CS4HS%20Workshop%20@%20Columbia%20University

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CS4HS Workshop _at_ Columbia University

• Injecting CS into High School
• Math and Science Classes
• Adam Cannon
• Department of Computer Science
• Columbia University
• July 8, 2011

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Outline

• Binary numbers
• Information theory
• Hiding information
• Digital Signatures
• Error Detection and Correction

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Binary Numbers

• We use binary numbers to represent information in
  computer systems
• Why?
• Its just more natural
• On/Off
• Positive/Negative Charges
• N-S/S-N Magnetic Fields

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Information Theory

• How do we measure information?
• Example Text message that reads
• See you at Starbucks later?
• or
• cu _at_ l8r?

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Information Theory

• 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

• 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

• 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?
• We play 20 questions.

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Information Theory

• The amount of information in a message can be
  quantified by how hard it is to guess whats
  there.

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Information Theory

• The amount of information in a message can be
  quantified by how hard it is to guess whats
  there.
• Example Pick a number

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Information Theory

• The amount of information in a message can be
  quantified by how hard it is to guess whats
  there.
• Example Pick a number
• Between 1-10

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Information Theory

• The amount of information in a message can be
  quantified by how hard it is to guess whats
  there.
• Example Pick a number
• Between 1-10
• Between 1-100

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Information Theory
Guessing a number between 0-7
From csunplugged.org
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Information Theory

• 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

• Sharing information online is a common and
  increasingly necessary activity today.

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Hiding Information

• 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

• Techniques like these may be used to guard
  information during online transactions.
• Ecommerce
• Medical Data
• Personal Data

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Digital Signatures

• How can we trust someone online?

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Digital Signatures

• How can we trust someone online?
• When would we need to do this?

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Digital Signatures

• How can we trust someone online?
• When would we need to do this?
• Online contracts

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Digital Signatures

• How can we trust someone online?
• When would we need to do this?
• Online contracts
• Identity verification

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Digital Signatures

• How can we trust someone online?
• When would we need to do this?
• Online contracts
• Identity verification
• Online gaming

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Digital Signature

• Example
• How can we flip a coin over the phone?

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Digital Signature

• 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

• Function / Inverse-Function pairs like this are a
  primary tool in modern public key cryptography.

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Digital Signatures

• 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

• 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

• 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

• 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

• These activities can be challenging and a lot of
  fun
• They stimulate curiosity
• They are relevant to everyday life in todays
  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_at_cs.columbia.edu
• Thanks!