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Welcome to. Math 105 Gödel, Escher, and Bach. Question 1. What is the name of this song?. Question 2. NOW what’s the name of this song?. (Question 2). Musical shape can be stretched yet still retain its identity. (Question 2). Oh - say can you see.

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  1. Welcome to Math 105Gödel, Escher, and Bach

  2. Question 1 What is the name of this song?

  3. Question 2 NOW what’s the name of this song?

  4. (Question 2) Musical shape can be stretched yet still retain its identity

  5. (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 Musical objects often contain internal symmetries

  6. Question 3 How many times does IT appear?

  7. (Question 3)

  8. Musical shape can be flipped yet still retain its identity

  9. J S Bach Bach 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

  10. J S Bach Endlessly rising canon Strange loop

  11. 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

  12. 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. KGodel@Richmond.Edu) your password (must have at least 2 digits!) • What to do when you’re there:

  13. 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

  14. HELP!!! • Consider problems in groups in class • Consider problems in groups outside of class • Consider problems in review sessions • 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

  15. M.C. Escher Ascending and Descending Strange loop

  16. Kurt Gödel Incompleteness Theorem Strange loop

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