Monthly Archives: March 2012

Power Series and Generating Functions (IV) – Exponential Generating Functions

Posted on March 26, 2012 by limsup

Note: this article is noticeably more difficult than the previous instalments. The reader is advised to be completely comfortable with generating functions before proceeding. We’ve already seen how generating functions can be used to solve some combinatorial problems. The nice … Continue reading →

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Power Series and Generating Functions (III) – Partitions

Posted on March 19, 2012 by limsup

One particularly fruitful application of generating functions is in partition numbers. Let n be a positive integer. A partition of n is an expression of n as a sum of positive integers, where two expressions are identical if they can be obtained from each … Continue reading →

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Kinetic Theory, Entropy and Information Theory

Posted on March 11, 2012 by limsup

This is really a continuation from the series “Thermodynamics for Mathematicians”. Our discussion then wasn’t quite complete without some justifications of the facts we used from kinetic theory of gases, in particular, we will figure out the constant c in the … Continue reading →

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Thermodynamics for Mathematicians (IV)

Posted on March 4, 2012 by limsup

Note: for this installation, we now require multi-variate calculus, specifically partial differentiation. 10. More State Parameters For this section, let’s consider the case of a homogeneous gas, whose state is parametrised by (P, V, N), where N is kept constant for now. … Continue reading →

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Thermodynamics for Mathematicians (III)

Posted on March 2, 2012 by limsup

Note: calculus, specifically integration, is essential in this article, though students can possibly just substitute it with summation to achieve the same result. In the previous installation, we defined a temperature scale by looking at the efficiency of a heat … Continue reading →

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Thermodynamics for Mathematicians (II)

Posted on March 1, 2012 by limsup

We continue our discussion of thermodynamics. Warning: some of the examples will involve calculus and a bit of (ordinary) differential equations. 3. Work Done by/on the System A system can do work, e. g. when a gas expands and pushes against … Continue reading →

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