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Title: Discrete structure
Description: this is the introduction to discrete structure
Description: this is the introduction to discrete structure
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Discrete Mathematics
Overview
Discrete Mathematics and its Applications
Bart Selman
CS2800
Continuous vs
...
Continuous Mathematics
Continuous Mathematics
It considers objects that vary continuously;
Example: analog wristwatch (separate hour, minute, and second hands)
...
m
...
m
...
Real-number system --- core of continuous mathematics;
Continuous mathematics --- models and tools for analyzing real-world
phenomena that change smoothly over time
...
)
Bart Selman
CS2800
3
Discrete vs
...
Example: digital wristwatch
...
M
...
M
...
The watch moves from one
time to the next
...
)
Bart Selman
CS2800
4
What is discrete
mathematics?
• Discrete mathematics is the branch of mathematics
that deals with the study of mathematical structures
that are fundamentally discrete rather
than continuous
...
Bart Selman
CS2800
Why study discrete
mathematics?
• Discrete mathematics is the mathematical language
of computer science
...
• As computers are discrete object operating on
discontinuous step at a time, Discrete Math is the
right framework for describing precisely Computer
Science concepts
...
)
• Discrete mathematics is the mathematics that is
necessary for decision making in IT and business
...
Bart Selman
CS2800
Why study discrete
mathematics? (Contd
...
)
Although discrete mathematics provides
the tools for creating and analyzing
sophisticated algorithms, we will study
algorithmic aspects in a course on data
structures
...
– For the router to support the new address space it’s necessary that the latest software release be installed
...
– The router does not support the new address space
...
15
Bart Selman
CS2800
Number Theory:
RSA and Public-key Cryptography
Alice and Bob have never met but they would like to
exchange a message
...
E
...
between you and the Bank of America
...
)
CS folks found the solution:
public key encryption
...
Bart Selman
CS2800
Number Theory:
Public Key Encryption
RSA – Public Key Cryptosystem (why RSA?)
Uses modular arithmetic and large primes Its security comes from the computational difficulty
of factoring large numbers
...
g
...
•
Examples:
– Distribution problems
– Routing problems
– Maximum flow problems
– Designing computer / phone / road networks
– Equipment replacement
– And of course the Internet
Aside: finding the right
problem representation
is one of the key issues
...
For a given loop, how
many index registers are needed?
•
•
Each vertex corresponds to a variable in the loop
...
• Chromatic number of the graph gives the number of index
registers needed
...
Back to checking proofs
...
(e
...
, the classification of so-called finite simple groups, also
called the enormous theorem, 5000+ pages)
Title: Discrete structure
Description: this is the introduction to discrete structure
Description: this is the introduction to discrete structure