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<html><head><title>198:206 - DISCRETE STRUCTURES II</title></head><body><center><h1>198-206: DISCRETE STRUCTURES II</h1><h3>Spring 1996</h3><h2>Course Syllabus</h2><b>INSTRUCTOR: Prof. Chitoor V. Srinivasan</b>,<br> Office:CoRE 324, Phone 908-445-2019, <br>Email: srinivas@cs.rutgers.edu.<p></center><b>TEXTS:</b><br><ul><li><b>Kenneth H. Rosen</b>, <i>Discrete Mathematics and itsApplications,</i> for the lectures on counting. This is the same textthat was used in Cs205.<li><b>Sheldon Ross</b> <i>A First Course inProbability</i>, MacMillan, 1994.<li>Notes to be bought from Copy Center in Busch Campus Student Center.</ul><p><b>Lectures:</b><br><ul><li><b>Lecture 1:</b> (Jan 16) Thought Experiments, SampleSpaces, Events, Probabilities and Counting. When is a countingcorrect? Sum and Product Rules.<br><i>Readings</i>: Relevant sections from Lecture notes, Chapter 4 Rosenand Chapter 1 of Sheldon Ross<p><li><b>Lecture 2:</b> (Jan 18) Subtraction and Division Rules(counting equivalence classes), Permutations, Combinations.<br><i>Readings</i>: Relevant sections from Lecture notes, Chapter 4 of RosenChapter 1 of Sheldon Ross.<p><li><b>Lecture 3:</b> (Jan 23) Permutations and Combinations,Selections with and without repetition, Pascal's Triangle.<br><i>Readings</i>: Relevant sections from Lecture notes, Chapter 4 of RosenChapter 1 of Sheldon Ross.<p><li><b>Lecture 4:</b> (Jan 25) Pigeon-Hole Principle.<br><i>Readings</i>: Relevant sections from Lecture notes, Chapter 4 of RosenChapter 1 of Sheldon Ross.<br><b>Start working on Review Problems I.</b><p><li><b>Lecture 5:</b> (Jan 30) Inclusion/Exclusion andDerangements.<br><i>Readings</i>: Relevant sections from Lecture notes, Rosen's book andChapter 1 of Sheldon Ross.<br> <b>Continue working on Review Problems I.</b><p><li><b>Lecture 6:</b> (Feb 1) Discussion of Review Problems I. Solutions will be distributed in Class.<br><i>Readings</i>: Complete your work on Review Problems I. You musthave questions to ask me during the review in class.<p><li><b>Lecture 7:</b> (Feb 6) Generating Functions I. <br><i>Readings</i>: Relevant sections from Lecture notes, Rosen's book andChapter 1 of Sheldon Ross. See Appendix 3 in Rosen's book. <br><b>Start working on Review Problems II.</b><p><li><b>Lecture 8:</b> (Feb 8) Generating Functions II. Workon review problems I and II. <br><i>Readings</i>: Class Notes and Appendix 3 in Rosen's Book. Continuework on Review Problems I and II.<p> <i> Supplemental Readings in theorder increasing sophistication</i>:<ul><li>Berman & Fryer, <i>Introduction to Combinatorics</i>, AcademicPress, 1972. Chaper 6. Gives a simple introduction with interestingexamples and problems. Easy reading.<li>C.L. Liu, <i>Introduction to Combinatorial Mathematics</i>,Computer Science Series, McGraw Hill, 1968. Chaper 2. Has somevery tough problems.<li>William Feller, <i>An Introduction to Probability Theory andits Applications</i>, Volume I (2nd Edition), John Wiley, 1958. ChapterX1. Discusses the subject thoroughly with advanced topics.</ul><p><li><b>Lecture 9:</b> (Feb 13) Recurrence Relations I: Using recurrence relations to state problems. Solutions of recurrencerelations.<br><i>Readings</i>: Class notes, Rosen Chapters 5.1 through 5.3 andAppendix 3. Continue work on review problems II.<p><li><b>Lecture 10:</b> (Feb 15) Recurrence Relations II: Closedform solutions for Homogeneous Recurrence Relations.<br><i>Readings</i>: Rosen Chapters 5.1 through 5.3 and Class Notes.Continue work on review problems II. <p><li><b>Lecture 11:</b> (Feb 20) Recurrence Relations III: UsingGenerating Functions to solve recurrence relations.<i>Readings</i>: Class notes and Appendix 3 in Rosen's book. Work onreview problems II.<p><li><b>Lecture 12:</b> (Feb 22) Discussion of Review Problems Iand II, Homework Problems and Previous Exam problems.<p><li><b>MID-TERM EXAMINATION: (Feb 27) Tuesday, 6:10 - 7:30 pm</b>.<p><li><b>Lecture 13:</b> (Feb 29) <i>Discrete Probability,Introduction</i>: Events, Axioms of Probability, Conditional Probability.<i>Readings</i>: Chapter 2 of Sheldon Ross. Start work on Review problems III.<p><li><b>Lecture 14:</b> (Mar 5) <i>Conditional ProbabilityI</i>: Joint and Conditional probabilities, total probability theoremand Bayes' theorem.<br><i>Readings</i>: Chapter 3 of Sheldon Ross. Continue work on Reviewproblems II and III.<p><li><b>Lecture 15:</b> (Mar 7) <i>Conditional ProbabilityII</i>: More on Total Probability and Bayes' theorems, andIndependence.<br><i>Readings</i>: Chapter 3 of Sheldon Ross. Continue work on Reviewproblems II and III.<p><li><b>Spring Recess</b>: Have a Happy Vacation!<p><li><b>Lecture 16:</b> (Mar 19) <i>Bernoulli Trials andDistributions\/</i>: <br><i>Readings</i>: Chapter 4 of Sheldon Ross. Continue work on Reviewproblems II and III.<p><li><b>Lecture 17:</b> (Mar 21) <i>Bernoulli Trials andDistributions\/</i>: <br><i>Readings</i>: Chapter 4 of Sheldon Ross. Continue work on Reviewproblems II and III. Start work on Review problems IV.<p><li><b>Lecture 18:</b> (Mar 26) <i>Random Variables,Expectation, Variance and Standard Deviation</i>:<br><i>Readings</i>: Chapter 4 of Sheldon Ross. Continue work on Reviewproblems III and IV.<p><li><b>Lecture 19:</b> (Mar 28) <i>Random Variables,Expectation, Variance and Standard Deviation</i>:<br><i>Readings</i>: Chapter 4 of Sheldon Ross. Continue work on Reviewproblems III and IV.<p><li><b>Lecture 20:</b> (Apr 2) <i>Distributions, Theirexpectations and Variance</i>.<br><i>Readings</i>: Chapter 4 of Sheldon Ross. Continue work on Reviewproblems III and IV.<p><li><b>Lecture 21:</b> (Apr 4) <i>Languages and Grammars andFinite State Machines</i>:<br><i>Readings</i>: Chapter 10.1 and 10.2 of book by Rosen.<p><li><b>Lecture 22:</b> (Apr 9) <i>Finite State Machines andLanguage Recognition</i>:<br><i>Readings</i>: Chapter 10 of Rosen. Continue work on Review problemsIII and IV.<p><li><b>Lecture 23:</b> (Apr 11) <i>Finite State Machines andLanguage Recognition</i>:<br><i>Readings</i>: Chapter 10 of Rosen. Continue work on Review problemsI, II, III and IV.<p><li><b>Lecture 24:</b> (Apr 16) <i>Graphs</i>.<br><i>Readings</i>: Chapter 7 of Rosen. Continue work on Review problemsI, II, III and IV. <p><li><b>Lecture 25:</b> (Apr 18) <i>Graphs</i>.<br><i>Readings</i>: Chapter 7 of Rosen. Continue work on Review problems I, II,III and IV.<p><li><b>Lecture 26:</b> (Apr 23) <i>Graphs</i>.<br><i>Readings</i>: Chapter 7 of book by Rosen. Continue work on Review problemsI, II, III and IV. <p><li><b>Lecture 27:</b> (Apr 25) <i>Review</i>.<br><i>Readings</i>: Do all review problems and look through all pastmid-term and final examination questions. <p><li><b>Lecture 28:</b> (Apr 30) <i>Review</i>.<p><li><b>FINAL EXAMINATION: Thursday, May 2nd, 8 to 11 pm</b>.</ul></body></html>⌨️ 快捷键说明
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