Post on 04-Jan-2016
CS4HS Workshop @ Columbia CS4HS Workshop @ Columbia UniversityUniversity
Injecting CS into High SchoolMath and Science Classes
Adam CannonDepartment of Computer Science
Columbia University
July 8, 2011
CS@CU
OutlineOutline
Binary numbers Information theory Hiding information Digital Signatures Error Detection and Correction
Binary NumbersBinary Numbers
We use binary numbers to represent information in computer systems
Why? It’s just more natural On/Off Positive/Negative Charges N-S/S-N Magnetic Fields
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Information TheoryInformation Theory
How do we measure information? Example: Text message that
reads:
“See you at Starbucks later?”
or“cu @ *$ l8r?”
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Information TheoryInformation 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 TheoryInformation 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 TheoryInformation 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 TheoryInformation Theory
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 TheoryInformation Theory
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 TheoryInformation Theory
The amount of information in a message can be quantified by how hard it is to “guess” what’s there.
Example: Pick a number Between 1-10
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Information TheoryInformation Theory
The amount of information in a message can be quantified by how hard it is to “guess” what’s there.
Example: Pick a number Between 1-10 Between 1-100
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Information TheoryInformation Theory
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Guessing a number between 0-7:
From csunplugged.org
Information TheoryInformation 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 InformationHiding Information
Sharing information online is a common and increasingly necessary activity today.
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Hiding InformationHiding 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 InformationHiding Information
Techniques like these may be used to guard information during online transactions. Ecommerce Medical Data Personal Data
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Digital SignaturesDigital Signatures
How can we “trust” someone online?
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Digital SignaturesDigital Signatures
How can we “trust” someone online?
When would we need to do this?
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Digital SignaturesDigital Signatures
How can we “trust” someone online?
When would we need to do this? Online contracts
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Digital SignaturesDigital Signatures
How can we “trust” someone online?
When would we need to do this? Online contracts Identity verification
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Digital SignaturesDigital 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 SignatureDigital Signature
Example:
How can we flip a coin over the phone?
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Digital SignatureDigital 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 SignaturesDigital Signatures
Function / Inverse-Function pairs like this are a primary tool in modern public key cryptography.
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Digital SignaturesDigital 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 CorrectionError 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 CorrectionError 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 CorrectionError 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 TeachGames and Puzzles That Teach
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?Want to learn more?
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!
Check out CS Unplugged at: