Math 208: Discrete Mathematics

Spring 2005, L. Peterson

Most recent assignments

Announcements

The final exam for this course will take place from 3:15 P.M. to 5:15 P.M. on Wednesday, May 11, 2005 in our usual classroom. You may not bring calculators or notes to the final exam. The exam will be comprehensive with an emphasis on chapters 25 through 30. You should be prepared to see problems on mathematical induction on the exam.

I have worked-out solutions to all of the handout problems and to the assigned exercises in Chapter 16. If you come to see me in my office, I will lend them to you. I may be out of the office for an hour or two in the morning on Monday, May 9.

You will probably need a simple pocket calculator to do some of the homework problems in Chapter 21 and following chapters. If you do not have a pocket calculator, and if you do not have a friend from whom you can borrow one, you might want to try using a regular computer. I have two suggested ways of doing this.

  1. You may use Mathematica. Go to my notebook page and use the notebook on “Simple Arithmetic.”

  2. Use a calculator simulator program. The computers in the Mathematics Learning Center and the Math Computer Lab have such calculator programs. To use these programs, left-click on “Start” and then “Programs,” “Accessories,” and finally “Calculator.” A picture of a pocket calculator should appear on the screen. You can simulate pressing buttons on the calculator by using the mouse and left-clicking. The Mathematics Learning Center and the Math Computer Lab are both in Witmer Hall. My guess is that just about any computer on the campus will have a calculator program and that it works as I have described here.

We will skip Chapter 20.

The “textbook” for this course will be a set of lecture notes entitled entitled “Math 208: Discrete Mathematics,” developed by the Mathematics Department at the University of North Dakota. We will use the version dated “Spring 2004.” You may obtain these notes from the Barnes & Noble bookstore, but you will probably have to go to the textbook counter and ask the bookstore to order the notes for you.

Errors in the Textbook

  1. On line 2 of page 70 of our textbook, where it says that 7 and 9 are elements of the set S, it should say that 7 and 8 are elements of S.

  2. Line 3 of page 71 should say that if x and y are in S, then bxy, xby, xyb, and xy are in S.

  3. On line 4 of page 80, where it says “an fro n=1 and n=2”, it should say “an for n=0 and n=1”.

  4. In the statement of the theorem on page 112 of our textbook, change “s - k(a/d)” to “t - k(a/d)”.

Assignments

  1. Chapter 1: 1, 2, 3, 4, 5, 6
    Due January 21, 2005

  2. Chapter 2: 1a, 1b, 2b, 2c, 3a, 3c, 4a, 4b
    Due January 24, 2005

  3. Chapter 3: 1, 2, 3, 4, 5, 6, 7
    Due January 28, 2005
    Note: Assume that Problem 5 reads as follows: “Negate each statement in Exercise 2 in logical symbols. Move each negation sign to the right of each quantifier.”

  4. Chapter 4: 1, 2, 3, 4, 5
    Due January 31, 2005
    Note: In problems 3, 4, and 5, give a list of statements together with a reason for each statement.

  5. Chapter 5: 1, 2, 3, 4, 5
    Due February 2, 2005

  6. Chapter 6: 1, 2, 3, 6, 7a, 7b, 8, 9, 10
    Due February 2, 2005

  7. Chapter 7: 1, 2, 3, 4, 5, 8
    Due February 7, 2005

  8. Chapter 8: 1, 2
    Due February 11, 2005
    Note: Study up through the middle of page 40 in Chapter 8.

  9. Chapter 9: 1, 2, 5, 6
    Due February 18, 2005
    Hint: In problems 5 and 6, assume that the domain of discourse is the set of all subsets of the set of integers.

  10. Chapter 10: 1, 2, 3, 5
    Due February 18, 2005
    Note 1: Problem 1(a) should read “aHb . . .”
    Note 2: Problem 5 refers to the theorem on page 48 of the textbook.

  11. Chapter 11: 1, 2, 4
    Due February 23, 2005

  12. Chapter 12: 1, 2
    Due February 25 2005

  13. Compute log325, log617, and log7149. Do so using Mathematica. Click on this link, and follow the instructions. Do the lab exercise on logarithms. Some of you may find that this is a very easy exercise. One of the main purposes of this is to learn how to do simple exercises with Mathematica. We will use Mathematica again later when we study the time complexity of algorithms.
    Due February 28, 2005

  14. Chapter 13: 2, 3, 4, 5, 6, 7, 8, 9
    Due March 2, 2005

  15. Chapter 14: 1, 2, 3, 4, 5
    Due March 4, 2005
    Note: In problems 1 and 2, change “by (1) a0=” to “by a0=”.

  16. Chapter 15: 1, 2, 3, 4, 5, 6
    Due March 7, 2005
    Hint for Problem 3: Plot some of the points in the xy-plane. Then give a precise answer.

  17. Chapter 16: 1, 2, 5
    Due March 11, 2005
    Hint for Problem 5: You may assume that if a is any real number, then
    (a+1)5 = a5+5a4 +10a3+10a2+5a+1.

  18. Chapter 16, additional problems: 3, 4, 7
    Due March 23, 2005

  19. Chapter 17: 1, 2, 3, 5, 6
    Due March 30, 2005

  20. Chapter 18: Do the three problems in Handout VII.
    Due April 1, 2005

  21. Do computer lab 3 on “Worst Case Scenario Efficiency.”
    Due April 8, 2005

  22. Chapter 19: 1, 5, 6, 7
    Due April 6, 2005
    Note: We will skip Chapter 20.

  23. Chapter 21: 1, 2, 3, 4
    Due April 8, 2005
    Note: You may need to use a pocket calculator to do some of these problems. If you do not have a calculator, see the announcement above.

  24. Chapter 22: 1, 2, 3, 4
    Due April 15, 2005
    Note: Show your work, especially on problems 1 and 2. In class I made comments about what I am looking for.

  25. Chapter 23: 1, 2, 3
    Due April 15, 2005
    Note: In Problem 1, use backsubstitution. If you wish, you may use the continued fraction method as a check. But the only part of the problem that I will grade will be the part where you use the backsubstitution method.

  26. Chapter 24: 1, 2, 3, 4
    Due April 18, 2005
    Notes: Show your work to a reasonable extent. In Problem 4, count the divisors, but do not find them. The numbers 5, 67, and 71 are prime numbers.

  27. Chapter 25: 1, 2, 3
    Due April 22, 2005

  28. Chapter 26: 1, 2, 3, 4, 5, 6, 7
    Due May 2, 2005
    Notes: Show your work. If you do part of a problem with a calculator, show your main logic on the papers you hand in.

  29. Chapter 27: 1, 2, 3, 4
    Due May 2, 2005
    Note: Show your work. If you do part of a problem with a calculator, show your main logic on the papers you hand in.

    Most recent assignments:

  30. Chapter 28: 1, 2, 3, 4, 5, 6, 7, 8, 9
    Due May 4, 2005
    Note 1: It is not necessary to expand your answers. For example, if the answer is 83154, you may leave the answer in this form instead of writing 25920000.
    Note 2: In Problem 7, the empty string (i.e. the string of length zero) is a legitimate string.

  31. Chapter 29: 1, 3, 4, 7a, 7b
    Due May 4, 2005
    Note 1: The above assignment differs from the one that I originally posted on this Web site. The assignment shown here is the correct one.
    Note2: It is not necessary to expand your answers, but give explicit formulas for how to compute them. Include specific numbers in your formulas.

  32. Chapter 30: 1, 2, 4
    Due date: None. I will not collect this assignment, but this material may appear on the final exam.

---- End of assignments for Discrete Mathematics ----

Links

Lawrence J. Peterson home page
Department of Mathematics home page
University of North Dakota home page

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Contact Person: Larry Peterson
E-mail: lawrence.peterson@und.nodak.edu
Phone: (701) 777-4609
Date of most recent update: 6 May 2005
University of North Dakota home page