LECTURE: M-Th 13:00-13:50pm, Sp-316; Mon: 16:00-16:50, Sp-316
INSTRUCTOR: Dr. Pante STANICA, 268 Spanagel, 656-2714,
pstanica@nps.edu,
http://faculty.nps.edu/pstanica/index.htm
(I prefer to be
contacted by email)
OFFICE HOURS: T,Th 12:00-12:40am;
M/W 10:00-10:40pm (or come by if my door is open).
(Be aware that office hours are not a substitute for regular class time)
TEXT: Discrete Mathematics and Its Applications (6th ed.); by Kenneth H. Rosen
2007.
The web site www.mhhe.com/rosen supplements
the text and helps you with some of the topics.
PREREQUISITE: MA1025/2025, or equivalent exposure to elementary
propositional and predicate logic and mathematical proof.
CALCULATOR POLICY: Using a CAS like Mathematica
or Maple can give more insight but it is not required.
MATERIAL TO BE COVERED (and Objectives for the course—subject to be
adjusted along the way):
Week 1: Review 1.1-1.8 (Logic, Methods of Proofs)
Week 2: A1, 2.1-2.4 Sets, Functions, Sequences
Week 3: 3.2-3.7 (Algorithms, Integers, Matrices)
Week 4: 4.1, 4.3, 5.1 Mathematical Induction; Basics of Counting
Week 5: 5.2-5.5 Counting, Pigeonhole Principle,
Permutations/Combinations, Binomial Theorem
EXAM I (in-class)
Week 6-7: 7.1-7.5 Recurrences, Generating Functions, Principle
of Inclusion/Exclusion
Week 8: 8.1, 8.2, 8.3, 8.5 Recurrence Relations
Week 9-11: Chapter 9 – Graphs, 10.1 (Trees)
End of Week 11: Problem Solving, Review
Week 11: FINAL (Take-Home) EXAM
HOMEWORK: You are encouraged to do as many problems as you can
from the book. However the standard (default) assignment for each week is to
read carefully the indicated sections and to prepare for homework the problems
I will assign in class. The homework will not be collected. However, the exams
may contain problems from the assigned homework.
GRADING: The number of possible points is 200 (well, a bit more than that, if
you take the quizzes). For the letter grade I will use the following scale (be
advised that class participation will be considered, especially in the
borderline grades) (there are no exceptions from this scale!!!!):
185-200: A
175-184: A-
170-174: B+
160-169: B
155-159: B-
145-154: C+
135-144: C
130-134: C-
125-129: D+
100-124: D
0-99: failing grade.
An unresolved absence from either of the two tests or the final examination
will result in a final grade of “FA”.
ACADEMIC
HONESTY: Cheating in this course will
not be tolerated and will be dealt with as harshly as the University
permits. I will report any student behavior that appears contrary to the
standards of discipline and academic honesty or violations of the provisions
described in the current edition of NPS Student's Catalog.
CLASS
ATTENDANCE AND ENVIRONMENT: You
should do every attempt to arrive on time and attend each class. You are
responsible for the material covered in missed classes. I do not tolerate any
rude behavior; however, I encourage constructive comments on the material
and/or lecture. We have to maintain a class environment conducive to learning
therefore I am against bringing “active” cell phones, pagers, and
other similar disruptive devices into the classroom.
NOTES: MA3025 is designed to provide a foundation in logic
and elementary discrete mathematics. The emphases are twofold: We begin with a
review of “naive” propositional and first-order predicate logic. We
then explore the way in which the logic is applied in some fundamental areas of
mathematics that are relevant to the study of both mathematics and computer
science. Topics from logic include truth tables, predicates, quantifiers, and
inference rules. Additional mathematical topics include elements of set theory,
mathematical induction, relations and functions, and number theory. There are
no formal laboratory projects.