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Message: <blockquote data-quote="bigbadwolf" data-source="post: 36073" data-attributes="member: 722">In field and Galois theory, among other things, the results that a general angle can't be trisected, a cube can't be doubled, and the circle can't be squared (i.e., using straightedge and compass) are proved. Pick up any respectable undergrad text in abstract algebra to see these standard results (e.g., Herstein, section 5.4)---------- Post added at 12:17 PM ---------- Previous post was at 12:08 PM ---------- Opinion seems to be divided here. I'm a math major myself but I wouldn't push the advantages of the definition-lemma-theorem-corollary style. It seems to me that engineers and physicists who gravitate towards quant finance do just fine without the rigors of pure math. In fact I would argue that the pure math style can often work against a heuristic style of thinking and feeling, which is probably much more important in applied areas like physics and finance than sterile rigor. Sometimes I think the sterile rigor of modern pure math is akin to the sterile theoretical arguments of scholastic philosophers a thousand years ago.  You definitely do not need abstract algebra. For analysis, at least work through a simple text by yourself -- say something like "Real Analysis" by Howie. This will come in handy if you look at stochastic theory. More important than this, however, is to learn to construct individual heuristic arguments by yourself. This is a valuable applied math and physics skill.</blockquote>

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