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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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Presentation Transcript
slide1

Mark Saul

Program Director

Elementary, Secondary, and Informal Education

National Science Foundation

slide2

Embroidery…

…Or Fabric?

slide4

Bronxville High School (ret.)

Bronx High School of Science (ret.)

slide5

1974

2004

slide6

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.

slide7

Examples (reading down):

Ø Ø {a} {b}

{a} {b} {a,b} {ab}

{a,b} {a,b} {b} {a}

{b} {a} Ø Ø

slide8

Ø

a

b

ab

slide9

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.

slide10

  Ø Ø Ø

a b c

ab cb ab

b c a

bc ac ab

c a b

ac ab bc

abc abc abc

slide11

bc

abc

c

ac

b

ab

Ø

a

slide12

“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

slide14

Binary Counting

0 000

1 001

2 010

3 011

4 100

5 101

6 110

7 111

slide15

Binary Gray Code

0 000

1 100

2 110

3 010

4 011

5 001

6 101

7 111

slide17

Tower of Hanoi

Chinese Rings

Space-Filling Curves

Campanology (Bell-ringing)

slide18

Subsets

Counting

Geometry

Dimension

Characteristic function

Coordinates

Graph theory

Hamiltonian Circuits

Symmetry

Induction

Recursion

What else?

slide21

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