MATH
327
Discrete Structures
Fall 2013
Professor:
Dr. Janet Vassilev
Office: SMLC 324
Office
Hours: MWF 9 -10 am and by appointment.
Telephone: (505)
277-2214
email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil
Texts
:
How To Prove It: A Structured Approach, 2nd Edition, by Daniel Velleman.
Course
Meetings: The course lectures will be held in SMLC 356 on MWF at 10-10:50 am.
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 Wenesdays and will
be collected the following Wednesday by the end of the day. 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 around 4 of the assigned
problems will be graded. 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 Thursday, October 6 and Thursday, November
17. The Final is on Thursday, 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 Dr. Vassilev’s Discrete Structures):
Date
|
Section
|
Topic
|
Homework
|
8/19
|
1.1
|
Introduction to
Logic and Deductive Reasoning
|
|
8/21
|
1.2
|
Truth Tables
|
p 13-14: 2, 3, 4, 6 p 24-26: 2, 3, 4, 8, 10, 13 |
8/23
|
1.3
|
Variables and
Sets
|
|
8/26
|
1.4
|
Operations on
Sets
|
|
8/28
|
1.5
|
The Conditional
|
p 41-43: 2, 5, 7, 8, 9, 15 p 53: 2, 3 |
8/30
|
1.5
|
The Biconditional
|
|
9/4
|
2.1
|
Quantifiers
|
p 53-54: 5, 7, 10 p 63-64: 3, 5, 8 |
9/6
|
2.2
|
Equivalences involving quantifiers |
|
9/9
|
2.3
|
More on Sets
|
|
9/11
|
3.1
|
Proof Strategies |
p 72-73: 2, 3, 5, 9, 10 p 81-83: 5, 6, 9, 12 |
9/13
|
3.2
|
Proofs involving negations and conditional statements |
|
9/16
|
3.3
|
Proofs
involving quantifiers
|
|
9/18
|
|
Proofs involving quantifiers |
p 106-107: 3, 4, 6, 10 p121-124: 2, 4, 5, 11, 19, 21, 24 |
9/20
|
|
Proofs involving conjunctions and bi-conditional statements |
|
9/23
|
3.5
|
Proofs involving disjunctions |
|
9/25
|
|
Finish up working in groups on proofs from sections 3.3-3.5
|
p 143-146: 2, 6, 12, 13, 14, 27 |
9/27
|
|
Review |
|
9/30
|
|
Midterm 1 |
|
10/2
|
3.6 |
Existence and Uniqueness Proofs |
p 170-171: 3, 7, 10, 11 |
10/4
|
4.1, 4.2
|
Cartesian Products and Relations |
|
10/7
|
4.2 |
Relations
|
|
10/9
|
4.3
|
More on
Relations
|
p 186-189: 2, 4, 9, 11, 12, 14, 21 |
10/14
|
4.4 |
Ordering
Relations
|
|
10/16
|
4.4
|
More on Ordering Relations
|
Handout |
10/18
|
|
Equivalence Relations |
|
10/21
|
5.1
|
Functions |
|
10/23
|
5.2
|
One to one and onto |
p 233-236: 2, 4, 8, 11, 14 p 243-245: 8, 9, 18 |
10/25
|
5.3 |
Inverses |
|
10/28
|
5.4 |
Images and Inverse Images |
|
10/30
|
6.1 |
Induction |
p 252-253: 4, 6, 12, 13 p 258: 1(b,c), 2(c,d) |
11/1
|
Review |
||
11/4 |
Midterm 2 |
||
11/6 |
6.1
|
Induction
|
p 265-267: 5, 6, 8, 11, 12, 16 |
11/8 |
6.4
|
The division algorithm and euclidean algorithm, Strong Induction
|
|
11/11 |
|
Euclidean Algorithm
|
|
11/13 |
6.3 |
Recurrence Relations |
p 295-300: 4, 5, 17 Handout |
11/15 |
|
Recurrence Relations
|
|
11/18 |
7.1-7.2 |
Countability
|
|
11/20 |
Countability, Principles of Counting |
p 312-315: 3,7, 15, 16 Handout |
|
11/22 |
Inclusion and Exclusion, Addition and Multiplication Rules
|
||
11/25 |
Permutations and Combinations (Counting notes)
|
|
|
11/27 |
Binomial Theorem and Counting with Repetitions
|
Handout | |
12/2 |
Pigeonhole Principle
|
||
12/4 |
Review
|
||
12/6 |
Review |
||
12/13
|
|
Final Exam 7:30
am
|
|