## Math 2513 - 001     Discrete Mathematics         Fall 2009

### Course Handouts and Messages

• Information Sheet. First week handout. Office hours, grade breakdown, exam dates, course policies etc.
• Clicking on the Collaboration Distance tab of the MathSciNet database will give you an author's Erdos number, and enable you to compute collaboration distances between authors.
• The Mathematics Genealogy Project is a wonderful database which locates all your math professors in relation to the greats.
• You can learn a little bit about Paul Erdos here. There is also an entry about Erdos on the OU MathClub blog, complete with an xkcd strip.
• Solutions to Quiz 1, and a blank Quiz I.
• As announced in class, Mid I is now taking place in class on Thursday, September 24. It will cover all of chapter I and will cover proofs by mathematical induction.
• You can look at an old Midterm I exam to help you prepare for our first midterm. Question 5 is on set theory. You should look at some induction problems in place of the set theory material.
• Solutions to Midterm 1, and a blank Midterm I.
• Solutions to Quiz 2, and a blank Quiz 2.
• permutations handout.
• symmetries handout.
• Solutions to Quiz 3, and a blank Quiz 3.
• Midterm II will take place in class on Tuesday, October 27.
There is a review on Monday evening (6:00pm in 809 PHSC) October 26.
Here is a midterm II exam from a previous semester. Try doing this before the review.
Here are some questions which you should also try to do before the review.
• Here is Midterm 2 and some solutions.
• Here is the cardinality handout that we are working through in class. It is updated from the original paper copy.
• Here are solutions to some problems from Hwk 10 and Hwk 11. There is also a write up of an answer to a question that was raised in class today (Thursday, Nov 19).
• Here is a cardinality problem which was asked on a past exam.
• Solutions to Quiz 4, and a blank Quiz 4.
• Midterm III will take place in class on Tuesday, November 24.
There is a review on Monday evening (7:00pm in 809 PHSC) November 23.
• Here are solutions to some problems from the cardinality handout which you were to look at for Monday, Nov 23.
• Here is Midterm 3 and some solutions.
• Here is the number theory handout for those of you who may have missed it in class, or misplaced it.

### Homework

• [01]. Due Tuesday 09/01.   Pages 16-21:   17, 18, 26, 28(b), 28(d), 32(e).
Pages 28-30:   8, 18, 24, 25, 32, 42, 43, 44, 45, 55.
• [02]. Visit my office hours sometime in the next week (by Thu Sept 3).
• [03]. Visit the OU MathClub Blog (you can find a link to it from my home page)
• [04]. Due Tuesday 09/08.   Pages 46-50:   10, 12, 19, 25, 36, 44, 50
Pages 58-62:   9, 24, 26, 30, 40, 46
• [05]. Due Tuesday 09/15.   Pages 85-86:   7, 8, 9, 16, 24, 38, 39, 40. Also...
a. Show where the proof that the square root of 2 is irrational breaks down in the case of the square root of 4.
b. Give a proof that the square root of 5 is irrational.
c. Give a proof that the square root of 6 is irrational.
d. Give a proof that the square root of 8 is irrational.
e. Formulate a conjecture about which square roots (of positive integers) are irrational.
• [XX]. For discussion in class next Thursday. Attempt, write notes, but you do not have to turn these in.
You may be asked to present answers on the board, so do attempt them.
Pages 102-104:   7, 12, 16, 21, 23, 32, 33, 34.
Pages 279-283:   4, 5, 6, 10, 11, 15, 16, 20, 21, 34, 35, 47.
• [06]. Due Tuesday, 10/06. Pages 119-121:   3, 5, 8, 19, 20, 23, 38.
Pages 130-133:   1, 15, 29, 30, 34, 35, 36, 40, 44, 48.
• [07]. Due Tuesday, 10/13. Pages 146-149:   8, 12, 15, 16, 22, 29, 36, 38, 40, 66, 67. (omit 36, 38, 40)
• [08]. Due Tuesday, 10/20. Pages 146-149:   36, 38, 40 and 67 (again!).
Let f : A --> B be a function, S a subset of A, and T a subset of B.
Show that the preimage of the image of S contains S, and that the two are equal if the function is injective.
Show that the image of the preimage of T is contained in T, with equality holding if the function is surjective.
• [XX]. Due Thursday, 10/22. Exercises 3, 4, 5, 10, 11, 12 and 19 from the symmetries handout.
• [09]. Due Tuesday, 11/03. Write up answers to the following questions (many of which were discussed in the review).
• [10]. Due Thursday, 11/12. Do Q1 from the following handout and Q31, Q32 from page 162 of the text.
• [11]. Due Tuesday, 11/17. Do 45, 46, 47 from page 163 of the text, and Q2 from the handout.
• [XX]. Due Monday, 11/23. Do 24, 26, 31, 34, 35, 36 from the cardinality handout. These are not for credit. We will discuss them in the review.
• [12]. Due Tuesday, 12/8. Pages 217-218:   4, 5, 6, 7, 8, 10, 35.
• [13]. Due Thursday, 12/10. Page 230:   24. (turn this in)   Also look over these.