Maths behind every it operation. (development and management)
1.
(Development and Management.)
Maths Behind Every IT Operations.
2.
Introduction:
People usually thinks about Number and calculation but it is not completely true.
Mathematics is the abstract study of quantity,[2] structure,[3] space,[2]
change,[4][5] and many other topics.[6] It has no generally accepted definition.[7][8]
Today we will discuss about some famous algorithms used in IT industry.
Fun @ Math?Yes :) (This part is FYI for readers. Please read following documents if you are interested. I'm not going to
explain discuss this points)
Some interesting stories:
• Évariste Galois : http://en.wikipedia.org/wiki/%C3%89variste_Galois
• https://en.wikipedia.org/wiki/Binary_number
3.
Benefits OF CPM, PERT
Benefits of CPM/PERT :
• Useful at many stages of project management
• Mathematically simple
• Give critical path and slack time
• Provide project documentation
• Useful in monitoring costs
CPM/PERT can answer the following important questions:
How long will the entire project take to be completed? What are the risks involved?
Which are the critical activities or tasks in the project which could delay the entire
project if they were not completed on time?
Is the project on schedule, behind schedule or ahead of schedule?
If the project has to be finished earlier than planned, what is the best way to do this
at the least cost?
4.
Situations in network diagram
A
B
C
A must finish before either B or C can start
A
B
C both A and B must finish before C can start
D
C
B
A
both A and C must finish before either of
B or D can start
A
C
B
D
Dummy
A must finish before B can start
both A and C must finish before D can start
5.
A. Toast Bread
B. Make an egg omelet
C. Spread butter on toast
D. Spread omelet on toast
3 minutes 2 minutes 1 minute
1 minute
7 minutes
Sandwich PERT Chart
5 minutes
3 minutes
2 minutes
1 minute
6.
PERT : Problem Evolution and Review technique.
CPM : Critical Path Method.
7.
Solution
•Critical Path
a, 6
f,f, 1515
b, 8
c, 5
e, 9
d, 13
g, 17 h, 9h,
9
i, 6i
j, 12
a, 6
c, 5
e, 9
8.
RSA Cryptography.
How simple the algoritm is ?
• We all knows : we have some number say 'message'
• let multiply(encrypt) it by some number say 'a' .
• we got encrypted 'a*'message' .
• Now multiply it by inverse of 'a' i.e '1/a'
• we got our 'message' Back.
RSA Factoring Challenge: http://en.wikipedia.org/wiki/RSA_Factoring_Challenge
RSA is an algorithm for public-key cryptography that is based on the presumed difficulty of factoring large integers, the factoring problem. RSA
stands for Ron Rivest, Adi Shamir and Leonard Adleman, who first publicly described the algorithm in 1977. Clifford Cocks, an English
mathematician, had developed an equivalent system in 1973, but it wasn't declassified until 1997.[citation needed]
A user of RSA creates and then publishes the product of two large prime numbers, along with an auxiliary value, as their public key. The prime
factors must be kept secret. Anyone can use the public key to encrypt a message, but with currently published methods, if the public key is large
enough, only someone with knowledge of the prime factors can feasibly decode the message.[1] Whether breaking RSA encryption is as hard as
factoring is an open question known as the RSA problem.
10.
Java Code for RSA encryption and
decryption.
Here is sample java code that you could use:
https://docs.google.com/file/d/0B80_St4pGDgqSEtlMzM5STB2bTg/edit
Fun @ Math?Yes :) (This part is FYI for readers and Please read following documents if you are interested. I'm not going to explain
discuss this points)
Theory behind Mathematical Singularity:- This function has singularity at x = 0. The actual world x ?
Read here. http://en.wikipedia.org/wiki/Gravitational_singularity
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