequirements><lom:string language="en">Adobe廬 Reader廬 software is required to view this .pdf file.</lom:string></lom:otherPlatformRequirements><lom:size>284062</lom:size><lom:requirement><lom:orComposite><lom:type uniqueElementName="type"><lom:source uniqueElementName="source">LOMv1.0</lom:source><lom:value uniqueElementName="value">browser</lom:value></lom:type><lom:name uniqueElementName="name"><lom:source uniqueElementName="source">LOMv1.0</lom:source><lom:value uniqueElementName="value">ms-internet explorer</lom:value></lom:name><lom:minimumVersion uniqueElementName="minimumVersion">5.1</lom:minimumVersion></lom:orComposite><lom:orComposite><lom:type uniqueElementName="type"><lom:source uniqueElementName="source">LOMv1.0</lom:source><lom:value uniqueElementName="value">browser</lom:value></lom:type><lom:name uniqueElementName="name"><lom:source uniqueElementName="source">LOMv1.0</lom:source><lom:value uniqueElementName="value">netscape communicator</lom:value></lom:name><lom:minimumVersion uniqueElementName="minimumVersion">4.7</lom:minimumVersion></lom:orComposite></lom:requirement></lom:technical><!--***************************--><!--**** EDUCATIONAL ****--><!--***************************--><lom:educational><lom:learningResourceType><lom:source uniqueElementName="source">LOMv1.0</lom:source><lom:value uniqueElementName="value">lecture</lom:value></lom:learningResourceType><lom:context><lom:source uniqueElementName="source">OCW_LOMv1.0</lom:source><lom:value uniqueElementName="value">Undergraduate</lom:value></lom:context><lom:description><lom:string language="en">Course notes.</lom:string></lom:description></lom:educational><!--***************************--><!--**** RIGHTS ****--><!--***************************--><lom:rights uniqueElementName="rights"><lom:copyrightAndOtherRestrictions uniqueElementName="copyrightAndOtherRestrictions"><lom:source uniqueElementName="source">LOMv1.0</lom:source><lom:value uniqueElementName="value">yes</lom:value></lom:copyrightAndOtherRestrictions><lom:cost><lom:source uniqueElementName="source">LOMv1.0</lom:source><lom:value uniqueElementName="value">no</lom:value></lom:cost><lom:description><lom:string language="en">This site (c) Massachusetts Institute of Technology 2003. Content within individual courses is (c) by the individual authors unless otherwise noted. The Massachusetts Institute of Technology is providing this Work (as defined below) under the terms of this Creative Commons public license ("CCPL" or "license"). The Work is protected by copyright and/or other applicable law. Any use of the work other than as authorized under this license is prohibited. By exercising any of the rights to the Work provided here, You (as defined below) accept and agree to be bound by the terms of this license. The Licensor, the Massachusetts Institute of Technology, grants You the rights contained here in consideration of Your acceptance of such terms and conditions.</lom:string></lom:description></lom:rights><!--***************************--><!--**** RELATION ****--><!--***************************--><lom:relation><lom:kind uniqueElementName="kind"><lom:source uniqueElementName="source">LOMv1.0</lom:source><lom:value uniqueElementName="value">ispartof</lom:value></lom:kind><lom:resource uniqueElementName="resource"><lom:identifier><lom:catalog uniqueElementName="catalog">OCW Master Course Number</lom:catalog><lom:entry uniqueElementName="entry">6.042J Mathematics for Computer Science Spring 2005</lom:entry></lom:identifier><lom:description><lom:string language="en">Mathematical tools and methods for computer science and engineering. Emphasis on development of rigorous thinking, analytical skills, and mathematical sophistication while learning elementary discrete mathematics. Topics: mathematical proofs; induction and well-ordering; divisibility and congruences; asymptotic notation and growth of functions; sets, relations, functions, and graphs; counting theory; recurrences and generating functions; and discrete probability.</lom:string></lom:description></lom:resource></lom:relation><!--***************************--><!--**** CLASSIFICATION ****--><!--***************************--><lom:classification><lom:taxonPath><lom:source uniqueElementName="source"><lom:string language="en">CIP</lom:string></lom:source><lom:taxon><lom:id uniqueElementName="id">300801</lom:id><lom:entry uniqueElementName="entry"><lom:string language="en">Mathematics and Computer Science</lom:string></lom:entry></lom:taxon></lom:taxonPath><lom:taxonPath><lom:source uniqueElementName="source"><lom:string language="en">CIP</lom:string></lom:source><lom:taxon><lom:id uniqueElementName="id">270303</lom:id><lom:entry uniqueElementName="entry"><lom:string language="en">Computational Mathematics</lom:string></lom:entry></lom:taxon></lom:taxonPath><lom:keyword><lom:string language="en">Elementary discrete mathematics for computer science and engineering</lom:string></lom:keyword><lom:keyword><lom:string language="en">mathematical definitions</lom:string></lom:keyword><lom:keyword><lom:string language="en">proofs and applicable methods</lom:string></lom:keyword><lom:keyword><lom:string language="en">formal logic notation</lom:string></lom:keyword><lom:keyword><lom:string language="en">proof methods</lom:string></lom:keyword><lom:keyword><lom:string language="en">induction</lom:string></lom:keyword><lom:keyword><lom:string language="en">well-ordering</lom:string></lom:keyword><lom:keyword><lom:string language="en">sets</lom:string></lom:keyword><lom:keyword><lom:string language="en">relations</lom:string></lom:keyword><lom:keyword><lom:string language="en">elementary graph theory</lom:string></lom:keyword><lom:keyword><lom:string language="en">integer congruences</lom:string></lom:keyword><lom:keyword><lom:string language="en">asymptotic notation and growth of functions</lom:string></lom:keyword><lom:keyword><lom:string language="en">permutations and combinations</lom:string></lom:keyword><lom:keyword><lom:string language="en">counting principles</lom:string></lom:keyword><lom:keyword><lom:string language="en">discrete probability</lom:string></lom:keyword><lom:keyword><lom:string language="en">recursive definition</lom:string></lom:keyword><lom:keyword><lom:string language="en">structural induction</lom:string></lom:keyword><lom:keyword><lom:string language="en">state machines and invariants</lom:string></lom:keyword><lom:keyword><lom:string language="en">recurrences</lom:string></lom:keyword><lom:keyword><lom:string language="en">generating functions</lom:string></lom:keyword><lom:keyword><lom:string language="en">6.042J</lom:string></lom:keyword><lom:keyword><lom:string language="en">6.042</lom:string></lom:keyword><lom:keyword><lom:string language="en">18.062J</lom:string></lom:keyword><lom:keyword><lom:string language="en">18.062</lom:string></lom:keyword></lom:classification></lom:lom>