SYLLABUS – MA 3025 – Logic and Discrete Mathematics, September-December 2008
NPS, Dr. Pante Stanica

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.

TESTS: One in-class midterm will be given (possibly on October 22nd or October 29th) and a final comprehensive take-home exam in Week 10 (to be returned one week later). Absolutely no collaboration is allowed. Both the midterm and the final exam will contain approx. 10-20 prob/que (each of the prob/que will be worth 5-10 points for a total of 80 points for the midterm and 120 points for the final). No make-up tests will be given except in extraordinary circumstances (e.g. illness - present verified doctor's excuse). I reserve the right to give in-class pop quizzes (1-5pts), which will be used toward the final grade, as an add-on (extra credit) to the final score. If the test dates will be changed I will announce it in class at least one week in advance. It is your responsibility to stay informed of such changes.

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.