Which 0F the Following represents +he Cartesian equcon 0F fhe parametric equarians
x = corsair) and y = 5cost'lfJ3 For 0 a r <15?
r a. y=-5:x-ng23
E: + 3f?
r . _
b 5"] 5m
@- c. y=5m1lm3
r d. y = Lam112
Ix+31m
r e. y=+1
51E
ix+3lm
r f. y=~1
S
lte_ Salve Fo
Exercises 6.2
1. R is the region bounded by the graphs ofy : x2+l, y I 0, X I 0, X I 2. Let S be the solid of
revolution generated by revolving R about the X-axis. Find the volume of S.
Volume ofS =H-E(X2 +1)2dx= H-EGC" +2.7C2 +l)dt
l 2
=H- 7x5 +7x3 +x
1. (a) The picture is
The inner circle has radius 1, the outer has radius
Tr w/i
f/IQH dA 2/ / (TCOSQ)2(T81116)T d7" d6
'rr/2 1
R
(b) No picture was requested. The answer is
7T/2 'rr/2 ~3
dV:/ / / pcosqpgsingb dpdgbdQ
D 0 'rr/4 0
2. (a) We have our pi
4.5 A Formula for Gaussian Curvature
The Gaussian curvature can tell us a lot about a surface. We compute K using the unit
normal U7 so that it would seem reasonable to think that the way in which we embed the
surface in three space would affect the value
0.1. ARBITRARY CURVES l
0.1 Arbitrary Curves
We have shown that all regular curves can be parametrized by arclength, but to explicitly
do this for all curves is impossible, due to the nature of the functions involved. We will
need to modify the Frenet for
1. Prove that an equiangular triangle is equilateral (all sides are congruent).
By the Converse to the Isosceles triangle theorem if in AABC we have that 4A 3 AB
then BC E AC. Since the triangle is equiangular, we also have that 4A E AC from
which it foll
Volumes of Solids of Revolution
The volume of a slice is the area of the slice multiplied by the
width of the slice. vi : (area of side of slicei)(widthi ). The total
b
volume will then be: V Z L A dw .
We are going to examine slice perpendicular to the a
Justify all work using complete sentences .1 Use only methods from class.
F(><)
1. [12] a) Let x) be defined by the graph given above. Determine the following limits, writing +00 or -oo as appropriate. If a
limit does not exist, explain why.
Iim f
Multiple Chaise
{3233,3132 choice that best (Templates Ilse statement 0:" answers the quesners
1. A ditrisicn c f Dittcn Industries manufactures the Futura mc de1 micrcwatre even. The daily:r cast (in dcllars) cf
prcducing these micrcwaire evens is CU) =
PreCalSection2.3Page 1 of 9
Math 1330
Section 2.3 Rational Functions
A rational function is a function of the form
r(x) = PW)
QOC)
where P(x) and Q(x) are polynomials.
The domain of a rational functions in the set of all real numbers EXCEPT the values o
Lac-,qure. 3:1 - Greas Theorem
Gunman 'Fu'urt'.I
CHM;
F. Mm T
eyeiqu ags ET; mg jsyplan $5?
@5323! 596cm CW. 6? SmVxs TLLorM= Elm/CS Thom
M A Mpg 9193555 c is a. dam) cum. 1M amnlr "Ink/ud-
wow.
In 9444, werés, 1C He has ou+ HLCAJM, achsb, MA
FC°~3= F003
CSC 8980 Graph Data Mining
Fall 2017
Proximity
Measurement
Top- Query
Facebook Friend Recommendation
Top- Query
Amazon Book Recommendation
13
56
54
34
45
6
32
6
8
42
21
18
TopQuery in
Graphs
Which nodes are most similar to the query node ?
Query
TopQuery
CSC 8980 Graph Data Mining
Fall 2017
Introductio
n
Graph Data
World Wide
Web
60
Individual
Trillion
Pages
Faceboo
k
1.6
Active
Billion
Twitter
320
Active
Million
Users
Users
[1] google.com/insidesearch/howsearchworks/thestory/
[2] http:/newsroom.fb.com/co
CSC 8980 Graph Data Mining
Assignment 1
Due Date: 11:59 pm, Monday, Sept. 4, 2017
Note: You need to provide an electronic version of the homework. Handwritten version
is not accepted. You also need to provide one .m Matlab file for Problem 1 and one
.m Ma
CSC 8980 Graph Data Mining
Assignment 2
Due Date: 11:59 pm, Sunday, Sept. 10, 2017
In Assignment 2, you need to use the GTgraph library to generate a set of synthetic
networks. You need to use Linux OS to run the GTgraph library.
GTgraph library
https:/gi
CSC 8980 Graph Data Mining
Fall 2017
Laws and Generators for
Graphs
Part 2
How to model real
networks?
1. Degree Distribution
2. Diameter (Longest Shortest Path)
3. Clustering Coefficient
Erds-Renyi random graph does not work well.
How to model real
netwo
CSC 8980 Graph Data Mining
Fall 2017
Laws and Generators for
Graphs
Part 1
Properties for Graphs
1. Degree Distribution
2. Diameter (Longest Shortest Path)
3. Clustering Coefficient
Degree
Let be a random variable representing
Distribution
the degree of a
CSC 8980 Graph Data Mining
Fall 2017
Graph
Representation
Network or Graph?
1. Network refers to real systems
Web, Social, Biological,
Terminology: Network, node, link/relationship
2. Graph is an abstract mathematical model of a network
Web graph, Soc
The PageRank Citation Ranking:
Bring Order to the web
Lawrence Page, Sergey Brin, Rajeev Motwani and Terry Winograd
Presented by Fei Li
1
Motivation and Introduction
Why is Page Importance Rating important?
New challenges for information retrieval on the
ON THE EVOLUTION OF RANDOM GRAPHS
by
P. ERD6S and A.
R~NYI
Dedicated to
Profe88m- P. Turdn at
his 60th birthday.
lotroduction
Our aim is to study the probable structure of a ra.ridom gra.ph r,.N
which ha.s n given labelled vertices P 1, P2 , , P, and N ed
CSC 8980 Graph Data Mining
Fall 2017
PageRank Part 2
Monte Carlo Computing Method
Linearity
Theorem
PageRank
: vector of all 1s
:
Personalized
PageRank
vector, ,
Personalized PageRank
a.k.a, Random Walk with Restart
Power Iteration
Method
PageRank
Persona
1) The angle [in degrEESJ loaded a+ ver+ax A of u: +riangle ABC.
wifh verfices N6, 9, 51, BM, 6, 51 and (:15, ~51, 81 is
r a. 35.0713
1* In. 23.1431
r c. 63.9969
(3 11. 42.9221
r" e. 71.0219
r f. 47.0?9
Note: The law of cosines i5 fhe aasles+ way fa Find