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
Solu
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
Soluti
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
Solution
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, 2
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
So
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
So
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
Sol
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
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
Solution
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
So
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
So
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
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 que
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
So
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
So
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/fals
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
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
Solution