Exploring Discrete Mathematics Summary

Monday - Friday, July 13 - 17, 2009

During the third week of our Discrete Math group meetings we worked on proofreading each other's solutions, deciding on the categories each problem belongs to, and writing the short abstracts to describe each category.

Cal was also working on organizing the Wiki page, providing all the links and cross references, and improving the visual presentations of some of the solutions.

Andrew explored a special strand within the project based on the "Elevator Problem" (the problem reads as follows: there are 6 floors in a building, 7 people enter an elevator on the ground floor; in how many ways can these people exit the elevator if only the number of people exiting on each floor is taking into consideration). Andrew worked on creating a series of problems/questions that can lead the students to discovering an elegant and compact solution based on partitioning a set of objects instead of solving the problem by brute force—the systematic listing.

On Monday Brian Hopkins from St. Peter's College went over a problem arising from the morning session and ended up with Euler's Theorem involving pentagonal numbers.

On Thursday we brainstormed the ideas for the group presentation, choose a scenario for it and put it together.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.