Mathematics for Social and Behavior Sciences

Mathematics forSocial and Behavior Sciences

Don SaariMath and

Institute for Math Behavioral Scienceswww.imbs.uci.edu

University of California, Irvine [email protected]

Monday, October 13, 14

http://www.imbs.uci.edu


mailto:[email protected]



Don SaariMath and



Interactive:







Don SaariMath and



Interactive: WGAD







Don SaariMath and



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Math of physical sciences:







Don SaariMath and



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Math of physical sciences:Historical source of power







Don SaariMath and



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Change of interest? Students:







Don SaariMath and



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Change of interest? Students: moved into math of social and

behavioral sciences







Don SaariMath and



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behavioral sciencesDirector of institute







Don SaariMath and



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Problems







Don SaariMath and



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Problems

Conference video link







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Problems


Opportunities: leadership







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Problems


Opportunities: leadershipOpportunities: Students







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Problems



Finance







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Problems



FinanceEconomics, management, OR







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Problems




Political Science







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Problems




Political Science Sociology







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Problems





Cognitive SciencesMonday, October 13, 14






Don SaariMath and



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Problems

What is needed; particularly in first couple of years?











Don SaariMath and



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Problems


I do believe that calculus is far more naturally connected to econ and stats than engineering.











Don SaariMath and



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Problems


I do believe that calculus is far more naturally connected to econ and stats than engineering.Much in calculus can be dropped!











Don SaariMath and



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Problems


I do believe that calculus is far more naturally connected to econ and stats than engineering.Much in calculus can be dropped!Conceptual understanding--they will be facing new problems











Don SaariMath and



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Problems


I do believe that calculus is far more naturally connected to econ and stats than engineering.Much in calculus can be dropped!Conceptual understanding--they will be facing new problemsE.g., Riemann sums vs integrals











Don SaariMath and



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Problems



Firm belief:











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Problems



Firm belief:All students need exposure to

computing and data











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Problems




computing and dataMatlab











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Problems





Statistics











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Problems





StatisticsBayesian “updating”










Party time! (Example of problems in social sciences)



6

5

4



6

5

4

Milk,Wine,Beer



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

PluralityMilk-6, Beer-5, Wine-4



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine

5 10



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine

5 10

PairwiseWine, Beer, Milk



6

5

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Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine

5 10


Beer?



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine

5 10


Beer?Runoff election



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine

5 10



Rather than voter preferences, an election outcome can



6

5

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Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine

5 10



Rather than voter preferences, an election outcome can reflect the choice of an election method!



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine

5 10




Basic problem faced by mathematics of social choice;



6

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Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine

5 10




Basic problem faced by mathematics of social choice;How do we find an “appropriate decision method?”



6

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4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine

5 10





But, this is a simple aggregation method: social and behavioral Basic problem faced by mathematics of economics;

How do we find an “appropriate ----”Monday, October 13, 14


6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine

5 10






How do we find an “appropriate ----”

Mathematics?



6

5

4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine

5 10







Mathematics?Reductionist



6

5

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Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk


Milk Wine

6 9

Milk Beer

6 9

Beer Wine

5 10







Mathematics?Reductionist

Symmetry groups


Differences in classes that make a difference



Dot products:



Dot products:Dimensions n=2, 3




Economics, Operations Research, Management, etc.





all dimensions





all dimensions

Example:





all dimensions

Example:You have n commodities w= (w1, w2, …, wn) that

will be sold a price p = (p1, …, pn) to buy new bundle at these prices.





all dimensions


will be sold a price p = (p1, …, pn) to buy new bundle at these prices.What can be afforded?





all dimensions



Money available





all dimensions



Money available(p, w)





all dimensions




Bundle x that can be purchased





all dimensions




Bundle x that can be purchased(p, x)





all dimensions





Budget plane





all dimensions





Budget plane(p, x-w) = 0





all dimensions






Lagrange multiplier but what does Lambda mean?





all dimensions







Taylor Series





all dimensions







Taylor Seriesf(x) = f(a) + f ’(a)(x-a) + ….





all dimensions








Computations





all dimensions








ComputationsBut, modeling





all dimensions









Why is base e “natural”





all dimensions









Why is base e “natural”x’ = f(x)





all dimensions










Too complicated





all dimensions










Too complicatedx’ = a x





all dimensions











Growth: financial, population, ecology, etc.





all dimensions












Eigenvalues, eigenvectors





all dimensions












Eigenvalues, eigenvectorsA v = L v





all dimensions













A is input-output





all dimensions













A is input-outputv is natural direction


Mathematics for Social and Behavior Sciences

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Transcript of Mathematics for Social and Behavior Sciences