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Industrial-strength Mathematics: Research Projects from Business and Industry

Industrial-strength Mathematics: Research Projects from Business and Industry Art Heinricher WPI Student Research Projects FOM Math Expo Industrial Math at WPI Resources Overview: Key Points… Business and Industry are good sources for very engaging mathematical research projects.

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Industrial-strength Mathematics: Research Projects from Business and Industry

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  1. Industrial-strength Mathematics: Research Projects from Business and Industry Art Heinricher WPI

  2. Student Research Projects FOM Math Expo Industrial Math at WPI Resources Overview: Focus on Mathematics

  3. 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

  4. Mathematics Research Expo June 11 at the Museum of Science “All students will participate in a mathematically significant research project.” Focus on Mathematics

  5. 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

  6. 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

  7. 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

  8. Project #1: Real Cost of a Ticket A speeding ticket costs you $75 today. What is the real cost? Focus on Mathematics

  9. Background Information Massachusetts has a point system: SDIP One speeding ticket = 3 points Premium increases 7% per point: Imagine being SDIP 35! Focus on Mathematics

  10. Chart the Cost of the Ticket Focus on Mathematics

  11. More questions… • 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

  12. Aside… 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

  13. #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

  14. Fair to the Companies Focus on Mathematics

  15. Assigned Risk Plan 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

  16. 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

  17. #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

  18. 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

  19. 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

  20. 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

  21. #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

  22. 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

  23. 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

  24. 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

  25. #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

  26. A 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

  27. Climbing Stairs What range of stairs can the iBot climb? Learn about the building code: Rise and Run and … Slope? Focus on Mathematics

  28. #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

  29. Prevalence Rates for Long-Term Care by Age Focus on Mathematics

  30. Flow Chart for LTC Focus on Mathematics

  31. 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

  32. #7: Portfolio Management Talk with Cuoco and Freedman: Nice applications for Geometer’s Sketchpad Focus on Mathematics

  33. On Guiding a Project Team • Define a clear goal… early and often. • You can use the goal to answer many questions… Focus on Mathematics

  34. 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

  35. 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

  36. 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

  37. 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

  38. 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

  39. Many Thanks! I hope to see you at the Museum of Science in June! Focus on Mathematics

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