Any physicists / CS uncomfortable with less-explained math?
I studied theoretical physics for BS, and the 5 years since I have a range of exposure to theoretical mathematics in analysis and combinatorics. Recently I looked into the notes on using Green's function to solve a particle in a 2D well. I cannot help notice how little Green's function is discussed - without justifying its validity in solving problems such as a 2D well. I remember that at the time, I knew how to solve the problem but not understood it enough to apply to it to another scenario.
I find similar discomfort in computer science. I learnt search trees, sorting algorithms with great ease through proofs in applied mathematics. Recently I was taking a class on mathematics in computer science, and I was surprised that those simple theorems were casted in so complicated language and description that I was very sure if I had not taken applied combinatorics in the math department, I would be twice confused and spend more than twice the time explaining the theorems to myself.
I couldn't quench the little noise in the back of my head that whenever I am introduced to something in physics or computer science, it says "sure I trust the professor ... but I don't know why I should be convinced otherwise."
Is this common among physicists and computer scientists here in the forum who have similar experiences?
Re: Any physicists / CS uncomfortable with less-explained math?
I have similar feelings about the matter. I'm a last year undergrad of physics, but I try to combine with math and whenever I've had a math course before a certain physics course where the physics course uses that kind of math (but independently of the math course, as most people have not taken that math), I also have the feeling that the way the physicists get the math is way more jumbled. Okay, of course, the physicists don't have time to see all the mathematical intricacies (which I'm fine with! It makes sense), they way they often present it is unnecessarily muddled.
I can give a few examples (an obvious one being Hilbert spaces and inproducts and the like in QM), but the one that struck me most was complex analysis. I had taken a complex variables course in my 2nd year in the math departement. The year after that, we handled complex analysis in a "mathematical methods in phyics" course and we hardly did any proofs (which I again understand, due to lack of time), but which I did not understand was the presentation of the theorems. The beautiful build-up of the theorems as shown in my math class had a lasting impression, and more so they built a conceptual picture, a way to figure out what the theorems said in case you forgot, and showing the logical procession of things, whereas in the physics class no attention was devoted to that, and I think my fellow physicists have a poorer understanding than if it were structured a bit more mathematically.
The thing is, I haven't yet figured out if such things are common, or if I just had bad professors up until now in the cases where heavy math was need for physics...
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