Discrete Mathematics Structures
6 1931
Predicate Logic - everybody loves somebody
Proposition, YES or NO?
YES
3+2=5
X+2=5
NO
X + 2 = 5 for any choice of X in cfw_1, 2, 3
X + 2 = 5 for some X in cfw_1, 2, 3
YES
YES
1391 6
-
2
Predicate Logic - ev
S. Palaniappan, International Journal of Computer Science and Mobile Computing, Vol.3 Issue.5, May- 2014, pg. 8-15
Available Online at www.ijcsmc.com
International Journal of Computer Science and Mobile Computing
A Monthly Journal of Computer Science and
ISSN: 2321-7782 (Online)
Volume 2, Issue 4, April 2014
International Journal of Advance Research in
Computer Science and Management Studies
Research Article / Paper / Case Study
Available online at: www.ijarcsms.com
Role of virtualization in cloud computi
Mayuri R. Gawande et al, International Journal of Computer Science and Mobile Computing, Vol.3 Issue.3, March- 2014, pg. 169-175
Available Online at www.ijcsmc.com
International Journal of Computer Science and Mobile Computing
A Monthly Journal of Compute
April 4, 2014
RT0959
Computer Science
8 pages
Research Report
Industry Cloud - Effective Adoption of Cloud Computing for Industry Solutions
Takayuki Kushida and Gopal Pingali (IBM GTS)
IBM Research - Tokyo
IBM Japan, Ltd.
NBF Toyosu Canal Front Building
6
Sonali Rathod et al, International Journal of Computer Science and Mobile Computing, Vol.3 Issue.5, May- 2014, pg. 229-238
Available Online at www.ijcsmc.com
International Journal of Computer Science and Mobile Computing
A Monthly Journal of Computer Scie
International Journal of Computer Science & Engineering Survey (IJCSES) Vol.5, No.2, April 2014
Firewall and VPN Investigation on Cloud
Computing Performance
Siddeeq Y. Ameen1, Shayma Wail Nourildean2
1
Department of Computer and Information Engineering,
108
IJCSNS International Journal of Computer Science and Network Security, VOL.14 No.5, May 2014
Replication of Enormous Data Process in Cloud Computing
K.Aishwarya,
R.Sathyan,
Assistant Professor/Dept of CSE,
Arulmigu Meenakshi Amman College of Engineeri
IBIMA Publishing
Journal of Cloud Computing
http:/www.ibimapublishing.com/journals/JCC/jcc.html
Vol. 2014 (2014), Article ID 901075, 8 pages
DOI: 10.5171/2014.901075
Research Article
Rationalizing the Cloud Computing
Concept: An Analogy with the Car
Rafik
M. Padma et al, International Journal of Computer Science and Mobile Computing, Vol.3 Issue.5, May- 2014, pg. 972-977
Available Online at www.ijcsmc.com
International Journal of Computer Science and Mobile Computing
A Monthly Journal of Computer Science a
Aalborg Universitet
Towards Trust Engineering for Opportunistic Cloud Services:
Kuada, Eric
Publication date:
2014
Link to publication from Aalborg University
Citation for published version (APA):
Kuada, E. (2014). Towards Trust Engineering for Opportunis
Discrete Mathematics Structures
62 2931
Mathematical Induction
Prove that if a set S has |S| = n, then |P(S)| = 2n
Base case (n=0): S=, P(S) = cfw_ and |P(S)| = 1 = 20
Assume P(k): If |S| = k, then |P(S)| =
2k
Inductive
hypothesis
Prove that if |S
Discrete Mathematics Structures
7 1931
Predicates - the meaning of multiple
quantifiers
xy P(x,y)
P(x,y) true for all x, y pairs.
xy P(x,y)
P(x,y) true for at least one x, y pair.
xy P(x,y)
xy P(x,y)
For every value of x we can find a (possibly di
Discrete Mathematics Structures
31 1931
Proofs - valid arg or fallacy?
If it rains then it is cloudy.
Denying the
hypothesis.
It does not rain.
It is not cloudy
February!
(p q) p) q
Not a tautology.
If it is a car, then it has 4 wheels.
It is not
Discrete Mathematics Structures
41 1931
Set Theory - Definitions and notation
A set is an unordered collection of elements.
Some examples:
cfw_1, 2, 3 is the set containing 1 and 2 and 3.
cfw_1, 1, 2, 3, 3 = cfw_1, 2, 3 since repetition is irrelev
Discrete Mathematics Structures
02 1931
Set Theory - 4 Ways to prove identities
Show that A B and that A B.
Use a membership table.
Like truth
tables
Use previously proven identities.
Use logical equivalences to prove
equivalent set definition
Discrete Mathematics Structures
81 2931
Growth of functions (examples)
iff
f(x) = O(g(x)
c,k so that x>k, f(x) cg(x)
3n = O(15n) since n > 0, 3 n 1 15 n
Theres k
1392 81
-
Theres c
2
Growth of functions (examples)
iff
f(x) = O(g(x)
c,k so that
Discrete Mathematics Structures
91 2931
Infinite Cardinality
Are there more evens than odds?
Are there more natural numbers than evens?
Are there more evens than multiples of 3?
1392 91
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2
Infinite Cardinality
Two sets A and B have the same car
Discrete Mathematics Structures
03 2931
Inductive Definitions
We want to show that my definition of S:
3S
x,y S x + y S
x,y S x - y S
No other numbers are in S.
Contains the same elements as the set:
T = cfw_x: x is a multiple of 3
To prove S = T,
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