COT 5507 - Analytic Methods in CS - Fall 2018 - List of Lecture Topics

LectureTopicReading assignments
Week 108/28Introduction. Generalization and specialization: Pythagorean, tiling, and lines in a plane. Chapter 1.2 and 1.3, Scribe 1
08/30Guessing and the Repertoire Method.
Scribe 2
Week 209/04No class. (Tung is out of town.)

   09/06More on the Repertoire Method: Josephus problem
Chapter 1.3
Week 309/11Integration and Perturbation Methods.
Chapter 2.1, 2.2, 2.4, and 2.5
09/13Quiz 1. Summation factor. Tower of Hanoi. Review of probability theory.
Chapter 1.1 and 8.1
Week 409/18Probabilistic analysis: the hiring problem and Randomized Quicksort. Scribe 3
09/20Review: summation factor and the perturbation method. Hw1 up. 
Week 5
09/25Review: repertoire method, integration method, and probabilistic analysis. 

09/27Hw1 due. Review: probabilistic analysis. 
Week 6
10/02Quiz 2. Hw2 up. Generating functions.  Chapter 7.1, 7.2, and 7.3
10/04Generating functions, continued. Scribe 4
Week 710/09No class. (School closed due to hurricane.)
10/11No class. (School closed due to hurricane.)
Week 8
10/16Basics of generating functions: partial fractions, expansion, and second-order linear recurrences.

10/18Hw2 due. Review of practice midterm. 
Week 9
10/23Midterm 1
10/25Manipulating generating functions. Catalan's number. 
Week 1010/30Catalan's number, continued. Randomized Quicksort and Generating Functions.Scribe 5
11/01Hw3 up. Coin Changing. Tiling. 
Week 11
11/06Exponential Generating Function: Derangement.  Variance: Definition and Example. Chapter 8.2 and 8.3
11/08Hw3 due. Quiz 3. Linearity of Variance. Chebyshev's inequality. LazySelect. Scribe 6
Week 12
11/13Hw4 up. LazySelect, continued.  
11/15Probability generating functions: definition and examples.
Week 1311/20Hw4 due. Sum of RVs and randomly stopped sum. Review of LazySelect. 
11/22No class (Thanksgiving)
Week 14
11/27Review of probability generating functions: negative binomial distribution. 

11/29Midterm 2. Quiz 2Review
Week 15