CS4HS Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University.

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CS4HS Columbia University Injecting CS into High School Math and Science Classes Adam Cannon Department of Computer Science Columbia University July 8, 2011

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

Binary 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

Information Theory How do we measure information? Example: Text message that reads: “See you at Starbucks later?” or *$ l8r?”

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.

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?

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.

Information Theory The amount of information in a message can be quantified by how hard it is to “guess” what’s there.

Information 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

Information 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

Information 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

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

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 to digital voice communication to streaming video.

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

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?

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

Digital Signatures How can we “trust” someone online?

Digital Signatures How can we “trust” someone online? When would we need to do this?

Digital Signatures How can we “trust” someone online? When would we need to do this? Online contracts

Digital Signatures How can we “trust” someone online? When would we need to do this? Online contracts Identity verification

Digital Signatures How can we “trust” someone online? When would we need to do this? Online contracts Identity verification Online gaming

Digital Signature Example: How can we flip a coin over the phone?

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!

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

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!

Error Detection and Correction Often noise corrupts digital communication. This can be due to all kinds of natural or unnatural sources.

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?

Error Checking and Correction Techniques like these are used on everything from internet message transmissions to credit card fraud detection.

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 today’s world. Will your students respond to these?

Want to learn more? If you do choose to use any activities like these, I would love to hear your feedback. Thanks! Check out CS Unplugged at: