1 / 21

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.

camden
Download Presentation

Mark Saul Program Director Elementary, Secondary, and Informal Education

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related