MAT 140-801 Dr.
S. Epp
Discrete Mathematics I Winter
2004
Syllabus
Prerequisites:
MAT
130 or a sufficiently high score on the Mathematics Diagnostic Examination.
Textbooks and other
materials:
Discrete Mathematics with
Applications,
3rd Edition, by Susanna S. Epp, Brooks/Cole Publishing, 2004.
A scientific calculator.
Supplementary
materials will occasionally be distributed in class.
Summary of Course: This course and its companion (Math 141) are intended
to provide a solid foundation for further study of mathematics, programming
languages, database theory, data structures, and analysis of algorithms. The
focus of Math 140 is on the basic principles of logical reasoning and how to
apply these principles to formulate and explore the truth and falsity of
statements in mathematics and computer science. Proof, disproof, and conjecture
all figure prominently. The main vehicle for exploration is number theory,
including divisibility properties of integers, the infinitude of the prime
numbers, the representation of real numbers on a number line, and properties of
rational and irrational numbers. The last part of the course deals with
combinatorial reasoning and its applications in a variety of different areas.
In this course you will find a much greater emphasis
on communication, both written and oral, than in other mathematics course you
may have taken. Justifying a belief in the truth or falsity of a mathematical
assertion requires a rational argument. A main theme of this course is learning
to express such arguments with clarity and precision.
The specific topics to be covered, together with the
corresponding sections of the course text, are as follows:
|
SECTIONS |
CONTENT |
|
1.1
-1.3 |
Logic
of Compound Statements (logical form and logical equivalence; logical
implication; valid and invalid arguments) |
|
1.4
-1.5 |
Application:
Digital Logic Circuits (relation among circuits, tables, and logical expressions;
binary representation of numbers; computer addition) |
|
2.1
- 2.4 |
Logic
of Quantified Statements |
|
3.1
- 3.7 |
Elementary
Number Theory and Methods of Proof (divisibility; division
theorem; rational and irrational numbers; floor and ceiling; mod and
div; direct and indirect proof; division into cases) |
|
3.8 |
Application:
Algorithms (division algorithm; Euclidean algorithm) |
|
4.1
- 4.3 |
Sequences
and Mathematical Induction |
|
6.1
- 6.4, 6.6, 6.7 |
Combinatorial
Reasoning (counting and probability; possibility trees and the multiplication
rule; combinations; the binomial theorem) |
Contact
Information
E-mail: sepp@condor.depaul.edu
Phone: (773) 325-4880 (Office) or (847)
256-6284 (Home)
Office Hours: M
Course homepage:
http://condor.depaul.edu/~sepp/MAT140/140-801homepage.htm
Homework and Grading
Policy: The importance of your
active involvement cannot be overstated. Mathematics is not a spectator sport.
Like any participatory activity, it must be practiced regularly to be mastered.
You will be assigned homework weekly. It will be posted on the course homepage
and will be collected, graded, and returned to you. Be sure to consult the course website for the assignment if you ever
need to miss a class.
Unless an announcement is made to the contrary,
there will be quizzes every week except on exam days, mostly done with partners
but without books or notes. The midterm exam will be February 9 and the
comprehensive final exam on March 15. Since the quizzes and exams will reflect
the homework, mastering the material in the homework will be essential for
success in this course.
The lowest quiz score will be dropped from the quiz
average used to compute the final grade. The midterm exam will count for 35% of
the final grade, the quizzes for 10%, the homework for 10%, class participation
for 5%, and the final exam for 40%. However, if the score computed on the basis
of quizzes and exams alone exceeds that computed taking homework and class
participation into account, the higher grade will be assigned. Alternate grades
such as Incomplete will be granted only in cases of documented medical
emergencies or other serious adversities.
Since students learn a great deal when they
verbalize their thoughts in mathematics, you are encouraged to work together on
homework and group quizzes. But anyone found cheating on an individual quiz or
an exam will receive an F for the course.
Make-up Exams: Generally speaking, you are expected to take all
examinations at their scheduled times. However, except for the weeks just
before the midterm and final exams, if you miss a class in which a quiz was
given, you may make up the quiz provided
you do so before the next scheduled class meeting. No make-up in-class quizzes will be given after that time. If you
are ill at the time of the midterm exam, you must contact me in advance of the exam to make special
arrangements.
Tutoring: Mathematics tutors are available to assist students
on the
Important Dates:
Friday,
January 16: Last day to drop classes with 100% tuition refund
Monday,
February 9: Midterm Exam
Friday,
February 20: Last day to withdraw from class
Monday,
March 15: Final Exam