National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
Emotional Intelligence
Outline
I. What is emotional intelligence ?
II. What is YOUR emotional intelligence?
A. A short 10 item questionnaire
III. Why is it important to know about emotional
intelligence
IV. Four Clusters of Emotional Intelligence
V. How d
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
6
1 Preliminaries
to Alice, three gumdrops to Bob, and one gumdrop to Chad. The set of people that
have received gumdrops is cfw_Alice, Bob, Chad. However, if we wish to know not
only who has received gumdrops but how many gumdrops they have received, the
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
124
5 Generating Functions
We can also consider the multiplication of two series.
!
!
n
n
Theorem 5.2.4 Let f (x) =
n=0 fn x and g(x) =
n=0 gn x . It follows that
# n
$
"
"
f (x)g(x) =
fk gnk x n .
n=0
k=0
Proof Note that
f (x)g(x) = (f0 + f1 x + + fk x
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
118
5 Generating Functions
We now turn our attention to rational functions and their decomposition into partial
fractions. A rational function is a function of the form f (x) = p(x)/q(x), where p(x)
and q(x) are polynomials such that q(x) = 0. If the degr
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
88
3 The Binomial Coefficient
(iv)
!
"
40
.
8, 8, 8, 8, 8
Exercise 3.6.13 Expand (x + y + z)5 .
Exercise 3.6.14 Find the coefficient of x 3 y 4 z5 in each of the following:
(i)
(ii)
(iii)
(iv)
(x + y + z)12 ;
(1 + x + y + z)17 ;
(1 + 2x + 3y + 4z)15 ;
(4
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
5.3 Single Variable Generating Functions
127
Exercise 5.2.14 Prove that for 1 < x 1,
ln (1 + x) =
!
(1)n x n+1
n=0
n+1
.
Exercise 5.2.15 Define the formal derivative of f (x) =
D[f ] =
!
n=0
(n + 1)fn+1 x n .
"
n=0
fn x n as
Show that
D[f g] = D[f ]g + f
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
70
3 The Binomial Coefficient
Hence the coefficient on x 4 is:
! "
6 4
3 (5y + 7)2 .
4
In Sect. 3.6, we will determine how to compute the coefficient of
expansion of (x1 + . + x )n .
x1k1 .xk
in the
Corollary 3.3.3 For all n N,
n ! "
#
n
k=0
k
= 2n .
Proo
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
36
2 Basic Counting
Fig. 2.3 Variations on the
same table setting
Example 2.3.2 Find the number of visually distinct ways of seating n men and n
women around a circular table with 2n seats labeled 1, ., 2n in such a way that sexes
alternate.
Solution The
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
Chapter 2
Basic Counting
2.1 The Multiplication Principle
Suppose that we are ordering dinner at a small restaurant. We must first order our
drink, the choices being Soda, Tea, Water, Coffee, and Wine (respectively S, T, W,
C, and I). Then, we order our a
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
2.4 Application: Legendres Theorem
39
To do this, we will need one of the earliest results from number theory. In fact, the
following result appears in Euclids Elements. Because this result is so well known,
we present it without proof. Interested readers
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
106
4 Distribution Problems
Similarly, suppose cfw_1 , ., k is a partition of n into k parts. This corresponds
to placing i unlabeled balls into the ith urn. Since the i > 0, no urn will be left
empty.
!
It would be desirable to find a concise formula fo
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
2.3 Permutations
33
The second has five choices for appetizer, nine entree choices, and six choices for
dessert. The third has four choices for appetizer, ten entree choices, and eight choices
for dessert. The fourth restaurant has two choices for appetiz
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
2.7 Stirling Numbers of the First Kind
!
P (15, 5)
5
"!
P (10, 3)
3
"!
P (7, 3)
3
51
"! "!
"!
"! "
1
P (4, 2)
P (2, 2)
1
2
2
2
2
= 1816214400.
We can apply this idea to the notion of table settings as well. In these examples,
we will assume that the seats
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
12
1 Preliminaries
of x, denoted x, is the largest integer less than or equal to x. Essentially, the floor
function rounds down to the nearest integer.
Example 1.4.2 Find the floor of each of the following real numbers:
(i)
(ii)
(iii)
x = 67;
y = 22/7;
z
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
3.6 The Multinomial Coefficient
85
Proof Let n = 1 + + k . Note that there are:
! "
(i) n1 ways to place the 1 stars labeled 1 in the n available slots;
! 1"
(ii) n
ways to place the 2 stars labeled 2 in the n 1 remaining slots;
2
!n
"
1 2
(iii)
ways to p
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
BATS
READING COMPREHENSION
RESOURCES FOR MIDDLE
SCHOOL STUDENTS
INFORMATIONAL TEXT
SUMMARY ACTIVITIES  POETRY ANALYSIS
CREATIVE WRITING
A PERFECT MINI UNIT FOR HALLOWEEN!
BATS:
FACT OR
FICTION?
Bats have a bad rap. Many people have really negative feelin
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
FAA1249A FORFF (1215)
Local Office Return Address
Use the DES166 envelope
ARIZONA DEPARTMENT OF ECONOMIC SECURITY
Family Assistance Administration
VERIFICATION OF DISABILITY
DATE OF REQUEST
APPLICANT/PATIENTS NAME (Last, First, M.I.)
CASE NO.
WORKER
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
21992_fcch01.indd 3
A systematic process that considers important
elements of an individuals financial affairs in
order to fulfill financial goals.
The necessities, comforts, and luxuries enjoyed or
desired by an individual or family.
Chapter 1
Chapter 1
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
ADHD
1
Name:
University:
ADHD
Wen Yang
Michigan State University
ADHD
2
ADHD
Introduction
Attention deficit hyperactivity disorder (ADHD) is a chronic neurological condition,
which is usually characterized with hyperactivity, inattention and impulsivity (
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
1.2 Induction and Contradiction
1.2
3
Induction and Contradiction
In this section, we give two commonly used methods of mathematical proof, namely
proofs by induction and proofs by contradiction. These methods will be used
sporadically throughout this boo
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
18
1 Preliminaries
Exercise 1.5.10 Show that in every group of n people, where n 2, there are at
least two people that know the same number of people within the group. We assume
that A knows himself and that A knows B if and only if B knows A.
Exercise 1.
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
5.4 Generating Functions with Two or More Variables
139
f (x, y) = 3x 11 y 23 + 3x 11 y 22 + x 10 y 23 + 2x 11 y 21
+3x 10 y 22 + x 9 y 23 + 3x 11 y 20 + 2x 10 y 21 + 2x 8 y 23 + 2x 11 y 19 + x 10 y 20 + 3x 9 y 21 + x 8 y 22
+x 11 y 18 + 2x 10 y 19 + 2x 9
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
64
3 The Binomial Coefficient
Similarly, we compute B:
!"
(i) Place 3 in the last position. There are now 23 = 3 ways to select positions for
cfw_1, 5, 7.
(ii) Assign numbers from the set cfw_1, 5, 7 to these positions. Since repetition are
allowed, the
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
5.5 Ordered Words with a Given Set of Restrictions
145
and the term corresponding to Chads restriction is:
1+
x
x2
x7
+
+ + .
1!
2!
7!
So the generating function is
! 5
"
x
x6
f (x) =
+
+
5!
6!
!
" !
"
x2
x4
x
x2
x7
1+
+
+ 1 + +
+ +
.
2!
4!
1!
2!
7!
Agai
National University of Sciences & Technology, Islamabad
Intro
PSYCOLOGY 100

Fall 2016
1.5 The Pigeonhole Principle
15
Fig. 1.7 Illustration of the Pigeonhole Principle
York City. We let the number of hairs on a persons head to be the pigeonholes and
each person in New York to be a pigeon. Since k 2000000 and n 8000001, it
follows that ther