1. Operations Research: Inquiring Minds Want to Know! Evan Glazer Evan.Glazer@fcps.edu Thomas Jefferson High School for Science and Technology

2. The origins of my interest in mathematics

3. Operations Research Scientific approach to analyzing problems and making decisions Develop algorithms from theory and simulation to make sense out of a system

4. Connecting OR to Math Curricula Local contributors include: Lisa Bredienbach Ellen Chien Ilana Hand Hazel Orth Helen Snyder http://www.hsor.org/

5. http://academics.tjhsst.edu/mathcs/courses.htm

6. OR student assignments/projects Optimizing ant colony heuristic to a dynamic traveling salesman problem Identifying transformations to improve a driving simulator Optimizing flow movement in and out of school Developing an algorithm to improve calculation of speed of planes as they approach an airport

7. TJHSST homecoming Raggedy Ann and Andy Hotdog and ketchup Teenage Mutant Nija Turtles We’re inseparable dy = x + y dx

8. Operations Research Encourages… a systematic approach to solving non-routine problems a systematic approach to evaluation simulation to understand the unknown

9. Encourages a Systematic Approach to Solving Problems Known algorithm Linear Programming

10. Navigating across Romania Try navigating Fairfax County

11. Dijkstra's shorters path algorithm 1. Create a distance list, a previous vertex list, a visited list, and a current vertex. 2. All the values in the distance list are set to infinity except the starting vertex which is set to zero. 3. All values in visited list are set to false. 4. All values in the previous list are set to a special value signifying that they are undefined, such as null.null 5. Current vertex is set as the starting vertex. 6. Mark the current vertex as visited. 7. Update distance and previous lists based on those vertices which can be immediately reached from the current vertex. 8. Update the current vertex to the unvisited vertex that can be reached by the shortest path from the starting vertex. 9. Repeat (from step 6) until all nodes are visited. Source: http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm

12. Develop an algorithm http://academics.tjhsst.edu/compsci/CSweb/Unit3/Lab15/Applet15.html

13. Develop an algorithm In a game of Nim, you start with 17 pennies The goal to win is to leave your opponent with the last penny on the table You can select 1, 2, or 3 pennies when it is your turn Keep taking turns until there is only one penny remaining

14. Unknown algorithm

15. Encourages a Systematic Approach to Evaluation

16. Google Page TM Rank http://en.wikipedia.org/wiki/PageRank

17. NCAA Quarterback Rating +++ NFL Quarterback Rating http://en.wikipedia.org/wiki/Passer_rating Guess this ranking formula

18. Appropriation of Seats to Congress The Constitution provides that each state will have a minimum of one member in the House of Representatives, and the current size of the House (435 seats) has not changed since the apportionment following the 1910 census. Thus, the apportionment calculation for Census 2000 will divide 385 seats among the 50 states. Congress decides the method used to calculate the apportionment….Adopted by congress in 1941 and used through the 1990 census, the method of equal proportions also results in a listing of the states according to a priority value--calculated by dividing the population of each state by the geometric mean of its current and next seats…. http://www.census.gov/population/www/censusdata/apportionment/history.html http://www.census.gov/population/www/censusdata/apportionment/calculated.html

19. Which factors influence the 2008 vote? Discuss issues that affect someone’s vote Identify corresponding weight Develop method for prediction 18% voters undecided (as of Sep 24, according to Yahoo polls)

20. Encourages Simulation to Understand the Unknown http://quantio.cz/demo/simul/ Note normal distribution, random selection

23. Queuing Theory L = a/(h – a) W = L/a L = average length of line W = total waiting and service time a = average arrival rate h = average help/service rate

24. How should you divide portables for equitable access? Think about: Service time for men and women Proportional usage by men and women L = a/(h – a) W = L/a

25. http://www.arcytech.org/java/population/index.html

26. Math applications Inquiry Hypotheses Discovery

27. Operations Research: Inquiring Minds Want to Know! Evan Glazer Evan.Glazer@fcps.edu Thomas Jefferson High School for Science and Technology