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Welcome to
Math 105Gödel, Escher, and Bach
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Question 1
What is the name of this song?
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Question 2
NOW what’s the name of this song?
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Musical shape can be stretched yet still retain its identity
(Question 2)
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Musical objects often contain
internal symmetries
(Question 2)
Oh - say can you see
By the dawn’s ear- ly light
What so proud- ly we hailed
At the twi- light’s last glea- ming
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Question 3
How many times does IT appear?
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(Question 3)
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Musical shape can be flipped yet still retain
its identity
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J S BachBach visits the court of Frederick the Great of Prussia
• Improvises fugues on King’s complex theme
• Later composes canons on theme: WEIRD canons.
Crab canon
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J S BachEndlessly rising canon
Strange loop
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Gödel, Escher, and BachThe course
Lecture and careful note taking• DOING PROBLEMS
• DISCUSSING PROBLEMS
• DOING MORE PROBLEMS
If you can’t do it, you don’t know it
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Gödel, Escher, and BachThe course web page
• How to get there: courses.richmond.edu (bookmark it!)
• How to log in: your net id (e.g. [email protected]) your password (must have at least 2 digits!)
• What to do when you’re there:
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Problems vs Questions vs…???• Quiz questions (daily) - Rather mindless - A carrot - Feedback about Study Questions• Study questions (daily) - Active reading - Directly related to text• Problem set questions (weekly) - Integrative - Many answers possible - Approach more important than answer• Exam questions (quarterly) - Derived from Problem Sets
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HELP!!!• Consider problems in groups in class
• Consider problems in review sessions
• Consider problems in groups outside of class
• Consider problems when you need it
Jeff Elhai Mike KerckhoveS-202 Gottwald 209 Jepsen289-8412 289-8774R&F 3:30-5:00 M&W 10:30-11:30
R 2:30-4:00
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M.C. EscherAscending and Descending
Strange loop
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Kurt GödelIncompleteness Theorem
Strange loop