EECS 70
Discrete Mathematics and Probability Theory
Spring 2013
Anant Sahai
Soln 7
1. Error-Detecting Codes
In the realm of error-correcting codes, we usually want to recover the original message if we detect any
errors, and we want to provide a guarantee
EECS 70
Spring 2013
Discrete Mathematics and Probability Theory
Anant Sahai
HW 9
Due April 1
1. Introductions
Its the rst discussion section and the GSI is trying to come up with a clever method to make students form
groups and introduce themselves to eac
EECS 70
Spring 2013
Discrete Mathematics and Probability Theory
Anant Sahai
HW 8
Due March 18
1. Deja Vu
Gandalf has this habit of pacing back and forth when he is in deep thought. Feeling a bit concerned, Bilbo
claims that this behavior will eventually g
EECS 70
Discrete Mathematics and Probability Theory
Spring 2013
Anant Sahai
1. (2 pts.)
Soln 1
Getting started
What is Anant Sahais second favorite number?
The answer is found on Piazza.
(Why are we having you do this? Piazza is your best source for recen
EECS 70
Discrete Mathematics and Probability Theory
Spring 2013
Anant Sahai
Soln 2
1. (4 pts.) Proof by induction
For n N with n 2, dene sn by
sn = 1
1
1
1
1
1
.
2
3
n
Prove that sn = 1/n for every natural number n 2.
Answer: We will use induction on n
EECS 70
Discrete Mathematics and Probability Theory
Spring 2013
Anant Sahai
Soln 3
1. Simple recurrence relations
Assume that you have a sequence of integers dened by an initial condition and a recursive relation. In each
case nd a simple expression that
EECS 70
Discrete Mathematics and Probability Theory
Spring 2013
Anant Sahai
Soln 4
Due Feb 18
1. Modulo arithmetic practice
1. Use Euclids algorithm (page 3 of note 5) to compute the greatest common divisor of 527 and 323.
List the values of x and y of al
EECS 70
Discrete Mathematics and Probability Theory
Spring 2013
Anant Sahai
Soln 5
Due Feb 25
1. Polynomials and modular arithmetic
Which of the following statements is true? In each case, if the statement is true give a brief explanation; if
it is false,
EECS 70
Discrete Mathematics and Probability Theory
Spring 2013
Anant Sahai
Soln 6
Due Mar 4
1. d + 2 points vs. a polynomial of degree d
1. Given 3 points (0, 1), (1, 1), and (2, 3), use Lagrange interpolation to construct the degree-2 polynomial
which g