Professor:
Dr. Janet Vassilev
Office: Humanities 467
Office
Hours: MWF 11 am12 pm and by appointment.
Telephone: (505)
2772214
email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil
Date

Section

Topic

Homework

8/23

handout

The Addition, Multiplication and Subtraction Principles^{} 

8/25

1.2

Division
Principle, Examples of the basic principles and Permutations


8/27

1.2, 1.3

Permutations
and Circular Permutations

Chapter 1
problems: 2, 3, 4, 5, 6, 10, 11(ii), 14(i, iv)
Additional Problems

8/30

1.3, 1.4

Circular
Permutations and Combinations


9/1

1.4

Combinations


9/3

1.5

Injection and
Bijection Principles

Chapter 1
problems: 15, 16, 17, 19, 20, 21, 23, 26, 30, 35, 37

9/8

1.5

Examples of IP
and BP


9/10

1.6

Arrangements with repetition_{} 
Chapter 1
problems: 25, 41, 42, 43, 47, 48, 50, 51, 77, 81(i, ii), 82

9/13

1.7

Selections with
repetition and distribution of distinct objects in distinct boxes


9/15

1.7

Distribution of
distinct objects in distinct boxes


9/17

1.7

Distribution of
indistinct objects in distinct boxes

Chapter 1
problems: 54, 55, 57, 58, 65, 66, 68, 72, 73, 84, 91

9/20

1.7

Distribution of
distinct objects in indistinct boxes and probability


9/22

2.2

Discrete
probability and the Binomial Theorem

Probability notes

9/24

2.2, 2.3

More on the
Binomial Theorem

Chapter 1
problems: 44
Chapter 2 problems: 1,
2, 10, 11, 14, 18, 24, 25, 26
Additional Problems

9/27

2.3, 2.5

Vandermonde’s
Identity and Chu Shih Chieh’s Identity


9/29

2.5, 2.6

Examples of CSC
and Shortest Paths and binomial coefficients


10/1

2.6

More on
Shortest paths and binomial coefficients

Chapter 2
problems: 12, 16, 19, 21, 30, 31, 34,
35, 40, 44

10/4

2.6, 2.7

Reflection
Principle and binomial coefficients modulo p


10/6

2.7, 2.8

Binomial coefficients
modulo p and the Multinomial Theorem


10/8


Review

Chapter 2
problems: 5, 7, 9, 15, 51, 52, 64, 66,
67

10/11


Midterm


10/13

3.2, 3.3

Pigeonhole
Principle


10/18

3.4

Ramsey Numbers


10/20

3.5, 4.1

Bounds for
Ramsey numbers and Principle of Inclusion and Exclusion


10/22

4.1, 4.2

Principle of
Inclusion and Exclusion

Chapter 3
problems: 1, 2, 4, 8, 10, 15, 22, 28, 31, 34, 35

10/25

4.3, 4.4

Generalized Principle of Inclusion and Exclusion


10/27

4.5

Derangements
and generalized derangements


10/29

4.6, 4.7

Euler phi
function and the problem of seating married couples around a table…

Chapter 4
problems: 1, 3, 6, 9, 11, 13, 14, 21, 27(4.6.2, 4.6.4, 4.6.6), 28, 32

11/1

5.1

Generating
Functions


11/3

5.1, 5.2

Solving
problems using generating functions


11/5

5.2, 5.3

More problems
and generating functions for partitions

Chapter 4
problems: 38, 39, 44, 46
Chapter 5 problems:
1, 2, 4, 6, 8, 10, 15

11/8

5.3, 5.4

Ferrer’s
diagrams and exponential generating functions


11/10

6.1, 6.2

Intro to
recurrence relations


11/12

6.3

Homogeneous
linear recurrence relations of order upto 2.

Chapter 5
problems: 17, 21, 31, 32, 34, 38, 39, 49, 53, 63

11/15

6.3

Homogeneous
linear recurrence relations of higher order


11/17

6.4

Nonhomogeneous
linear recurrence relations


11/19

6.4

Nonhomogeneous
linear recurrence relations

Chapter 6
problems: 1, 2, 4, 7, 9, 11, 12, 18, 19, 22
Additional Problems

11/22

6.5, 6.6

Applications of
recurrence relations, Systems of recurrence relations


11/24

6.7

Generating
functions and recurrence relations


11/29

6.8

Nonlinear
recurrence relations


12/1

6.9

Nonlinear
recurrence relations


12/3



Chapter 6
problems: 14, 15, 16, 26, 27, 28, 32,
35, 37, 39, 41

12/6




12/8




12/10




12/17


Final exam

