Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
September 9
revised September 8, 2005, 1167 minutes
Solutions to In- lass Problems Week 1, Fri.
Problem 1. lber
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
September 30
revised March 11, 2006, 1239 minutes
Solutions to In- lass Problems Week 4, Fri.
Problem 1. (a) Fo
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
September 7
revised
ugust 30, 2005, 955 minutes
Solutions to In- lass Problems Week 1, Wed.
Problem 1. Identify
Massachusetts Institute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Quiz 1 Solutions | Fall 2010)
Quiz 1 Solutions:
October 12, 2010
Problem 1.
1. (10 points) Let Ri be the amount of t
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
September 26
revised September 26, 2005, 1050 minutes
Solutions to In-Class Problems Week 4, Mon.
Problem 1. In
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
September 23
revised September 19, 2005, 1433 minutes
Solutions to In-Class Problems Week 3, Fri.
Problem 1. Gi
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
September 28
revised September 29, 2005, 934 minutes
Solutions to In-Class Problems Week 4, Wed.
Problem 1. Rec
Final xam
2
Problem 1. [13 points] Give an inductive proof that the Fibonacci numbers Fn and Fn+1
are relatively prime for all n 0. The Fibonacci numbers are dened as follows:
F0 = 0
F1 = 1
Fn = F n
1
+ Fn
2
(for n
2)
Solution. We use induction on n. Let
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 5
revised October 5, 2005, 1119 minutes
Solutions to In-Class Problems Week 5, Wed.
Problem 1. Let Ln b
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
September 14
revised September 13, 2005, 1279 minutes
Solutions to In- lass Problems Week 2, Wed.
Problem 1. Fo
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
September 16
revised September 20, 2005, 1273 minutes
Solutions to In- lass Problems Week 2, Fri.
Problem 1. Su
Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. lbert R. Meyer
February 17
revised February 14, 2010, 1412 minutes
Solutions to Mini-Quiz eb. 17
Problem 1 (5 points).
Prove that log4 9 is irrational.
Massachusetts nstitute of Technology
Department of Electrical Engineering & Computer Science
6.041/6.431: Probabilistic Systems Analysis
(Quiz 2 Solutions | Spring 2008)
Question 1
Multiple choice questions. CLEARLY circle the best answer for each questio
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
September 12
revised September 12, 2005, 1214 minutes
Solutions to In- lass Problems Week 2, Mon.
p
Problem 1.
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
September 21
revised September 19, 2005, 1425 minutes
Solutions to In-Class Problems Week 3, Wed.
Problem 1. Us
6.042/18.062J Mathematics for Computer Science
Tom Leighton and Marten van Dijk
December 17, 2008
Final Exam
Problem 1. [25 points] The Final Breakdown
Suppose the 6.042 nal consists of:
36 true/false questions worth 1 point each.
1 induction problem wo
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 3
revised October 4, 2005, 667 minutes
Solutions to In- lass Problems Week 5, Mon.
Problem 1. There is
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. Albert R. Meyer and Prof. Ronitt Rubinfeld
October 7
revised October 9, 2005, 719 minutes
Solutions to In-Class Problems Week 5, Fri.
Problem 1. Figures