# MATH 311W: Concepts of Discrete Mathematics

I am Stephen
G. Simpson, a Professor of Mathematics at Penn State University.
In Fall 2011 I taught Section 003 of MATH 311W. We met
Monday-Wednesday-Friday 1:25-2:15 PM in 115 Osmond.

MATH 311W is a transition course. The transition is from lower-level
(100- and 200-level) mathematics courses to higher-level (400- and
500-level) mathematics courses. Therefore, the course includes a
writing component. Students are expected to write proofs.

### Syllabus

The required textbook is *Numbers, Groups & Codes*, Second
Edition, by J. F. Humphreys and M. Y. Prest, Cambridge University
Press, 2004, XVI + 338 pages. My plan is to go through the entire
book in order. Grades will be based on homework (40 percent), a
midterm exam (25 percent), and a final exam (35 percent).
- The midterm exam was administered in-class on Monday, October 17. The
midterm exam, with solutions, is here.
- The final exam was administered on Thursday of Final Exam Week,
December 15, 12:20-2:10 PM, in 102 Chem. The final exam questions are
here.

### Homework

All homework must be neat and legible, with pages stapled together.
When writing proofs, students must use grammatical sentences, and
there must be a logical chain of reasoning leading to the desired
conclusion.

- Homework #1 due Wednesday September 7: Section 1.1 of the
textbook, Exercises 3, 6, and Section 1.2, Exercises 2, 3, 5, 7, 8,
9, 10.
- Homework #2 due Wednesday September 21: Section 1.3 Exercises 2,
5, 6, 7, 8, 9, and Section 1.4 Exercises 5, 6, 7, 8, 9.

(Only
Section 1.3 Exercise 6 and Section 1.4 Exercise 5 will be graded.)
- Homework #3 due Wednesday October 12: Section 1.5 Exercises 1, 2,
3, 4, 5, and Section 1.6 Exercises 3, 4, 7, 8.

(Only Section
1.5 Exercise 4 and Section 1.6 Exercise 7 will be graded.)
- Homework #4 due Wednesday November 2: Section 1.6 Exercises 9, 10,
11, 12, and Section 2.2 Exercises 8, 9, 10, 11.

(Only Section
1.6 Exercise 11 and Section 2.2 Exercise 10 will be graded.)
- Extra Credit Homework, due Monday November 14: Assume that X, Y,
and Z are sets.
- Prove that there exists an injection from X to P(X).
- Prove that there is no injection from P(X) to X.
- Assume that f is a function from X to Y and g is a function
from Y to Z. Prove the following.
- If f and g are injections then gf is an injection.
- If f and g are surjections then gf is a surjection.

- Prove that at least one of the following holds.
- There exists an injection from X to Y.
- There exists an injection from Y to X.

- Assume that there exist injections from X to Y and from Y to
X. Prove that there exist bijections from X to Y and from Y to
X.

- Homework #5 due Monday December 5: Section 2.4 Exercises 1, 2, 3,
4, 5, 6, and Section 4.1 Exercises 1, 2, 3, 4, 5, 6.

(Only
Section 2.4 Exercise 4 and Section 4.1 Exercise 4 will be graded.)

Some hints and partial solutions for some of the textbook exercises
are here.
### Term Paper

For extra credit, students may write a term paper on a topic chosen by
them and approved by me. The topic should be related to something in
the textbook. The term paper should be well-written, neatly typed,
and at least 5 to 10 pages long. Term paper proposals are due Friday
November 18, the Friday before Fall Break. Term papers are due Friday
December 9, the last day of classes. Term paper proposals and term
papers are to be submitted electronically.
### Office Hours

My office hours for Fall 2011 are:
- Wednesdays, 4:40-5:30 PM, 305 McAllister.
- Thursdays, 9:30-11:00 AM, 305 McAllister.

t20@psu.edu / 9 December 2011