Download - Mark Saul Program Director Elementary, Secondary, and Informal Education National Science Foundation
Mark Saul
Program Director
Elementary, Secondary, and Informal Education
National Science Foundation
…Or Fabric?
Embroidery…
City University of New York Research Foundation
New York City Interscholastic Mathematics League
American Regions Mathematics League
Research Science Institute, MIT
Bronxville High School (ret.)
Bronx High School of Science
Bronxville High School (ret.)
Bronx High School of Science (ret.)
1974
2004
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.
Ø Ø {a} {b}
{a} {b} {a,b} {ab}
{a,b} {a,b} {b} {a}
{b} {a} Ø Ø
Examples (reading down):
Ø a
b ab
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.
Ø Ø Ø
a b c
ab cb ab
b c a
bc ac ab
c a b
ac ab bc
abc abc abc
Ø a
bab
bc
acc
abc
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
“Characteristic Functions”
(0,0,0)(1,0,0)
(0,0,1)
(1,1,1)
(0,1,1)
(0,1,0)
X
YZ
(1,0,1)
(1,1,0)
Binary Counting 0 0001 0012 0103 0114 1005 1016 1107 111
Binary Gray Code
X
YZ
0 0001 1002 1103 0104 0115 0016 1017 111
Hamiltonian Circuits
Tower of Hanoi
Chinese Rings
Space-Filling Curves
Campanology (Bell-ringing)
Subsets
Counting
Geometry
Dimension
Characteristic function
Coordinates
Graph theory
Hamiltonian Circuits
Symmetry
Induction
Recursion
What else?
IS THIS EMBROIDERY ON THE FABRIC OF
MATHEMATICS?
OR IS THIS THE FABRIC OF
MATHEMATICS?
• NSF 04-600• EMSW21 (Enlarging the Mathematical
Science Workforce for the 21st Century)• MCTP (Mentoring Through Critical
Transition Points)
Funding? Check out:
Or talk to:John Conway, DMS: [email protected]
Liz Teles, DUE: [email protected]