Monthly Archives: February 2012

Thermodynamics for Mathematicians (I)

Posted on February 29, 2012 by limsup

“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

Posted on February 19, 2012 by limsup

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

Posted on February 5, 2012 by limsup

[ 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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