MATH 327 Discrete Structures
Fall 2009
Professor:
Dr. Janet
Vassilev
Office:
Humanities
467
Office
Hours: TWTh
11-12
Telephone:
(505) 277-2214
Email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil
Text
:
Discrete Mathematics with Graph Theory, 3rd Edition by Goodaire and
Parmenter
Course
Meetings: The course lectures will be held 302 Anderson
Topics: Fundamentals of mathematical proof in the context of discrete structures, logic, sets and relations, functions, integers, induction and recursion, counting, permutations and combinations and algorithms.
Homework
(200 points): Homework will be assigned weekly on Tuesdays and will be
collected the following Tuesday. Late homework will not be accepted. If
you miss class, either slip the homework under my door or send it to me via the
email listed on the syllabus.
Homework will not be graded unless it is written in order and labeled
appropriately. The definitions and theorems in the text and
given in class are your tools for the homework proofs. If the theorem has a
name, use it.
Otherwise,
I would prefer that you fully describe the theorem in words that you plan to
use, than state by Theorem 3. Each week I will select about 4 or 5 of the
assigned problems to grade. The weekly assignments will each be worth 20
points.
I
will drop your lowest two homework scores and the remaining homework will be
averaged to get a score out of 200.
Exams (400
points): I will give two midterms (100 points) and a final (200
points). There are no make up exams. If a test is missed, notify me as soon as
possible on the day of the exam. For the midterms only, if you have a
legitimate and documented excuse, your grade will be recalculated without that
test. The Midterms are tentatively scheduled for Tuesday, September 29
and Tuesday, November 10. The Final is on Tuesday, December 15, from
7:30-9:30 am.
Grades: General guidelines
for letter grades (subject to change; but they won't get any more strict):
90-100% - A; 80-89% - B; 70-79% - C; 60-69% - D; below 60% - F. In
assigning Final Grades for the course, I will compare your grade on all course
work (including the Final) and your grade on the
Final Exam. You will receive the better of the two grades.
Tentative
Schedule (for Discrete Structures):
Date
|
Section
|
Topic
|
Homework
|
8/25
|
0.1, 0.2 and 1.1
|
Logic
|
0.1 1(e,f),
2(f,h,k), 3(b,c,g), 5(b,I,j), 6(d,f,k)
1.1
2a, 10a 11d
|
8/27
|
2.1 and 2.2
|
Sets and Set
Operations
|
|
9/1
|
2.2 and 2.3
|
More Set
Operations and Relations
|
2.1 2(b,d), 3(d,e), 5(b,e,g), 10b, 12(b,f), 14b
2.2 1b, 6b,
18, 19a, 21, 28a
2.3 4(c,d),
5(a,d,h), 9(d,g)
|
9/3
|
2.4
|
Equivalence
Relations
|
|
9/8
|
2.5
|
Partial Orders
|
2.4 2(b,c), 4, 9, 13(c,d), 15(a,b), 23
2.5 1(c,d),
3(c,d), 4(c,d), 5, 10a, 11b, 13b, 16b,17
|
9/10
|
3.1
|
Functions
|
|
9/15
|
3.2
|
Inverses and
Compositions
|
3.1 1(d,e), 4(b,c), 7b, 13b, 15b, 24b, 26a, 29
3.2 3, 6b, 7c,
10(b,c), 15, 18
3.3 3b, 7, 18,
20(c,f), 22b
|
9/17
|
3.3
|
1-1
Correspondence
|
|
9/22
|
4.1
|
Division
Algorithm
|
4.1 5(a,c), 6(a,e), 7, 11b
4.2 2,
10(b,c), 11, 12(d,e), 19, 20, 22, 24, 29
|
9/24
|
|
Review
|
|
9/29
|
|
Midterm 1
|
|
10/1
|
4.2
|
Euclidean
Algorithm
|
|
10/6
|
4.3
|
Prime Numbers
|
4.3
1(c,d), 4(b,c), 6, 9, 12a, 17(a,b), 20a, 22, 35
4.42, 3(b,e), 9(b,g,i), 10a, 11c, 16, 18a, 20a
|
10/8
|
4.4
|
Congruence
|
|
10/13
|
4.5
|
Chinese
Remainder Theorem
|
4.5 1c,
2e, 6b, 9d, 13, 15, 18(c,g), 24d
5.1 1(a,f),
4(d,g), 5b, 6(c,e), 9(d,g), 17
|
10/15
|
5.1
|
Induction
|
|
10/20
|
5.2
|
Recursively
defined sequences
|
|
10/22
|
5.3
|
Homogeneous
recurrence relations
|
|
10/27
|
5.3
|
Non-homogeneous
recurrence relations
|
5.2 1(b,c), 6, 15, 20, 23, 26, 43
5.3 2, 6, 8,
13, 15
|
10/29
|
6.1 and 6.2
|
Inclusion-Exclusion
Principle and Counting
|
|
11/3
|
6.3
|
Pigeonhole
Principle
|
5.4 1(b,e), 2(d,g), 4, 6
6.1 3, 5, 9,
11
6.2 4, 6(a,b),
8(a,b), 17(a,b), 20b, 22(b,c)
|
11/5
|
|
Review
|
|
11/10
|
|
Midterm 2
|
|
11/12
|
7.1
|
Permutations
|
|
11/17
|
7.2
|
Combinations
|
6.3 5,
8, 12, 15, 24
7.1 2, 4, 11,
15
7.2 4, 7(a,b,e), 12, 16(a,b), 18
7.3 2, 4, 9,
14, 17
|
11/19
|
7.5 and 7.6
|
Repetitions
and Derangements
|
|
11/24
|
7.7
|
The Binomial
Theorem
|
No homework
this week – Happy Thanksgiving
|
11/26
|
9.1 and 9.2
|
Intro to
graphs
|
|
12/1
|
9.3
|
Graph
Isomorphisms
|
7.5 2,
6, 8, 9, 12, 14
7.6 4, 6(a,b,e)
7.7 3(a,c), 12, 22
9.2 2, 6, 7,
15, 21, 22a, 32
|
12/3
|
13.2
|
Coloring
Graphs
|
|
12/8
|
|
Review
|
|
12/10
|
|
Review
|
|
12/17
|
|
Final Exam
|
|