MATH 327- Introduction to Mathematical Thinking

and Discrete Structures

Fall 2016

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  MWF 9:20 am-9:50 am and 1 pm -1:30 pm and by appointment.
Telephone: (505) 277-2214
email: jvassil@math.unm.edu

webpage: http://www.math.unm.edu/~jvassil

Text :  Discrete Mathematics with Graph Theory, 3rd Edition, Goodaire and Parmenter or the  custom version of the book sold at the bookstore.

Course Meetings:  The course lectures will be held in Dane Smith Hall 333 on Mondays, Wednesdays and Fridays from 10-10:50 am. 

Topics:  Fundamentals of mathematical proof in the context of discrete structures, logic, sets, relations, functions, integers, induction, recursion, counting, perumtations, combinations and algorithms.

Homework (200 points):  Homework will be assigned weekly on Wednesdays and will be collected the following Wednesday at the beginning of class.  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, than state by Theorem 3.  Each week around 4 or 5 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 Monday September 26 and Monday, November 7.  The Final is on Friday, December 16, from 7:30 am-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 Abstract Algebra):

Date

Section

3rd/Custom

Topic

Homework

8/22

0.1/1.1

Mathematical Statements

 

8/24

0.2/1.2

Typical proofs

0.1/1.1 1(a,b,c,e,f), 2(b,d,l,m,o), 4(a,b,e,f), 5(a,b,d,f,j,n), 6(a,c,f), 7(a,d,e)

0.2/1.2 3(a,b,f), 8, 10, 15, 16, 19, 24

8/26

0.2/1.2

Typical proofs continued

 

8/29

1.1/2.1

Truth Tables

8/31

1.2/2.2

Algebra of Propositions

1.1/2.1 1(b,d,e), 5, 6, 10

1.2/2.2 2, 3, 5(a,f,g), 6

1.3/2.3 1(a,e,f), 3

9/2

1.3/2.3,

2.1/4.1

Logical Arguments, Sets

 

9/7

2.2/4.2

Set Operations

2.1/4.1 1, 3(a, b, c, d), 4, 5(a,b,c,e), 6, 8, 11, 12(a,b,d,f), 14

2.2/4.2 1, 3(b,c), 5(a,e,f), 6, 16

9/9

2.2/4.2

Set Operations

9/12

2.3/4.3

Relations

 

9/14

2.3/4.3

Relations continued

2.2/4.2 19, 22, 24, 27, 28(a,b,e)

2.3/4.3 4, 5(a,b,c,d), 7, 9(b,c,e,g), 11

scanned homework p 179 4, 5, 8 (on unm learn)

9/16

2.3/4.3

Relations continued

 

9/19

2.4/4.4

Equivalence Relations

 

9/21

2.4/4.4

Equivalence Relations continued

2.4/4.4 2, 4, 7, 9, 11, 14, 15, 16, 18(c,d,e), 21

9/23

 

Review

 

9/26

 

Midterm 1

 

9/28

2.5/4.5

 Partial Ordering


2.5/4.5 1(a,b,c,d), 3(a,b,c,d), 4(a,b,c,d), 5, 6, 9, 10(a), 11, 13, 15, 16

9/30

2.5/4.5

Partial Ordering continued

10/3

2.5/4.5

Partial Ordering continued


10/5

3.1/3.1

Functions

3.1/3.1 1(a,c,d,e), 3, 4, 8, 9, 12, 13, 19(a), 22(a,b), 26, 27, 28, 32

10/7

3.2/3.2

Inverses and Compositions


10/10

3.3/3.3

Cardinality


10/12

3.3/3.3

Cardinality continued

3.2/3.2 1, 2, 5, 6(b,c,d), 7(b,c), 10, 19, 22, 25

3.3/3.3 3, 6, 7, 12(a), 19(a,c), 26

10/17

4.1/5.1

Division Algorithm


10/19

4.2/5.2

Euclidean Algorithm and gcds

4.1/5.1 4(a,c), 5(a,b), 6(a,d,e), 7, 8, 11(a)

4.2/5.2 3, 4, 5, 9, 11, 12(a,e,g)

10/21

4.2/5.2

Euclidean Algorithm continued


10/24

4.3/5.3

Prime numbers


10/26

4.4/5.4

Congruence modulo n

4.2/5.2 18, 23, 24

4.3/5.3 4(a,b,f), 12(a), 14, 17, 28, 29, 32(a,b), 35

10/28

4.4/5.4

Congruence modulo n continued


10/31

4.5/5.5

Chinese Remainder Theorem


11/2

5.1/6.1

Induction

4.4/5.4 2, 6(e,f), 7, 9(a,b,c,d,e,f), 10(a). 13, 16, 20, 21(a,b), 22(c,e)

4.5/5.5 2(a,b), 9(a,b), 18(a,b,g)

11/4

 

Review


11/7

 

Midterm 2

 

11/9

5.1/6.1

 Induction


5.1/6.1 4(c,d,f), 5, 6(a,c,e,f), 9(a,c,d), 12, 15

11/11

5.1/6.1

Induction


11/14

5.2/6.2

Sequences

11/16

5.3/6.3

Recurrence Relations

5.1/6.1 13, 14, 30a, 41

5.2/6.2 1(a,b,c), 2a, 6, 8, 10, 20, 23, 27, 33(a,b)

5.3/6.3 1, 2, 6, 7

11/18

5.3/6.3

Recurrence Relations


11/21

6.1/7.1

Principle of Inclusion/Exclusion

11/23

6.2/7.2

Principle of Addition and Multiplication

5.3/6.3 8, 10, 12, 16, 18

6.1/7.1 4, 9, 10, 14, 19

11/28

6.3/7.3,

7.1-2/8.1-2

Pigeonhole Principle

Permutations


11/30

7.2/8.2

Combinations

6.2/7.2 2, 4, 8, 14, 20, 25

6.3/7.3 4, 5, 12, 18, 24

7.1/8.1 4, 9, 11, 16

12/2

7.3-4/8.3-4

Probability

12/5

7.5-6/8.5-6

Repetition, Derangements

Suggested counting review:

7.2/8.2 1, 3, 5, 11, 17
7.3/8.3 3, 5, 9, 17, 19, 23
7.4/8.4 9
7.5/8.5 1, 3, 7, 13
7.6/8.6 3, 7

12/7

 

Review

 

12/9

 

Review

 

12/16

 

Final

 7:30 am

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