Massachusetts Institute of Technology
6.042J/18.062J, Fall 09: Mathematics for Computer Science
Prof. Albert R. Meyer
February 3
revised January 25, 2010, 1076 minutes
In-Class Problems Week 1, Wed.
Problem 1.
Identify exactly where the bugs are in each o

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
February 5
revised March 6, 2010, 795 minutes
In-Class Problems Week 1, Fri.
Problem 1.
p
Generalize the proof from lecture (reproduced

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
March 1
revised February 27, 2010, 1329 minutes
In-Class Problems Week 5, Mon.
Problem 1.
If a and b are distinct nodes of a digraph, t

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
February 22
revised February 18, 2010, 16 minutes
In-Class Problems Week 4, Mon.
Problem 1.
Prove by induction:
1+
1 1
1
+ + + 2 < 2
4

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
February 17
revised February 11, 2010, 1155 minutes
In-Class Problems Week 3, Wed.
Problem 1.
For each of the logical formulas, indicat

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
February 8
revised January 26, 2010, 74 minutes
In-Class Problems Week 2, Mon.
Problem 1.
The proof below uses the Well Ordering Princi

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
April 7
revised March 31, 2010, 99 minutes
In-Class Problems Week 9, Wed.
Problem 1.
Recall that for functions f, g on N, f = O(g) iff

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
March 29
revised March 20, 2010, 738 minutes
In-Class Problems Week 8, Mon.
Problem 1.
A number is perfect if it is equal to the sum of

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
May 5
revised May 4, 2010, 1304 minutes
In-Class Problems Week 13, Wed.
Problem 1.
Lets see what it takes to make Carnival Dice fair. H

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
May 10
revised May 7, 2010, 1069 minutes
In-Class Problems Week 14, Mon.
Problem 1.
A recent Gallup poll found that 35% of the adult po

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
April 26
revised April 22, 2010, 667 minutes
In-Class Problems Week 12, Mon.
Problem 1.
The famous mathematician, Fibonacci, has decide

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
April 21
revised April 16, 2010, 1284 minutes
In-Class Problems Week 11, Wed.
Problem 1.
Find the coefcients of
(a) x5 in (1 + x)11
(b)

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
April 12
revised April 6, 2010, 982 minutes
In-Class Problems Week 10, Mon.
Problem 1.
Solve the following problems using the pigeonhol

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
March 15
revised March 2, 2010, 734 minutes
In-Class Problems Week 7, Mon.
Problem 1.
Let G be the graph below1 . Carefully explain why

Massachusetts Institute of Technology
6.042J/18.062J, Spring 10: Mathematics for Computer Science
Prof. Albert R. Meyer
March 8
revised March 2, 2010, 734 minutes
In-Class Problems Week 6, Mon.
Problem 1.
Four Students want separate assignments to four VI