Monthly Archives: February 2012

Thermodynamics for Mathematicians (I)

“Every mathematician knows it is impossible to understand an elementary course in thermodynamics.” – V. I. Arnold. The following is the culmination of at least three attempts to understand thermodynamics at various times during the last two years. Why’s it … Continue reading

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Power Series and Generating Functions (II): Formal Power Series

For today’s post, we shall first talk about the Catalan numbers. The question we seek to answer is the following. Let n be a positive integer. Given a non-associative operation *, find the number of ways to bracket the expression … Continue reading

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Power Series and Generating Functions (I): Basics

[ Background required: basic combinatorics, including combinations and permutations. Thus, you should know the formulae and and what they mean. Also, some examples / problems may require calculus. ] Note: this post is still highly relevant to competition-mathematics. 🙂 To … Continue reading

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