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Industrial-strength Mathematics: Research Projects from Business and Industry

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## Industrial-strength Mathematics: Research Projects from Business and Industry

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Key Points…

Business and Industry are good sources for very engaging mathematical research projects.

Research is about digging deeper…

…and asking Why?

You will be amazed at what students can do.

Focus on Mathematics

Mathematics Research Expo

June 11 at the Museum of Science

“All students will participate in a mathematically significant research project.”

Focus on Mathematics

Background: Industrial Math at WPI

- Projects for everyone at WPI since 1972

Three required projects: Humanities, Society, Major

- Center for Industrial Mathematics and Statistics

founded in 1997

- 50 projects with more than 25 companies
- Bose, Blue Cross, DEKA, Deutsche Bank, Ferrite,

John Hancock, Lehman Brothers, Morgan Construction, National Grid, Premier Insurance, Presmet Metals,

Veeder-Root, +++

Focus on Mathematics

Projects are a Resource

- Industrial Math Projects with our students
- Industrial Math Projects for Teachers

Mathematics in Industry Institute for Teachers

July 11-15, 2005

Students (and teachers) learn to

be comfortable with ill-posed and fuzzy problems.

Focus on Mathematics

Industrial Impact

At practice presentation: Students presented detailed analysis of fluctuations in the company’s reserves process.

The company rep said:

“It is clear that you have done lots of work, but nothing that you said made any sense at all.”

Focus on Mathematics

Project #1: Real Cost of a Ticket

A speeding ticket costs you $75 today.

What is the real cost?

Focus on Mathematics

Massachusetts has a point system: SDIP

One speeding ticket = 3 points

Premium increases 7% per point:

Imagine being SDIP 35!

Focus on Mathematics

Focus on Mathematics

- Ask the student:
- What will you pay for auto insurance?
- (Change the base premium.)
- What is your parent’s SDIP rating?
- (Dangerous)
- Are women better drivers than men?
- (Yes, but still dangerous.)

Focus on Mathematics

Teacher uses geometry to beat a ticket:

The teacher argued that the reading on the radar gun was too high because she was coming around a curve when the officer took the reading.

Focus on Mathematics

#2 Assigned Risk Plans in Auto Insurance

The State is redesigning its method for managing “bad” drivers.

(the residual pool)

Your Job: Make the system fair.

Massachusetts drivers are special.

Focus on Mathematics

Focus on Mathematics

Drivers must have insurance…

…insurance must be available to all drivers.

Companies will be able to reject “bad” drivers.

About 30,000 drivers will be assigned to companies.

Current plan: A simple lottery.

Focus on Mathematics

Aside: One Dilemma

Ask a professional to give an example of math from the workplace. The answer:

If Red Sox hats cost $1.50 each and Yankee hats cost

$2.00 each, how many hats should Theo order if his company has $250 to spend and needs twice as many Red Sox hats as Yankee hats?

He was confusing mathematical thinking with math problems.

Focus on Mathematics

#3: Child Rider Policies

JH sells a policy that covers all children in a family for one fixed premium.

(Data is expensive!)

Compute the expected cost for the policy.

- Census says:
- The average number of children per family is 1.7.

Focus on Mathematics

Background Information

- 1970’s: John Hancock Insurance Company used 1953 child mortality data to determine the cost of a child rider.
- The estimated cost of the policy was $2.30 based on an average mortality rate of 1/1000 and an average children per family of 2.3.
- The policy did not cover the first 14 days of life, dubbing it too risky because of the high morality rate in that period.

John Hancock doing the original calculations

Focus on Mathematics

Question:

- Most recent census says:
- “The average number of children per family is 1.7.”
- What is the average number of children per family in your school?
- (It’s all about conditioning.)

Focus on Mathematics

CIMS Story

At a final presentation: Students described an optimal reinsurance strategy… beat the company strategy by $6 million on one year’s data.

“Nice work, but tell me, would you be willing to bet your career on this algorithm?”

Focus on Mathematics

#4: Certification Testing

Diagnostic systems in gas stations must catch 95% of true failures

CARB Proposal: 3 out of 3 in failure test.

(14% of good will fail)

Company Proposal: 6 out of 7 in failure test.

(8% of good will fail)

Focus on Mathematics

Background: Binomial Trials

X = number of failures caught

p = accuracy of the system

What is the probability of 6 successes in 7 trials?

Focus on Mathematics

Big Question:

- What is the probability that a bad system will miss at least 2 failure in 7?
- What defines a bad system?

Focus on Mathematics

From an Industrial Mathematician:

Problem solving is harder than problem doing.

Problem formulation is harder than problem solving.

“When I finally get an equation,

95% of my work is done.”

Focus on Mathematics

#5: Geometry of the iBot

The iBot is a “wheelchair” developed at DEKA R&D that can go across rough terrain, over curbs, up and down steps.

Focus on Mathematics

Geometry of the iBot

The wheels are 30cm in diameter with 35cm between the centers. When going up stairs, the wheel assembly rotates about the midpoint (A) between the two wheels.

Focus on Mathematics

Climbing Stairs

What range of stairs can the iBot climb?

Learn about the building code:

Rise and Run and … Slope?

Focus on Mathematics

#6: Incidence from Prevalence

Company has good data for one year:

The fraction of the population in each age group that is on long-term care

The company needs data:

What fraction in each age group that will go on long-term care next year.

Focus on Mathematics

Prevalence Rates for Long-Term Care by Age

Focus on Mathematics

Focus on Mathematics

What is Industrial Math?

Most of the challenges we face in our professions

do not take the form “Here’s the data, find some solution.”

Instead, it’s “Here’s some partial data and a partial solution. How can I determine the right questions to ask, the additional data I need?”

Wayne Harvey, EDC interview

Focus on Mathematics

#7: Portfolio Management

Talk with Cuoco and Freedman:

Nice applications for Geometer’s Sketchpad

Focus on Mathematics

On Guiding a Project Team

- Define a clear goal… early and often.
- You can use the goal to answer many questions…

Focus on Mathematics

Math Expo 2005: FAQ

Work in groups or alone?

Choose topics or given direction?

-- goal is the math!

Credit or no credit? Required or not?

Answer = “That’s fine!”

Focus on Mathematics

The Fine Print…

Need Posters for Table Display

Time Line: 11 June is MoS event

need a couple of weeks before then

FoM people can help:

Review the projects and talk to students

Focus on Mathematics

Resources

- FoM Math Folks
- BU, UMass-Lowell, WPI
- Visitors
- Bob LaBarre, United Technologies
- Derek Kane, DEKA R&D
- Art Heinricher, Suzanne Weekes, WPI

Focus on Mathematics

More Resources

- FoM Web Site
- www.focusonmath.org
- Making Math at EDC
- www2.edc.org/makingmath/
- CIMS Web Site at WPI
- www.wpi.edu/~CIMS
- ADP Math Standards and Projects
- www.achieve.org
- Micron Technologies
- www.micron.com/k12/math/index.html

Focus on Mathematics

Math Students…

…have valuable skills:

- are not afraid of data
- understand abstraction
- can ask new questions

… need to develop:

- Problem formulation skills
- Confidence… Take a stand!

“Mathematics is clear thinking, nothing more.”

Focus on Mathematics

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