Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 31
revised October 30, 2005, 722 minutes
Solutions to In-Class Problems Week 9, Mon.
Problem 1. Prove t
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
November 2
revised November 2, 2005, 106 minutes
Solutions to In- lass Problems Week 9, Wed.
Problem 1.
license
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
November 9
revised November 9, 2005, 191 minutes
Solutions to In- lass Problems Week 10, Wed.
Problem 1. Find t
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 26
revised October 25, 2005, 1134 minutes
Solutions to In-Class Problems Week 8, Wed.
Problem 1. We beg
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 28
revised October 27, 2005, 988 minutes
Solutions to In- lass Problems Week 8, Fri.
Problem 1. There i
inal
2
Problem 1. [8 points] Prove that for all n 2 N, the following identity holds
n
X
i2 =
i=1
Solution. By induction on n
n(n + 1)(2n + 1)
.
6
1, with induction hypothesis
P (n) :
n
X
i=0
i2 =
n(n + 1)(2n + 1)
6
for all n 2 N
ase case (n = 1):
Inductiv
Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. lbert R. Meyer
March 17
revised March 27, 2010, 1280 minutes
Solutions to Mini-Quiz Mar. 17
Problem 1 (8 points).
Starting with some number of 4-cent a
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
November 18
revised November 19, 2005, 1120 minutes
Solutions to In-Class Problems Week 11, Fri.
Problem 1. (a)
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 12
revised October 11, 2005, 598 minutes
Solutions to In-Class Problems Week 6, Wed.
Problem 1. This pr
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
November 4
revised November 4, 2005, 1254 minutes
Solutions to In- lass Problems Week 9, Fri.
Problem 1. Solve
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 24
revised October 24, 2005, 1211 minutes
Solutions to In- lass Problems Week 8, Mon.
Problem 1. Given
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
November 7
revised November 7, 2005, 1088 minutes
Solutions to In-Class Problems Week 10, Mon.
Problem 1. bipar
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 19
revised October 18, 2005, 704 minutes
Solutions to In-Class Problems Week 7, Wed.
Problem 1. Lets tr
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 21
revised October 21, 2005, 1019 minutes
Solutions to In- lass Problems Week 7, Fri.
Problem 1. By now
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 14
revised October 11, 2005, 701 minutes
Solutions to In- lass Problems Week 6, Fri.
Problem 1. This pr
Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. lbert R. Meyer
March 3
revised March 12, 2010, 718 minutes
Solutions to Mini-Quiz Mar. 3
Problem 1 (6 points).
Each year, Santas reindeer hold Reindeer