Mathematical Techniques for Computer Science Applications
CSCI GA 1180

Fall 2012
Exercises 1: NOT TO HAND IN
If you are not familiar with vector or matrix operations, do these computations by hand and then
check your answer in Matlab. This may seem like busy work, but there is really no other way to
get a feel for what these mathemati
Mathematical Techniques for Computer Science Applications
CSCI GA 1180

Fall 2012
Programming Assignment 4
Assigned: Nov. 5
Due: Nov. 19
Consider the following situation: There is a network of links between nodes that is, an undirected
graph whose vertices are the nodes and whose edges are the links. Each links fails with probability
P
Mathematical Techniques for Computer Science Applications
CSCI GA 1180

Fall 2012
Assignment 3
Assigned: Oct. 8
Due: Oct. 29
In this assignment, you will use Matlab to show how the appearance of a 3D object changes as a
result of rotation (assuming that the distance to the object is constant, and large as compared to
the size of the ob
Mathematical Techniques for Computer Science Applications
CSCI GA 1180

Fall 2012
Programming Assignment 2
Assigned: Sept. 24
Due: Oct. 8
Note: The assignment is long, but the code is actually very short; perhaps 20 lines in total.
Suppose that A and B are electrically charged objects, located at points pA and pB with charges
QA and QB
Mathematical Techniques for Computer Science Applications
CSCI GA 1180

Fall 2012
Programming Assignment 1
Assigned: Sept. 10
Due: Sept. 24
Problem 1
Write a MATLAB function DocSimilarity(D,E) which computes the similarity of text documents
D and E using the vector model of documents. Specically, the arguments D and E are each cell
arr
Mathematical Techniques for Computer Science Applications
CSCI GA 1180

Fall 2012
Problem Set 4
Assigned: Nov. 19
Due: Dec. 3
Problem 1
Using paper and pencil, but no computer, estimate condence intervals for polls over sample sizes
with N = 2500, and N = 160, 000; f = 0.4 and f = 0.8; and condence levels of 0.95 and 0.999.
(Consider a
Mathematical Techniques for Computer Science Applications
CSCI GA 1180

Fall 2012
Problem Set 4
Assigned: Nov. 5
Due: Nov. 19
Problem 1 (20 points)
Let C be a twodimensional coordinate system with origin o and axes x , y and let D be a coordinate
system with origin p and axes i , j .
Let Coords(p, C ) = 1, 2 ; Coords( i , C ) = 2, 5 a
Mathematical Techniques for Computer Science Applications
CSCI GA 1180

Fall 2012
Problem Set 3
Assigned: Oct. 8
Due: Oct. 29
For exercises 13 you may use Matlab. You should show the computation involved, not just give the
answer. (Only 0.5 out of 2.5 credit will be given for the correct answer with no computation.) You
should be able
Mathematical Techniques for Computer Science Applications
CSCI GA 1180

Fall 2012
Problem Set 2
Assigned: September 24
Due: Oct. 8
Problem 1
For each of the following sets of vectors, state whether it is linearly dependent or linearly independent
and explain your answer in a sentence. You should refer to theorems in the book when they
Mathematical Techniques for Computer Science Applications
CSCI GA 1180

Fall 2012
Programming Assignment 5
Assigned: Nov. 19
Due: Dec. 3
Consider the same problem as in programming assignment 4, of a network with links that fail at
random.
Part A
Write a function MCProbConnected(E,P,PairA) with the same functionality as the function Pr