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Mark Saul Program Director Elementary, Secondary, and Informal Education

Mark Saul Program Director Elementary, Secondary, and Informal Education National Science Foundation. Embroidery…. …Or Fabric?. Bronxville High School (ret.) Bronx High School of Science (ret.). 1974. 2004.

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Mark Saul Program Director Elementary, Secondary, and Informal Education

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  1. Mark Saul Program Director Elementary, Secondary, and Informal Education National Science Foundation

  2. Embroidery… …Or Fabric?

  3. Bronxville High School (ret.) Bronx High School of Science (ret.)

  4. 1974 2004

  5. There are 22= 4 subsets of the set {a,b}. Arrange these in a sequence so that each subset differs from the previous one in having exactly one new element added or exactly one old element deleted.

  6. Examples (reading down): Ø Ø {a} {b} {a} {b} {a,b} {ab} {a,b} {a,b} {b} {a} {b} {a} Ø Ø

  7. Ø a b ab

  8. There are 23=8 subsets of the set {a,b,c}. Arrange these in a sequence so that each subset differs from the previous one in having exactly one new element added or exactly one old element deleted.

  9.   Ø Ø Ø a b c ab cb ab b c a bc ac ab c a b ac ab bc abc abc abc

  10. bc abc c ac b ab Ø a

  11. “Characteristic Functions” a b c 0 0 0 (0,0,0) {a} 1 0 0 (1,0,0) {b} 0 1 0 (0,1,0) {c} 0 0 1 (0,0,1) {a,b} 1 1 0 (1,1,0) {b,c} 0 1 1 (0,1,1) {a,c} 1 0 1 (1,0,1) {a,b,c} 1 1 1 (1,1,1) Ø

  12. Binary Counting 0 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111

  13. Binary Gray Code 0 000 1 100 2 110 3 010 4 011 5 001 6 101 7 111

  14. Hamiltonian Circuits

  15. Tower of Hanoi Chinese Rings Space-Filling Curves Campanology (Bell-ringing)

  16. Subsets Counting Geometry Dimension Characteristic function Coordinates Graph theory Hamiltonian Circuits Symmetry Induction Recursion What else?

  17. IS THIS EMBROIDERY ON THE FABRIC OF MATHEMATICS?

  18. OR IS THIS THE FABRIC OF MATHEMATICS?

  19. Funding? Check out: • NSF 04-600 • EMSW21 (Enlarging the Mathematical Science Workforce for the 21st Century) • MCTP (Mentoring Through Critical Transition Points) Or talk to: John Conway, DMS: jconway@nsf.gov Liz Teles, DUE: ejteles@nsf.gov

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