Alan Davis recap

In his lectures about combinatorics, Mr. Davis touched upon various topics. He gave students problems about counting the ways to rearrange and pick items, using candy as a visual to help the students understand. He also talked about the various strategies used to solve these problems. These strategies included using “bars and stars” to represent the problem, and using the Inclusion-Exclusion Principle. Lastly, he demonstrated the numerous applications of the famous Pascal’s Triangle.

Sample Problems:

Say there are 5 Jolly Ranchers and 3 Starbursts. How many ways are there to pick a Jolly Rancher or a Starburst? How many are there to pick a Jolly Rancher and a Starburst?

How many different ways are to rearrange the letters in the word ALABAMA?

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A
How many paths are there from point A to point B only going up and right?

If there are 3 people and 5 different candies, how many ways are there to distribute the candies if each person has to get at least one candy?

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March 7, 2009 – Alan Davis – “Combinatorics Continued”

Alan Davis will continue his previous talk on Combinatorics with more challenging problems and concepts.  Those who missed his first talk are encouraged to attend promptly for a quick review at 2:00.

Mr. Davis will focus on the essence of the inclusion-exclusion principle with some interesting problems.

For the curious students who are eager to sharpen their problem-solving skills in Combinatorics, Mr. Davis recommends these two collections that Titu Andreescu and Zuming Feng collaborated on:

• A Path to Combinatorics for Undergraduates: Counting Strategies
• 102 Combinatorial Problems

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February 21, 2009 – Alan Davis – Combinatorics

We are very fortunate to have Alan Davis talk about combinatorics on February 21, 2009. His talk about combinatorics will include the following topics: Counting permutations and combinations, counting with repetition, binomial coefficients, Pascal’s triangle, Pascal’s identity, Vandermonde’s identity, and the inclusion-exclusion principle.
Combinatorics is related to many other areas of mathematics such as algebra, probability, and geometry, and also computer science and statistics. More information about this interesting branch of mathematics can be found here.

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