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![Page 1: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/1.jpg)
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
![Page 2: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/2.jpg)
OutlineOutline
Binary numbers Information theory Hiding information Digital Signatures Error Detection and Correction
![Page 3: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/3.jpg)
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
CS@CU
![Page 4: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/4.jpg)
Information TheoryInformation Theory
How do we measure information? Example: Text message that
reads:
“See you at Starbucks later?”
or“cu @ *$ l8r?”
CS@CU
![Page 5: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/5.jpg)
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.
CS@CU
![Page 6: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/6.jpg)
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?
CS@CU
![Page 7: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/7.jpg)
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.
CS@CU
![Page 8: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/8.jpg)
Information TheoryInformation Theory
The amount of information in a message can be quantified by how hard it is to “guess” what’s there.
CS@CU
![Page 9: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/9.jpg)
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
CS@CU
![Page 10: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/10.jpg)
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
CS@CU
![Page 11: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/11.jpg)
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
CS@CU
![Page 12: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/12.jpg)
Information TheoryInformation Theory
CS@CU
Guessing a number between 0-7:
From csunplugged.org
![Page 13: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/13.jpg)
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.
CS@CU
![Page 14: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/14.jpg)
Hiding InformationHiding Information
Sharing information online is a common and increasingly necessary activity today.
CS@CU
![Page 15: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/15.jpg)
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?
CS@CU
![Page 16: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/16.jpg)
Hiding InformationHiding Information
Techniques like these may be used to guard information during online transactions. Ecommerce Medical Data Personal Data
CS@CU
![Page 17: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/17.jpg)
Digital SignaturesDigital Signatures
How can we “trust” someone online?
CS@CU
![Page 18: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/18.jpg)
Digital SignaturesDigital Signatures
How can we “trust” someone online?
When would we need to do this?
CS@CU
![Page 19: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/19.jpg)
Digital SignaturesDigital Signatures
How can we “trust” someone online?
When would we need to do this? Online contracts
CS@CU
![Page 20: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/20.jpg)
Digital SignaturesDigital Signatures
How can we “trust” someone online?
When would we need to do this? Online contracts Identity verification
CS@CU
![Page 21: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/21.jpg)
Digital SignaturesDigital Signatures
How can we “trust” someone online?
When would we need to do this? Online contracts Identity verification Online gaming
CS@CU
![Page 22: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/22.jpg)
Digital SignatureDigital Signature
Example:
How can we flip a coin over the phone?
CS@CU
![Page 23: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/23.jpg)
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!
CS@CU
![Page 24: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/24.jpg)
Digital SignaturesDigital Signatures
Function / Inverse-Function pairs like this are a primary tool in modern public key cryptography.
CS@CU
![Page 25: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/25.jpg)
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!
CS@CU
![Page 26: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/26.jpg)
Error Detection and CorrectionError Detection and Correction
Often noise corrupts digital communication. This can be due to all kinds of natural or unnatural sources.
CS@CU
![Page 27: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/27.jpg)
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?
CS@CU
![Page 28: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/28.jpg)
Error Checking and CorrectionError Checking and Correction
Techniques like these are used on everything from internet message transmissions to credit card fraud detection.
CS@CU
![Page 29: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/29.jpg)
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?
CS@CU
![Page 30: CS4HS Workshop @ Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.](https://reader035.fdocuments.us/reader035/viewer/2022062720/56649f125503460f94c24dcb/html5/thumbnails/30.jpg)
CS@CU
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.
Thanks!
Check out CS Unplugged at: