CS 206: Intro to Discrete Structures II.
Instructor: S. Muthukrishnan, x2379, Core 319. muthu@cs.rutgers.edu.

Meeting:  Mondays and Thursday  12--1.20 pm, Hill 254. Office hours: Thursdays: 10--11.

TA: Nikos Leonardos. Office hours: Mondays 10am-12pm. Recitation: Thursdays.

Details: There will be suggested problems and exercises, grade will be based  on homeworks, mid term and finals.

Course Text Book: Sheldon Ross, “A First Course in Probability”, 8/e, Prentice Hall, 2008.
There will be a copy in the library at Hill center (reserved for graduates), and two will be
send at the library in CIRC building (where reserved books for
undergraduate courses are held).

Schedule:

Jan    20, 24, 27, 31
Feb   3, 7, 10, 14, 17, 21, 24, 28
Mar   3, 7, 10, 14, 17, 21, 24, 28, 31
Apr  4, 7, 11, 14, 18, 21, 25, 28
May 2, 5

Schedule constraints: March 14--17 (Spring break).

Notes:
* Recitations will begin on Jan 27.
* HWs: Form groups of 3, and HWs are due at the beginning of the class on the due date.

Jan 20: Review of counting, binomial theorem.
Jan 24: Review of set theory, number of solutions for an equation.
HW1:  Problems 10, 33. Theoretical exercises: 12(a), 21. Self-Test Problems and Exercises: 17. (Chapter 1, Pages 16--21). Due Jan 31st.
Jan 27: Cancelled, due to being snowed out of Newark airport.
Jan 31: Deadline for forming groups and getting on mailing list.
Jan 31: Probability (assuming all outcomes equally likely), Connection to set theory.
Feb 1: HW 2:  Chapter 1, Theoretical exercise: 12(b). Chapter 2, Problems 3, Theoretical exercise: 6, 8. Due Feb 7.
Feb 4:  Conditional probability, Bayes Rule
Feb 7:  Independence. HW3: Problems 3.20 (Page 103), 3.43 (Page 105), Theoretical Exercise 3.4, 3.8. Self Test Problems: 3.20 (Page 115).
Feb 10: Examples.
Feb 14: Random variables, prob mass and cumulative distributions, and expectations. HW4: Problems 4.17, 4.21 (Page 174), Theoretical exercises 4.5 (Page 180), Selftest Problems 4.6 (Page 183).
Feb 18: Variance, Bernoulli and Binomial random variables (and their expectation and variance)
Feb 21: Other examples of random variables: Poisson, Geometric, etc.
Feb 24: Other r.v: hypergrometric, negative binomial, Zipf. Proof of  linearity of expectation. HW5: Problems 4.83 and 4.85 (Page 179), Theoretical exercises 4.10  (Page 180), 4.19 (Page 181) and 4.36 (Page 183). Due Date: March 3.
Feb 28: Continuous random variables (definitions, uniform, normal): HW6:  Problems 5.14 (Pg 225), Theoretical Exercises 5.9 (Pg 228).  Due Mar 07.                                                                      
Mar 03: Lecturer: Nikos Leonardos. Normal, Cauchy and other random variables. NO RECITATION.
Mar 07: Finish chapter 5
Mar 10: MIDTERM.   Exam.
Mar 21: More distributions.
Mar 24: Nikos: expectation properties.
Mar 28: Nikos: probabilistic method examples. 
Mar 31: Chap 6: Joint prob Dist: Discrete, cumulative, marginal, independent, sums of random variables (convolution).
Apr 04: Chap 6: Joint Prob Dist: Continuous.
Apr 07: Probability and its uses (estimate pi, sample mean, Probabilistic Method, Examples.  Cut.
Apr 11: Ways to estimate E(), E(g()), for joint distributions. n,k such that no monochromatic k clique. Coupon collecting. Some NOTES.
HW6. P1: Each  student i in a class has F(i) friends. Show that the students can be partitioned into two groups such that each student has no more than F(i)/2 friends in their group. P2: 6.10 (Pg 287)
P3: 6.22 (Pg 288). P4: 6.28 (Pg 293).  Due Apr 21.
Apr 14:
Apr 18: Nikos:

May 2: