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 92697-5100dsaari@uci.edu

Monday, October 13, 14

Don SaariMath and

Interactive:

Don SaariMath and

Interactive: WGAD

Don SaariMath and

Interactive: WGAD

Math of physical sciences:

Don SaariMath and

Interactive: WGAD

Math of physical sciences:Historical source of power

Don SaariMath and

Interactive: WGAD

Change of interest? Students:

Don SaariMath and

Interactive: WGAD

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

behavioral sciences

Don SaariMath and

Interactive: WGAD

behavioral sciencesDirector of institute

Don SaariMath and

Interactive: WGAD

Problems

Don SaariMath and

Interactive: WGAD

Problems

Conference video link

Don SaariMath and

Interactive: WGAD

Problems

Opportunities: leadership

Don SaariMath and

Interactive: WGAD

Problems

Opportunities: leadershipOpportunities: Students

Don SaariMath and

Interactive: WGAD

Problems

Finance

Don SaariMath and

Interactive: WGAD

Problems

FinanceEconomics, management, OR

Don SaariMath and

Interactive: WGAD

Problems

Political Science

Don SaariMath and

Interactive: WGAD

Problems

Political Science Sociology

Don SaariMath and

Interactive: WGAD

Problems

Cognitive SciencesMonday, October 13, 14

Don SaariMath and

Interactive: WGAD

Problems

What is needed; particularly in first couple of years?

Don SaariMath and

Interactive: WGAD

Problems

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

Don SaariMath and

Interactive: WGAD

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

Interactive: WGAD

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

Interactive: WGAD

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

Interactive: WGAD

Problems

Don SaariMath and

Interactive: WGAD

Problems

Firm belief:

Don SaariMath and

Interactive: WGAD

Problems

Firm belief:All students need exposure to

computing and data

Don SaariMath and

Interactive: WGAD

Problems

computing and dataMatlab

Don SaariMath and

Interactive: WGAD

Problems

Statistics

Don SaariMath and

Interactive: WGAD

Problems

StatisticsBayesian “updating”

Party time! (Example of problems in social sciences)

Milk,Wine,Beer

Beer, Wine, Milk

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

PluralityMilk-6, Beer-5, Wine-4

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

PairwiseWine, Beer, Milk

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

Beer?Runoff election

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

Rather than voter preferences, an election outcome can

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

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

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

Basic problem faced by mathematics of social choice;

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

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

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

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

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

How do we find an “appropriate ----”

Mathematics?

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

Mathematics?Reductionist

Milk,Wine,Beer

Beer, Wine, Milk

Wine, Beer, Milk

Milk Wine

Milk Beer

Beer Wine

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

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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