CS4HS Workshop @ Columbia University
Injecting CS into High School
Math and Science Classes
Adam Cannon
Department of Computer Science
Columbia University
July 8, 2011
CS@CU
Outline
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Binary numbers
Information theory
Hiding information
Digital Signatures
Error Detection and Correction
Binary Numbers
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We use binary numbers to represent
information in computer systems
Why?
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It’s just more natural
On/Off
Positive/Negative Charges
N-S/S-N Magnetic Fields
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Information Theory
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How do we measure information?
Example: Text message that reads:
“See you at Starbucks later?”
or
“cu @ *$ l8r?”
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Information Theory
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Both convey the same information so
measuring the length of the message is
not really useful if we are trying to
measure the amount of information
conveyed.
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Information Theory
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Both convey the same information so
measuring the length of the message is
not really useful if we are trying to
measure the amount of information
conveyed.
So how do we do it?
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Information Theory
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Both convey the same information so
measuring the length of the message is
not really useful if we are trying to
measure the amount of information
conveyed.
So how do we do it?
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We play 20 questions.
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Information Theory
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The amount of information in a
message can be quantified by how hard
it is to “guess” what’s there.
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Information Theory
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The amount of information in a
message can be quantified by how hard
it is to “guess” what’s there.
Example: Pick a number
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Information Theory
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The amount of information in a
message can be quantified by how hard
it is to “guess” what’s there.
Example: Pick a number
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Between 1-10
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Information Theory
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The amount of information in a
message can be quantified by how hard
it is to “guess” what’s there.
Example: Pick a number
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Between 1-10
Between 1-100
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Worksheet Activity: Decision Trees
Information
Theory
If you already know the strategy for asking the questions, you can tran
message without having to ask anything.
Guessing a number between 0-7:
Here is a chart called a ‘decision tree’ for guessing a number between
From csunplugged.org
What are the yes/no decisions needed to ‘guess’ the number 5?
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Information Theory
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Understanding how much information is
really contained in any kind of message
is the cornerstone of compression
technologies. These technologies are
used for everything from email to digital
voice communication to streaming
video.
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Hiding Information
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Sharing information online is a common
and increasingly necessary activity
today.
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Hiding Information
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Sharing information online is a common
and increasingly necessary activity
today.
How can we share information and still
maintain a reasonable level of privacy?
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Hiding Information
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Techniques like these may be used to
guard information during online
transactions.
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Ecommerce
Medical Data
Personal Data
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Digital Signatures
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How can we “trust” someone online?
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Digital Signatures
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How can we “trust” someone online?
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When would we need to do this?
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Digital Signatures
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How can we “trust” someone online?
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When would we need to do this?
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Online contracts
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Digital Signatures
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How can we “trust” someone online?
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When would we need to do this?
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Online contracts
Identity verification
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Digital Signatures
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How can we “trust” someone online?
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When would we need to do this?
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Online contracts
Identity verification
Online gaming
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Digital Signature
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Example:
How can we flip a coin over the phone?
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Digital Signature
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Example:
How can we flip a coin over the phone?
The math behind this is simple. The key is
to find a function that is easy to compute
but whose inverse is tough!
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Digital Signatures
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Function / Inverse-Function pairs like
this are a primary tool in modern public
key cryptography.
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Digital Signatures
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Function / Inverse-Function pairs like
this are a primary tool in modern public
key cryptography.
Examples like these can be used to
motivate the study of functions and
inverses in high school algebra!
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Error Detection and Correction
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Often noise corrupts digital
communication. This can be due to all
kinds of natural or unnatural sources.
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Error Detection and Correction
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Often noise corrupts digital
communication. This can be due to all
kinds of natural or unnatural sources.
How can I know that the message I
received is the message you sent?
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Error Checking and Correction
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Techniques like these are used on
everything from internet message
transmissions to credit card fraud
detection.
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Games and Puzzles That Teach
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These activities can be challenging and
a lot of fun
They stimulate curiosity
They are relevant to everyday life in
today’s world.
Will your students respond to these?
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Want to learn more?
Check out CS Unplugged at:
http://csunplugged.org
If you do choose to use any activities like these, I would
love to hear your feedback.
cannon@cs.columbia.edu
Thanks!
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