LECTURE:
M, W
10
INSTRUCTOR:
Dr. Pante
STANICA, 242B Spanagel, 656-2714,
pstanica@nps.edu (reliable and preferred means
of communication);
http://faculty.nps.edu/pstanica/
OFFICE HOURS: M,W 12
(Be aware that office hours are not a
substitute for regular class time)
TEXT:
Discrete
Mathematics and Its Applications (7th ed.); by
Kenneth H.
Rosen 2012.
The web site www.mhhe.com/rosen supplements
the text and helps you with some of the topics.
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):
|
3-3 |
Propositional Logic and Applications |
1.1, 1.2 |
|
2-5 |
Propositional Equivalences |
1.3 |
|
2-7 |
Predicates and Quantifiers |
1.4 |
|
2-9 |
Nested Quantifiers |
1.5 |
|
2-11 |
Rules of Inference |
1.6 |
|
3-14 |
Introduction to proofs |
1.7 |
|
1-15 |
Proof Methods and Strategy |
1.8 |
|
2-17 |
Sets |
2.1 |
|
2-19 |
Set Operations |
2.2 |
|
2-21 |
Functions |
2.3 |
|
1-22 |
Exponential and Logarithmic Function |
A.2 |
|
2-24 |
Divisibility and Modular Arithmetic |
4.1 |
|
1-25 |
Integer Representations and Algorithms |
4.2 |
|
1-26 |
Primes and Greatest Common Divisors |
4.3 |
|
2-28 |
Sequences and Summations |
2.4 |
|
3-31 |
Mathematical Induction |
5.1 |
|
1-32 |
The Basics of Counting |
6.1 |
|
2-34 |
The Pigeonhole Principle |
6.2 |
|
2-36 |
Permutations and Combinations |
6.3 |
|
|
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 the homework problems I will assign in class. The homework will not be collected. However the exams may contain problems from the assigned homework.
TESTS: Two tests will be given in (approximately) Week 4 (Th) and Week 8 (Th) and a final comprehensive take-home exam. The tests will contain approx. 5-10 problems/questions 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 50 for the tests, respectively, 100 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 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. Class attendance is mandatory, and I may use your attendance for the borderline grades.
GRADING: The number of
possible points is 200(50test1+50test2+100final). 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!!!!):
186-200:
A
175-185: A-
170-174: B+ 160-169: B 150-159:
B-
140-149: C+ 130-139: C 125-129:
C- 120-124: D+ 100-119: D
000-099: 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. Children may not be brought into the
classroom except in emergency circumstances and with my permission. Do not
bring food in classroom. When on breaks, please respect other classes in
sessions and avoid disturbing them.
NOTES:
* MA2025, Logic and Discrete Mathematics I, is a first
course in discrete mathematics for students of mathematics and computer science.
Topics include propositional and predicate logic up to the deduction theorem,
methods of mathematical proof, naive set theory, properties of functions,
sequences and sums, mathematical induction, an introduction to divisibility and
congruences, and an introduction to enumerative combinatorics.
* It is a bit of material to be covered, so do not fall behind.
* If it is necessary, there will be
updates of this handout. Make sure you check my homepage regularly
for info on the course.
* Good Luck !
I hope you will all make good grades!
Homework assignment for 2025 (may change, as we go along, though):
Text: Kenneth Rosen - Discrete
Mathematics and Its Applications
(7thed.)
Section 1.1: 1,3(c,d),9,12,13,17,27,33,44
Section 1.2:
5,7
Section 1.3:
5,10,14,15,23,30
Section 1.4:
5,9,11,13,17
Section 1.5:
3,9,27
Section 1.6:
3,5,11,17,19,27
Section 1.7:
8,11,12,13,17,26,27
Section 1.8:
1,3,9,10
Section 2.1:
1,5,9,17,18,21,24
Section 2.2:
3,16,19,31
Section 2.3:
1,5,12,13,23,36
Section 2.4:
3,5(a-d),9(c),15(a,b),31,33
Section 2.5:
No homework
Appendix A2: 1,2,4
Section 4.1: 9
Section 4.2: 3(a),5(a,b),7(a,b)
Section 4.3: 5,21,24(a,b),25(a,b),33
Section 4.4: 1,3,5(b),6(b),11(a),12(a),21,33,37,39
Section 4.5: No
homework
Section 5.1: 3,7,13,21,31,33,35
Section 6.1: 1,3,7,11,23,25,29,33,59
Section 6.2: 1,3,9,11,14,37
Section 6.3: 5(a,b),6(a,b),7,9,13,17,21,27,31,33,35,37
Some section(s) may be added later!