What is it?

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What is it?
It is an applications driven course that is based
upon the study of events that occur in small, or
discrete, chunks.
Discrete concepts are used extensively in
business, industry, government, and the digital
world.
The major areas of study are counting and
probability, graph theory, the mathematics of
social choice (voting and fair division), and
coding and encryption.
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Graphing Theory
is embedded throughout Management Science and
Operations Research.
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As an example
Find the most efficient route for the
parking-control officer, who travels on foot, to
check the meters in an area.
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The previous situation can be represented by a
graph
in order to simplify the problem
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and analyze the information
to optimize the most efficient route.
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Many of the topics in Discrete Math have been
developed since the dawn of the computer.
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and the development of the Management Sciences.
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Graphs are analyzed quantitatively to determine
the optimal solutions to problems
and various types of graphs (such as Euler and
Hamiltonian) are introduced as more and more
situations are analyzed.
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Counting and Probability

• What is the probability of winning the jackpot in
  the lottery?
• In how many ways can a lottery participant choose
  several numbers from those on a lottery ticket?
• How may different phone numbers are possible in a
  given exchange (same three digit prefix)?

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Discrete Math will help to answer some of these
questions.
as well as explore all possibilities for a given
event such as
What is the probability of rolling two number
cubes that have a sum of 7?
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The Digital World
Identification numbers and codes are associated
with many aspects of our modern world.
Plane Tickets
Check Digits are found on many items for error
detection.
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The Digital World
Identification numbers and codes are associated
with many aspects of our modern world.
Money Orders
This check digit is the remainder when dividing
the sum of the identification numbers by 9.
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The Digital World
Identification numbers and codes are associated
with many aspects of our modern world.
Euro
The letter preceding the identification number is
a code for the country in which the bill was
issued. The check digit is then chosen so that
the the sum of all digits including the number
assigned to the letter is divisible by 9. (X 7)
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The Digital World
Identification numbers and codes are associated
with many aspects of our modern world.
This credit card is a fake!
Codabar
Add the digits in positions 1, 3, 5, 7, 9, 11,
13, and 15 and double the result Next, count the
number of digits in those positions that exceed 4
and add this to the total. Now add in the
remaining digits. The check digit is the number
needed to bring this final tally to a number that
ends in 0.
(42013579) x 2 3 (1802468) 0
94
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The Digital World
A bar code is a series of dark and light spaces
that represent characters
Postnet code

• 52 vertical bars
• 2 guard bars
• 10 sets of 5
• Represents the Zip 4 Code
• Check digit is such that the sum of the zip code
  digits and the check digit is divisible by 10

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The Digital World
A bar code is a series of dark and light spaces
that represent characters
And, the more complex UPC barcode.
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The Digital World
A graph can be used to represent the internet
where information is presented in binary code
and sent electronically.
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Social Choice
This area of discrete math involves election
theory, voting and fair division techniques.
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There are different types of processes by which
the preferences of individuals are combined to
produce a group decision.
What if you were asked to rank your favorite
flavor of the following drink?
Borda Method Grape, Runoff Method Orange,
Plurality Method Cola and the Arrow Method
Lemon-Lime
Depending upon the Ranking Method used, the
results could be different.
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The electoral college is an example of a weighted
voting system.
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Social choice also involves strategies for
conducting elections.
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Fair Division is a process where certain things
are divided among a given number of people so
that each person feels he/she received the best
piece (also known as envy free division).
Other models and applications of fair division
will also be studied.
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Many of the ideas in Discrete Math will be
represented by Matrices.
In addition, operations with matrices will be
studied.
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The following Task Group worked to develop this
Discrete Math Course. Your comments and
suggestions will be appreciated as you attend
Discrete Math Training and work with the course
during the first Pilot Year.
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The following slides display the Draft Version of
the Curriculum Guide for Discrete Math
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is
to a school near you!
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