Introduction to Discrete Mathematics

22m:150, Fall 2002
Instructor: Fred Goodman

Contact Information:


325G Maclean Hall


goodman at math dot uiowa dot edu


Office: 319-335-0791

Mobile: 319-331-1939

Paper Mail:

Fred Goodman
Department of Mathematics MLH
The University of Iowa
Iowa City, IA 52242-1419 USA

Office Hours:

M and W 11-12

Class Hours:

10:55-12:10, Tuesdays and Thursdays


Click here to read the syllabus.


Richard Brualdi, Introductory Combinatorics, 3rd Edition, Prentice Hall, 1992.

This text is required.


Assignment lists:

There will be 8 to 12 written assignments. Details will appear here as the assignments are made.

1st assignment: Exercises xxxxx from Chapter 2.

2nd assignment: Establish bijections between three combinatorially defined sets, as described in class. The sets are as follows, for given k <= n.

A = the set of arrangments of k non-attacking rooks on a k by n board.

B = the set of arrangements of the numbers 1, 2, ... , k in a single column of n boxes.

C = the set of k - permutations of n elements.

3nd assignment: From text, Chapter 3, Exercises 8-20 even and 26-30 even.

4th assignment:

Part 1: Calculate the number of configurations of 5 non-attacking rooks on an 9 by 9 board, such that all four outer rows and columns are occupied; that is the first and last rows and the first and last columns are all occupied. Attack the problem in two ways, as discussed in class.

Part 2: Exercises 36-38 from Chapter 3.

5th assignment: Chapter 3, Exercises 32-33. Chapter 5, Exercises 3, 7, 8-12.

6th assignment:

Part 1: Chapter 5, Exercises 14-18, 24, 25, 26, 34, 37, 39, 40.

Part 2: Find out what binomial identities can be derived from the functional identity:

(1 + x)^(a + b) = (1+ x)^a ( 1 + x)^b.

Expand both sides using the binomial theorem and match coefficients on both sides.

Part 3, MIDTERM FEEDBACK: End of term student review are helpful, but midterm feedback could be even more helpful for making this course productive and satisfying. Please let me know what aspects of this course you find most satisfying and what aspects could most use improvement. Kindly type your responses and give them to me unsigned.

7th assignment:

Chapter 6, Exercises 1, 4, 8, 11, 12, 14, 15, 16, 24, 28.

8th assignment:

Chapter 7, Exercises 1-3, 6, 7. Exercises 4 and 5 can be tried for an extra challenge. (They are quite challenging.) These will be due the week after Thanksgiving.

9th assignment:

Chapter 7, Exercises 24 (a) and (d), 3, 31, 33, 37 (a) and (b), 38.


Midterm exam: Thursday Oct. 31 in class

There will be a comprehensive final exam at the time specified in the Fall, 2002 course schedule, namely Friday, Dec. 20 at 4:30. Students who wish may take the exam at the alternative time: Sunday, Dec. 15 at noon.

Here are some exams from previous semesters, in pdf format.

Midterm, 1996.

Midterm, 1998.

Midterm, 1999.

Final, 1998.

Final, 1999.


Habits of Mind, an interesting essay about school mathematics, by Al Cuoco, E. Paul Goldenberg, and June Mark.


Remark on obtaining explicit coefficients for a generating function.