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 Graduate School of Management on Tuesday and Thursday from 9:30-10:45 p.m.   There

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