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Welcome to Math 105: Gödel, Escher, and Bach

Explore the intriguing world of Gödel, Escher, and Bach in this course. Learn about musical shapes, internal symmetries, and the fascinating connections between mathematics, art, and music.

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Welcome to Math 105: Gödel, Escher, and Bach

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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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