
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 1621: 17, 18, 26, 28(b), 28(d), 32(e).
Pages 2830: 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)
and post a comment on some article in the next two weeks
(by September 10).
 [04]. Due Tuesday 09/08.
Pages 4650: 10, 12, 19, 25, 36, 44, 50
Pages 5862: 9, 24, 26, 30, 40, 46
 [05]. Due Tuesday 09/15.
Pages 8586: 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 102104: 7, 12, 16, 21, 23, 32, 33, 34.
Pages 279283: 4, 5, 6, 10, 11, 15, 16, 20, 21,
34, 35, 47.
 [06]. Due Tuesday, 10/06. Pages 119121:
3, 5, 8, 19, 20, 23, 38.
Pages 130133: 1, 15, 29, 30, 34, 35, 36, 40, 44, 48.
 [07]. Due Tuesday, 10/13. Pages 146149:
8, 12, 15, 16, 22, 29, 36, 38, 40, 66, 67. (omit 36, 38, 40)
 [08]. Due Tuesday, 10/20. Pages 146149:
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 217218: 4, 5, 6, 7, 8, 10, 35.
 [13]. Due Thursday, 12/10.
Page 230: 24. (turn this in) Also look over
these.
