# mark saul program director elementary, secondary, and informal education national science foundation

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• Mark SaulProgram Director

Elementary, Secondary, and Informal EducationNational Science Foundation

• Or Fabric? Embroidery

• City University of New York Research FoundationNew York City Interscholastic Mathematics LeagueAmerican Regions Mathematics LeagueResearch Science Institute, MIT Bronxville High School (ret.)Bronx High School of Science

My affiliations. Mention Bronx Science and NYC schools

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

• 19742004

• 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.

• {a} {b}

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

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

{b} {a} Examples (reading down):

• a bab

• 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.

• abcabcbabbcabcacabcabacabbcabc abcabc

• ababbcaccabc

• abc000(0,0,0){a}100(1,0,0){b}010(0,1,0){c}001(0,0,1){a,b}110(1,1,0){b,c}011(0,1,1){a,c}101(1,0,1){a,b,c}111(1,1,1)

Characteristic Functions

• Binary Counting00001001201030114100510161107111

• Binary Gray Code00001100211030104011500161017111

• Hamiltonian Circuits

• Tower of HanoiChinese RingsSpace-Filling CurvesCampanology (Bell-ringing)

• Subsets CountingGeometryDimensionCharacteristic functionCoordinatesGraph theory Hamiltonian CircuitsSymmetryInduction Recursion What else?

• IS THIS EMBROIDERY ON THE FABRIC OF MATHEMATICS?

• OR IS THIS THE FABRIC OF MATHEMATICS?

• NSF 04-600EMSW21 (Enlarging the Mathematical Science Workforce for the 21st Century)MCTP (Mentoring Through Critical Transition Points)

Funding? Check out: Or talk to:John Conway, DMS: jconway@nsf.govLiz Teles, DUE: ejteles@nsf.gov

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