What do normal subgroups look like?

I am in the process of writing a longer post on Galois Theory (see here), and one of the central concepts is that of a normal subgroup. We all know the definition (and their equivalents) from classes/books, but anyone who likes to 'see their mathematics' is left with the question: ... but what do they … Continue reading What do normal subgroups look like?

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Understanding the credit crisis

In an earlier post (see here) I put a link to an online book that explains all the main concepts of economics in terms of the classic 'Island Economy'. If you think about it in theoretical terms, this book is a 'proof' that the Island Economy is a sufficiently rich model into which many important … Continue reading Understanding the credit crisis

The power of notation in problem solving

It's trivial when you think about it: good mathematical notation is one way of making a problem easier to solve. In my introduction to advanced probability theory I put emphasis on how probability theory has developed a clever and natural way to describe the processes we deal with. If you think about it some more, … Continue reading The power of notation in problem solving