EECS 70
Discrete Mathematics and Probability Theory
Fall 2014
Anant Sahai
Homework 10
This homework is due November 10, 2014, at 12:00 noon.
1. Section Rollcall!
In your self-grading for this question, give yourself a 10, and write down what you wrote for
EECS 70
Discrete Mathematics and Probability Theory
Spring 2014
Anant Sahai
Homework 4
This homework is due Feb 17 2014, at 12:00 noon.
1. Pentagons, Pentagrams, and Pythagoreans: a high-school geometry proof of the existence of irrational
numbers by way
EECS 70
Discrete Mathematics and Probability Theory
Spring 2014
Anant Sahai
Homework 2
This homework is due Feb 3 2014, at 12:00 noon.
1. Matrix Induction
1 1
Guess a formula for the matrix computation
0 1
n
and prove by induction that your formula is cor
EECS 70
Discrete Mathematics and Probability Theory
Spring 2014
Anant Sahai
Homework 9
This homework is due Mar 31 2014, at 12:00 noon.
1. Virtual Lab 3: Biased Coins Continued
In this problem we will continue the lab from last HW. We will start from the
EECS 70
Discrete Mathematics and Probability Theory
Spring 2014
Anant Sahai
Homework 13
This homework is due April 28 2014, at 12:00 noon.
1. Von Neumanns Unbiaising Method
In 1951, John Von Neumann gave the following simple procedure to simulate a perfec
EECS 70
Discrete Mathematics and Probability Theory
Spring 2014
Anant Sahai
Homework 7
This homework is due Mar 10 2014, at 12:00 noon.
1. Programming Question and Virtual Lab: Intro to Randomness
This problem is a simple exercise in programming that is d
EECS 70
Discrete Mathematics and Probability Theory
Fall 2014
Anant Sahai
Homework 8
This homework is due October 27, 2014, at 12:00 noon.
1. Section Rollcall!
In your self-grading for this question, give yourself a 10, and write down what you wrote for p
EECS 70
Fall 2014
Discrete Mathematics and Probability Theory
Anant Sahai
Discussion
8M
1. Corruption
Alice wants to send Bob a message of size 3 and guard against 1 corrupt packet. Bob receives from Alice
the packets (0, 1), (1, 2), (2, 3), (3, 3), (4, 4
EECS 70
Discrete Mathematics and Probability Theory
Fall 2014
Anant Sahai
Homework 7
This homework is due October 20, 2014, at 12:00 noon.
1. Section rollcall!
In your self-grading for this question, give yourself a 10, and write down what you wrote for p
EECS 70
Discrete Mathematics and Probability Theory
Fall 2014
Anant Sahai
Homework 8
This homework is due October 27, 2014, at 12:00 noon.
1. Section Rollcall!
In your self-grading for this question, give yourself a 10, and write down what you wrote for p
EECS 70
Discrete Mathematics and Probability Theory
Spring 2014
Anant Sahai
Homework 11
This homework is due Apr 14 2014, at 12:00 noon.
1. Virtual Lab
The Birthday Paradox concerns the probability of two people in a group of m people having the same birt
EECS 70
Discrete Mathematics and Probability Theory
Spring 2014
Anant Sahai
Homework 10
This homework is due Apr 7 2014, at 12:00 noon.
1. Maze
Lets assume that Tom is located at the bottom left corner of the maze below, and Jerry is located at the top ri
EECS 70
Fall 2014
Discrete Mathematics and Probability Theory
Anant Sahai
Discussion
9W
1. Balls and Bins
You have n empty bins and you throw balls into them one by one randomly. A collision is when a ball is
thrown into a bin which already has another ba
EECS 70
Fall 2014
Discrete Mathematics and Probability Theory
Anant Sahai
Note 15
Random Variables: Distributions, Independence, and Expectations
In the last note, we saw how useful it is to have a way of thinking about quantities that are inherently rand
EECS 70
Discrete Mathematics and Probability Theory
Fall 2014
Anant Sahai
Midterm 1
Exam location: 10 Evans, Last name starting with A-B or R-T
P RINT your student ID:
,
P RINT AND S IGN your name:
(last)
(rst)
(signature)
P RINT your Unix account login:
EECS 70
Fall 2014
Discrete Mathematics and Probability Theory
Anant Sahai
Discussion
9M
1. Probability Practice
(a) A message source M of a digital communication system outputs a word of length 8 characters, with the
characters drawn from the ternary alph
lab6sol
October 9, 2014
1
Virtual Lab 6 Solution: Public Key Cryptography and Lagrange
Interpolation
1.0.1
EECS 70: Discrete Mathematics and Probability Theory, Fall 2014
Due Date: Monday, October 13th, 2014 at 12pm
Instructions:
Complete this lab by lli
EECS 70
Fall 2014
Discrete Mathematics and Probability Theory
Anant Sahai
Discussion
2W-S
1. Prime Factors
Prove that every integer n 2 can be written as a product of prime numbers.
2. Bit String
Prove that every positive integer n can be written with a s
EECS 70
Fall 2014
Discrete Mathematics and Probability Theory
Anant Sahai
Discussion
12M
1. Lets give you cookies!
The GSIs want to distribute k cookies and k glasses of milk to students. They will blindly pick a student and
give her/him a cookie. Same go
EECS 70
Fall 2014
Discrete Mathematics and Probability Theory
Anant Sahai
Discussion
2M
1. Two Color Theorem
Consider a scenario where we have a 2D plane that we divide into regions by drawing straight lines. Using
induction, prove that we can color this
EECS 70
Discrete Mathematics and Probability Theory
Fall 2014
Anant Sahai
Homework 7
This homework is due October 20, 2014, at 12:00 noon.
1. Section rollcall!
In your self-grading for this question, give yourself a 10, and write down what you wrote for p
EECS 70
Fall 2014
Discrete Mathematics and Probability Theory
Anant Sahai
Discussion
10W
1. Story Problems
Prove the following identities by combinatorial argument:
(a)
n
n1
n1
=
+
k
k1
k
(b)
2n
n
=2
+ n2 .
2
2
(c)
n
k
k=0
(d)
n
k= j
EECS 70, Fall 2014, D
EECS 70
Discrete Mathematics and Probability Theory
Fall 2014
Anant Sahai
Homework 12
This homework is due November 24, 2014, at 12:00 noon.
1. Section Rollcall!
In your self-grading for this question, give yourself a 10, and write down what you wrote for
EECS 70
Discrete Mathematics and Probability Theory
Fall 2014
Anant Sahai
Homework 12
This homework is due November 24, 2014, at 12:00 noon.
1. Section Rollcall!
In your self-grading for this question, give yourself a 10, and write down what you wrote for
EECS 70
Fall 2014
Discrete Mathematics and Probability Theory
Anant Sahai
Discussion
3W-S
1. Anti-Soulmates
1. Create an example where, when the traditional propose-and-reject algorithm is run, all the women end
up with their least preferred partner.
2. P
EECS 70
Fall 2014
Discrete Mathematics and Probability Theory
Anant Sahai
Discussion
4M
1. Modular decomposition of modular arithmetic
Complex systems are always broken down into simpler modules. In this problem you will learn how this
might be done in mo
EECS 70
Discrete Mathematics and Probability Theory
Fall 2014
Anant Sahai
Homework 9
This homework is due November 3, 2014, at 12:00 noon.
1. Section Rollcall!
In your self-grading for this question, give yourself a 10, and write down what you wrote for p
EECS 70
Fall 2014
Discrete Mathematics and Probability Theory
Anant Sahai
Discussion
7M
1. Lagrange Interpolation in Finite Field
Find a unique polynomial p(x) of degree at most 3 that passes through points (1, 3), (0, 1), (1, 2), and
(2, 0) in modulo 5 a
EECS 70
Fall 2014
Discrete Mathematics and Probability Theory
Anant Sahai
Note 6
This note is partly based on Section 1.4 of Algorithms," by S. Dasgupta, C. Papadimitriou and U. Vazirani,
McGraw-Hill, 2007.
Public Key Cryptography
In this note, we discuss
lab8sol
October 27, 2014
1
Virtual Lab 8 Solution: Intro to Randomness
1.0.1
EECS 70: Discrete Mathematics and Probability Theory, Fall 2014
Due Date: Monday, October 27th, 2014 at 12pm
Login: cs70Instructions:
1.1
Name:
Please ll out your name and login