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CMSC 203 - Discrete Structures

Spring 1999

Syllabus

**Text:** *Discrete Mathematics with Applications* by Susanna S. Epp

**Prerequisites:** Math-151 (Calculus 1) and CMSC-101, CMSC-103, or CMSC-201

**Course Description:**
Fundamental tools, topics, and concepts of discrete
mathematics needed to study computer science are covered. This course
emphasizes counting methods, proof techniques, and problem-solving
strategies. Topics include sets, numbers, functions, relations,
graphs, combinatorics, modular arithmetic, summations and recurrences.
By the end of the course, each student should be able to do the following
types of proofs: direct proof (including applying definitions, case analysis
and construction), indirect proof (aka proof by contradiction or proof by
negation), proof by counterexample, proof by counting argument (e.g. proof
by Pigeonhole Principle), and proof by both the weak and strong forms of
induction.

Also, by the end of the semester, each student should be able to count and
estimate discrete objects using the following techniques: fundamental
principle of counting (addition and product rules), permutations,
combinations, k-permutations, permutations with repeated elements,
D'Alembert's counting method, and the principle of inclusion/exclusion.

**Course Outline:**
The course covers most of the sections of Chapters 1-8
and 10 of the text. The course material will be taught in approximately
the same order as it appears in the text.

**Required Work and Expectations:**
Required work consists of graded
homework assignments, two 1 hour 15 minute exams, and a cumulative, two hour
final exam. In addition, each student is expected to participate actively in
class. Refer to the Course Calendar or Required Homework sections for the
due dates and assigned problems for the homework.
Each homework assignment consists of required readings and problems to be
solved in writing. Solving problems is the only way to learn the course
material and prepare for the examinations; consequently, the homework is the
most important activity of the course. Students are encouraged to work
together, but each solution must be written up individually.
Plagiarism will be dealt with
severely.

Each exam is a written, closed-book, in-class test. These tests are learning
experiences which enable you to demonstrate what you can do.

**Grading Policy:**
This course is offered as Pass/Fail, Audit, or Regular
Grading. The course grade is based on a combination of 2 regular exams,
average course homework grade, and a comprehensive final exam. Each exam and
each homework is graded on a scale of 100%. The course homework grade is
also based on a scale of 100%. It is the average of all homeworks remaining
after the two lowest scoring homeworks have been deleted. Each missed or
late homework assignment counts as a homework with a grade of 0%.
The course grade is defined by the formula:

Course Grade = ( Exam I + Exam 2 + Avg Hwk + Final)/4

Letter grades are assigned according to the following table:
A: 100-90%
B: 89-80%
C: 79-70%
D: 69-60%
F: 59-50%

There will be two hard and fast rules:
**No late homeworks will be accepted** and
**No Make-up Exams!**

**Required Homework: **
Be sure to
write your name and section on each page you hand in. Write in complete,
grammatically correct English sentences. Always justify your answers and
explain your reasoning clearly! Unjustified answers risk receiving no
credit. Late homeworks will not be accepted!

**Computational Facilities:**
Each student should obtain a permanent, named
account on the UMBC8 computer. To obtain an account, go to any computer lab
(e.g. the first floor lab in the ECS building) and follow the instructions
for applying for an account. Although there will be no programming
assignments, per se, students are strongly encouraged to use the computer
facilities for email, newsgroups, network access (ftp, telnet, lynx,
mosaic, netscape), word processing, symbolic computation (Maple V),
and access to course materials. Special tutorials
are offered throughout the semester by University Computing on the use of
these and other tools which are essential to working Computer Scientists and
students. Please feel free to ask the instructor for help using the
facilities and software. If you are accessing UMBC computers from home, you
must abide by the rules and regulations administered by University Computing
Facilities. UMBC can be reached via modem at 744-8000 (slower than 9600
baud) and 744-8622/766-UMBC (9600-14400 Baud). University computing advisors
can suggest software that may be useful for working from home.

**Academic Misconduct:**
Each student is expected to be familiar with all
University and Department policies on academic misconduct. An egregious type
of academic misconduct is plagiarism, which, in each of its many forms
involves representing someone else's work as your own. For example, copying
phrases from someone's written homework is one form of plagiarism. It is the
policy of the instructor and of the department to deal severely with any
student found guilty of academic misconduct. Offenders risk suspension from
UMBC.

**Advice:**
The most effective way to learn the course material is to solve
problems, at least a few each day. It is recommended that you solve every
problem in every assigned section of the text. Start early, keep up, and
manage your time effectively. Do not passively listen to lectures, but
actively participate in each class meeting. Ask questions when you do not
understand completely or when you see an alternate route. Take advantage of
the resources at your disposal. If you find yourself falling into trouble,
seek help from the instructor and TA immediately. If you get stuck on a
homework problem, don't ask someone to solve it for you, but rather look for
copious hints to allow you to find the rest of the solution. Open you mind
to the joy of Discrete Mathematics!

##### Last Modified: October 30, 1998