Math 210
Fall 2008
H omework Set 4, Due Thurs. Oct. 9 in Class
(Late papers OK until 1:00 Friday under Ms. Li's door, DRL 2C11)
1. a). Choose a number c at random from the interval [0,1]. Find the probability
that:
i). |c - 0.5| < 0.25
ii). 3c2 < c
b). Si
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Problem Set # 3
Math 221 - Discrete Mathematics - Winter 2017
Professor R. Andrew Hicks
1. Find the number of hands of the type two pair: two pairs plus another
card with a different value. For example,
1010KK9.
You can check your work using the fact that
Solutions to Problem Set # 3
Math 221 - Discrete Mathematics - Winter 2017
Professor R. Andrew Hicks
1. Find the number of hands of the type two pair: two pairs plus another
card with a different value. For example,
1010KK9.
You can check your work using
Figure 2: Problem 23: A plot of some of the integer solutions to 4x+6y = 2.
Dont do this Dont
Solution: Note that we have already solved 4x + 6y = 2 completely. To
it isdo
notthis
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it isshortcut.
not a valid
Do the solve 4x + 6y = 4 we multiply tho
Problem Set # 5
Math 221 - Discrete Mathematics - Winter 2017
Professor R. Andrew Hicks
Remember that when we say that a Diophantine equation has solutions
that it means that the solutions are in Z.
1. If (a, b) > 1 and (b, c) > 1, is it true that (a, c)
Problem Set # 6
Math 221 - Discrete Mathematics - Winter 2017
Professor R. Andrew Hicks
This material will be on exam 2, on Friday, March 10th.
A Partial Review
Remember that when we say that a Diophantine equation has solutions,
we mean that it has solut
Solutions to Problem Set # 6
Math 221 - Discrete Mathematics - Winter 2017
Professor R. Andrew Hicks
This material will be on exam 2, on Friday, March 10th.
A Partial Review
Remember that when we say that a Diophantine equation has solutions,
we mean that
Problem Set # 7
Math 221 - Discrete Mathematics - Winter 2016
Professor R. Andrew Hicks
Something to bear in mind - when considering these cryptographic systems, we often choose small values for their parameters (p, q, etc.) just
for convenience, because
Math 210
Fall 2008
H omework Set 3, Due Thurs. Oct. 2 in Class
(late papers OK until 1:00 Friday)
1. [Blood Test] A large number, N, of people are subjected to a blood test, the
result of which is either "positive" or "negative". It can be given in two wa
Math 210
Fall 2008
Reminder: You can work together in groups of at most three people. I n this case,
the group submits one c opy of each Homework Set with the names of all the
people in the group. Essentially the same groupings should work together all
se
Math 210
Fall 2008
H omework Set 5, Due Thurs. Oct. 23 in Class
(Late papers OK until 1:00 Friday)
Least Squares
1. U se the method of least squares to find a plane of the form
z = ax + by + c
that best fits the following five points in three dimensional
Math 210
Fall 2008
Problem Set 6, Due: Thursday, Oct. 30, 2008
(late papers OK until 1:00 Friday)
Some Graphics. Our lecture notes on Vectors and Least Squares may be useful here.
1. a). For which values of the constants a and b are the vectors U = (1+a,
Math 210
Fall 2008
Problem Set 7, Due: Thursday, Nov. 6, 2008
(late papers OK until 1:00 Friday)
Because of elections this week, the homework assignment is a bit shorter.
Markov Chains
1. There is a long long queue to buy tickets for a Red Hot Chilli Pepp
Math 210
Fall 2008
Problem Set 8, Due: Tuesday, Nov. 13, 2008 (in class)
(late papers OK until 1:00 Friday)
The following sections E igenvalues and Eigenvectors f rom Strang's Linear Algebra and its Applications
may be helpful.
1. You are given an inverti
Math 210
Fall 2008
Problem Set 9, Due: Thursday, Nov. 21, 2008
(late papers OK until 1:00 Friday)
1. [Kendall-Wei Ranking Method] The table on the right gives
A 03 1
the number of times each of three teams won games from the
B203
other two teams. For inst
Math 210
Fall 2008
Problem Set 10, Due: Never
1. a). Write the number 704 in base 2.
b). If a number is 100101 in base 2, what is it base 10?
2. Verify that 12704 is congruent to 1 (mod 391).
3. For a simple RSA encryption, you use n = pq , where p = 5 an
Printed Name
Signature
Math 210
October 16, 2008
Exam 1
Jerry L. Kazdan
9:00 10:20
Directions: Part A has 4 shorter problems (10 points each) while Part B has 4 problems (15
points each). To receive full credit your solution should be clear and correct. Y
Printed Name
Signature
Math 210
Dec. 4, 2008
Exam 2
Jerry L. Kazdan
9:00 10:20
Directions: This exam has 2 parts. Part A has 4 shorter problems (5 points each ) while Part B
has 7 standard problems (12 points each ). To receive full credit your solution m
Math 210
Fall 2008
Problem Set 1, Due Thurs. Sept. 11 in Class
(late papers OK until 1:00 Friday)
1. C alendar Problems
Given a date, such as March 17, 2011, determine the day of the week (Monday,
Tuesday, etc.). [Hint: If today is a Saturday, a day 700 d
Solutions to Problem Set # 7
Math 221 - Discrete Mathematics - Winter 2016
Professor R. Andrew Hicks
Something to bear in mind - when considering these cryptographic systems, we often choose small values for their parameters (p, q, etc.) just
for convenie