Math 210
Assignments
Assignments are due in class on the due date.
Please show your work. Problems with only an
answer may not receive credit (homework and exams)
Always write at
least a brief note saying how you got your answer.
Please note that
answers to some questions may be found in the back of the book.
When turning in an assignment, please turn in only that assignment - not
any late assignments you might have. Late assignments should be turned in
to me separately, and late assignments can not be accepted after the graded
assignment is returned to the class.
No homework can
be turned in past our last day of class (Tuesday, May 3) in class
- Assignment #9, due Monday, May 2. Please work
- On pages 197 - 198, problems 11 and 14
- On page 212, problems 1 and 2
- From the handout on finite state automata (we should have this in
hand Thursday or Friday), problems 1 - 6.
Please note that the textbook problems and problems 1 - 3 in the handout
refer to material which may be covered on next Friday's exam.
- Assignment #8, due Monday, April 18. Please work:
- On pages 180 - 183 (section 4.1), problems 1 - 7, 12, 15 (statement
4.7 is on page 172), and 17. Look at, but do not work (unless you
want to, of course), problems 13 and 14.
- On page 197 (section 4.2), problems 1 - 7. Equation 4.13 is
corollary 4.2, and equation 4.16 can be found on page 194.
- Some Fibonacci problems from Rosen, Kenneth H.: Discrete
Mathematics and Its Applications: Rosen defines Fibonacci numbers
as f(0) = 0, f(1) = 1, f(n) = f(n-1) + f(n-2) for n > 1. With this
definition, prove that
- f^2(1) + f^2(2) + ... + f^2(n) = f(n)*f(n+1) (where f^2(n) means
the square of the nth Fibonacci number.)
- f(1) + f(3) + ... + f(2*n-1) = f(2*n)
- f(0)f(1) + f(1)f(2) + ... + f(2n-1)f(2n) = f^2(2n)
- Assignment #7, due Monday, April 4. Please work
- On pages 147 - 148, problems 1 - 4, 7, 9, 10, 12, and 13 (Section 3.2)
- On pages 159 - 160, problems 1 - 4, 7, 8, 10, and 15 (section 3.3)
- Assignment #6, due Friday, March 25. Please work
(remembering to show your work)- On pages 104 - 106 (section 2.3), problems 5 - 8
(all), 12 (a and b), and 13. For problem 13, turn in
the working program and the sample run (with output) of your sample
message. You do not need to send the message to anyone, but I need
to know the output of your program (the encrypted message) together with
your public key together with the sample run of the decryption program
verifying that the encryption/decryption worked. To further simplify matters, let's make the
message a number that can be represented in 16 bits. Your program
should follow the usual standards for internal documentation, etc.
- On pages 114 - 115 (section 2.4), problems 1, 2, 8, 10, 13, and 14
- On pages 131 - 132 (section 3.1), problems 1, 6, 7, 8, 12, and 13
- Assignment #5, due Thursday, March 3. Please work
- Please re-work problem 18 on page 92, turning in the source listing
for your program together with sample runs on the pairs
- 576, 482
- 16, 103
- Please verify your results on both inputs. You will need
your results on the second pair for some of the following problems.
- Your program should print out the two input numbers, the greatest
common divisor of those two numbers, and the numbers x and y which are
given by the program. Your program should print these numbers with
appropriate text. You should turn in the program source listing together
with printouts of the sample runs.
- Use your answer to the second part of the problem above to work problem 13 on
page 91. Your answer should be a number strictly between 0 and
103. Check your answer - you will need it later on in this
exercise set.
- The following numbers have been encrypted by adding 16 (modulo 103)
to the original (plaintext) numbers. What are the original
numbers?
Answers should be strictly between 0 and 103
- The following numbers have been encrypted by multiplying 16 (modulo
103) to the original (plaintext) numbers. What are the original
numbers?
Answers should be strictly between 0 and 103. You will want to
use your answer to the second part of the first problem in doing this
problem.
- Please work problems 1, 2, and 3 on page 104 (Section 2.3)
- Please note that although this problem is not due until after our
exam on Tuesday, the material covered in this homework assignment will
be covered on Tuesday's exam. Please be prepared to ask questions
you may have on the homework before Tuesday's exam.
- Assignment #4, due Monday, February 21. Please work
- On pages 73 - 74, problems 8, 10, 11, 12, 13 (section 2.1)
- On pages 90 - 92, problems 1, 2, 4, 6, 7, 8, 11, 12, 18 (section
2.2)
- Convert the following arithmetic problems to base 2 and do the
calculation indicated. Please show enough of your work that I can
see what you are doing (i.e., doing the arithmetic base 10 and
converting back to base 2 is not enough):
- 23+42
- 42 - 23
- 85 / 9 (find quotient and remainder)
- Convert the following numbers to two-complement integer
representation. Write your answers base 16.
- Assignment #3, due Monday, February 14. Please work
- On Pages 54 - 57, problems 1 - 3, 5, 11, 13, 14, and 15 (except c
and d)
- On pages 72 - 73, problems 1 - 5, 7
- Please construct addition and multiplication tables for the integers
mod 6 and mod 7. Do you notice any interesting differences in the
multiplication tables?
- Assignment #2, due Friday, February 4. Please work
- On pages 30 - 32, problems 1 - 5, 10, 11, 14, 15, and 17
- On pages 42 - 43, problems 1 - 4 (that is, all of them)
- Assignment #1, due Friday, January 28 (please note change in due
date). Please work
- On pages 8 - 9, please work problems 1 - 12
- On pages 20 - 22, please work problems 1 - 8, 10, 13, 17, 18