Instructor: Jey Ratnaswamy
Office Culm 521
Phone #: (973) 5658556
E-mail: Ratnaswa@njit.edu
Office Hours: T, W, R, F: 3-4pm.
Syllabus: MATH226
DISCRETE MATHEMATICS – MATH 226 SPRING
2003
Credits: 4.
Text: Discrete Mathematics and Its
Applications (4-th edition).
By
Kenneth Rosen, McGraw - Hill Inc. ISBN
0-07- 289905-0.
Prerequisites: Calculus II.
Examinations: Two common examinations and
three in class quizzes will be given.
The dates of the common exams are:
April 09 4:15 – 5:45pm
The times for the three 45 minutes in class quizzes
are:
Friday
February 07 (last meeting).
Second
meeting during the 8-th week of the semester.
First meeting of the 13-th week of the semester.
Evening sections will have common examinations on the above listed dates, but the time for them will be from 5:45pm to 7:00pm. The quizzes in the evening class will be as listed above. A comprehensive final examination will be given at the end of the semester. The date for this final examination will be announced at the end of the semester.
Final grade: The scores received on the two common
exams, the three quizzes and the final examinations will determine the final
grade. The weighting factors will
be: common examinations 35%, the three
quizzes 30% and the final examination 35%.
Examination time conflicts: If a student is scheduled for more than one common Mathematics
Department examination, then the examination in the course with a lower
numerical designation will be taken at the regularly scheduled time and the
other examination with the evening section.
Thus if the conflict is because of Math 226 and Math 222, the Math 222
examination will be taken at the scheduled time and the
Math 226 examination with the evening section.
Missed common examinations or quizzes: There will be no make-up examinations permitted for whatever
reason. A grade of “0” will be given
for missed tests. If a student in good
standing misses one examination or quiz, the instructor may in rare
instances decide to give a final grade of “INC” and request that a
pertinent test be taken after the end of the semester.
Tardiness and absences: Students should try to come to class a few minutes before the
scheduled time. On occasion,
instructors will discuss the subject matter in a manner that differs from the
presentation given in the book - absences make it very difficult to obtain the
necessary material. If a student is
absent frequently (4 or 5 times - and that’s more than a week of school!)
she/he may be asked to drop the course due to excessive absences. High exam and quiz grades are not sufficient
for a passing grade the Math 226 course.
Homework assignments: Very many homework problems are given. They are an integral part of the
course. Homework problems will not be
graded. The instructors will answer
questions pertaining to the homework problems in sessions held during the
regularly scheduled class times.
Additional information may be obtained from the Learning Center or from
the instructors during office hours.
COURSE OUTLINE FOR MATH 226
Week 1 Introduction to logic, propositional
equivalences, sets.
Section 1.1 - probs:
2,3,4,6,7,9,11,16,19,22,25,26,29-30
Section 1.2 - probs:
1,2,3-6,8ab,10ab,11,13,15,16,18,25,26
Section 1.4 - probs:
1,2,3,5,6,7,9,10-13,15-17,20,22,23,24
Week 2 Set operations, functions, integers and
division.
Section 1.5 - probs:
1,2,4,5,6,7,8,11,12,14,16,17,18,20,22,24,25-26,30,38-40
Section 1.6 - probs: 1-4,6,8-12,14,16-17,22,24,28,29,49,50,53
Section 2.3 - probs:
1,3,5,6,9,10,11,15,16,24,25,28,30,31,32,34,36,45-48
Week 3 Integers and algorithms, applications
to number theory.
Section 2.4 - probs: 2-5,8,11,12,15,16
Section 2.5 - probs: 2,4,6,12,15,23,25
Week 4 Methods of proof, mathematical induction, recursive definitions,
Section 3.1 - probs: 1,4,10,16-19,34,36,39,40,66,67
Section 3.2 - probs:
1,4,6,7,9,11,12,15,17,18,21,23,29,32,33,47,60
Section 3.3 - probs: 2,4,5,7,8,12
Week 5 Basics of counting, the pigeonhole
principle.
Section 4.1 - probs:
1,3,4,8,9,17-19,21,24,27,29,30-33,36,38,39,41-43,48-51
Section 4.2 - probs: 1-4,10,14,16,18-20,22,23,27,30,35
Week 6 Permutations and combinations, generalized permutations and
combinations, generation.
Section 4.3 - probs:
1-3,6,7,8,10,15-17,19-20,24,26,27,31,33,39,40,48,55
Section 4.6 - probs:
2,5,6,10-12,14-17,20,22,27,28,31,34,35,42,46
Section 4.7 - probs: 1,2,9 +additional problems given by
instructor
Week 7 Recurrence
relations, solution of recurrence relations, inclusion-exclusion principle.
Section 5.1 - probs: 2,4,5,6,7,13,17-19,21-22,24,25,30,31
Section 5.2 - probs: 2,3,12,14,19,24,25,27,28,30,32
Section 5.5 - probs: 1,4,5,7,10,11,14,15,18
Week 8 Applications of inclusion-exclusion,
relations, representation of relations.
Section 5.6 - probs: 2,3,4,8,10,11,13,15,17,25,26
Section 6.1 - probs: 1,3,4,6,8,11,14,15,16,18,20,21,34
Week 9 Closures of relations, equivalence
relations
Section 6.3 - probs: 1,2,4-9,12,15,17
Section 6.4 - probs: 2,3,9,10,11,16,17,19,20,26
Section 6.5 - probs: 1-3,5,7,10,12,14,16,19,22,24,25,31,35
Week 10 Partial order relations, graphs, graph
terminology and representation.
Section 6.6 - probs: 1,2,4,5,8,9,11,14,15ac,16,18,19,20,24,26-28,35,48,50
Section 7.1 - probs: 1,4,6,8,11,15,17
Section 7.2 - probs:
1,3,4,5,6,8-10,12,14,15,17-21,24,25,30,32-34
Week 11 Isomorphism, connectivity.
Section 7.3 - probs:
2,4,6,8,10,12,14,16,18,20,22,24,26,29,30,35,37-39,41,43,46,48,52,54,55,57ab,58,62,63
Section 7.4 - probs: 2,4,5,7,8,10,14,16,17,18,29,34,37
Week 12 Euler
and Hamilton paths, shortest path problems.
Section 7.5 - probs: 1,2,4,5,7,9,11,12,14,16,22,24,26-29,31-
33,36,37,40,41,47,48,51,53
Section 7.6 - probs: 2,3,6,11,17
Week 13 Planar graphs, graph coloring.
Section 7.7 - probs: 1,3,4,6,9,10,14,18,20,22
Section 7.8 - probs: 1,2,4,6,8,9,13,15,17
Week 14 Introduction to trees, spanning trees,
review.
Section 8.1 - probs: 1,2,4,6,9,10,12,14,16-20
Section 8.5 - probs: 1,3,6,7,9,11,13,14,17,24,26
Week 15 Review.
November 8, 2002