COT 5507  Analytic Methods in CS  Fall 2018  List of Lecture Topics 
 Lecture  Topic  Reading assignments 
Week 1  08/28  Introduction. Generalization and specialization: Pythagorean, tiling, and lines in a plane.  Chapter 1.2 and 1.3, Scribe 1

 08/30  Guessing and the Repertoire Method.
 Scribe 2

Week 2  09/04  No class. (Tung is out of town.)


 09/06  More on the Repertoire Method: Josephus problem
 Chapter 1.3 
Week 3  09/11  Integration and Perturbation Methods.
 Chapter 2.1, 2.2, 2.4, and 2.5 
 09/13  Quiz 1. Summation factor. Tower of Hanoi. Review of probability theory.
 Chapter 1.1 and 8.1 
Week 4  09/18  Probabilistic analysis: the hiring problem and Randomized Quicksort.  Scribe 3 
 09/20  Review: summation factor and the perturbation method. Hw1 up.  
Week 5
 09/25  Review: repertoire method, integration method, and probabilistic analysis.  
 09/27  Hw1 due. Review: probabilistic analysis.  
Week 6
 10/02  Quiz 2. Hw2 up. Generating functions.  Chapter 7.1, 7.2, and 7.3 
 10/04  Generating functions, continued.  Scribe 4 
Week 7  10/09  No class. (School closed due to hurricane.)  
 10/11  No class. (School closed due to hurricane.)  
Week 8
 10/16  Basics of generating functions: partial fractions, expansion, and secondorder linear recurrences.  
 10/18  Hw2 due. Review of practice midterm.  
Week 9
 10/23  Midterm 1  
 10/25  Manipulating generating functions. Catalan's number.  
Week 10  10/30  Catalan's number, continued. Randomized Quicksort and Generating Functions.  Scribe 5 
 11/01  Hw3 up. Coin Changing. Tiling.  
Week 11
 11/06  Exponential Generating Function: Derangement. Variance: Definition and Example.  Chapter 8.2 and 8.3 
 11/08  Hw3 due. Quiz 3. Linearity of Variance. Chebyshev's inequality. LazySelect.  Scribe 6 
Week 12
 11/13  Hw4 up. LazySelect, continued.  
 11/15  Probability generating functions: definition and examples.  
Week 13  11/20  Hw4 due. Sum of RVs and randomly stopped sum. Review of LazySelect.  
 11/22  No class (Thanksgiving)  
Week 14
 11/27  Review of probability generating functions: negative binomial distribution.  
 11/29  Midterm 2. Quiz 2. Review  
Week 15
 12/04   
 12/06   