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What is the most difficult mathematics? 
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#1
Feb2506, 09:46 PM

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I am about a year into an undergraduate degree in Physics and I am wondering what might lay ahead. What do the more experienced mathematicians think is the most difficult subject?
a couple things happended recently that made me ponder the subject.  My calc2 professor was lecturing on applicaitons of the deginate integral, specifically in regard to the work function. In doing so, he admitted to the class that this was his least favorite lecture becuase he was not as comfortable with the Physics. I thought it was an odd coment becuase he seems like the most intelligent professor I have ever had. W=Fd is so simple, how could that seem difficult to a guy that knows all the ins and out of calculus?  I was reading an interview of a Mathematic PHD. He was asked what he thought was the most difficult mathematics. "Definetly Advanced Calculus" was his reply. I had always just assumed the math gets more and more difficult as you progress. I may be showing how green I am, but what is 'Advanced Calculus'? Is that Calc 3? Or, are there more higher level calculus classes? If calc3 is as hard as it gets, that does not seem too difficult. Honestly, I really enjoy calculus when you really get to apply it, as in optimization and applications of the definate integral. They just make a lot of sence. I enjoy them because it is like writing an essay, except in the most efficiant of language. I like applying the concepts of calculus, rate of change and the limit of summations. You can spend all this time in math playing logic games, but what is the point unless you can use it to tell you something about the world. I'll work all day trying to figure out a problem if the answer will actually tell me something interesting like how much work is required to move an object. It is the nitty gritty algebra at the end that always causes me trouble. Algebra is what I would consider the most difficult. My physics professor is always setting up problems for us, and then saying "the rest is just algebra, and if you cant do that, you should not be in this class" Which is true, no doubt, but I dont like the implication that it is "just algebra". Algebra can be a major in pain in the arse. Anyway, just curious, what someone with more experience might think. 


#2
Feb2506, 10:00 PM

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The most difficult mathematics is that which you do not know.
A surprising amount of mathematics is actually easy once you've learned it. Of course, once you learn the easy stuff, then you have to start tacking the deep stuff, and that gets harder. One teacher I had was introducing a new concept, and we did an example in class. (and this was a class for good mathematicians  not your average students) There was a lot of blank stares, and not everybody seemed to follow all the way through. The very next thing he asked was for us to differentiate the function x² with respect to x. Of course, everybody could do that very easily. His response? "The reason you can do differentiation, but not the other thing, is that you've differentiated things hundreds of times, but you haven't done this other thing very much yet." 


#3
Feb2606, 04:01 AM

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If for instance I were to take such a class and write on the board ...=42/64, I would leave it as that and would be mightily annoyed if any student pointed out that that is the same as 21/32 since that shows that they're focusing on the wrong thing. Mathematics is such a huge subject with so many opinions you're not going to get a simple answer. Perhaps a more reasonable question would be: what is the hardest part of mathematics that I'm likely to need to master? 


#4
Feb2606, 08:01 AM

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What is the most difficult mathematics?



#5
Feb2606, 08:37 AM

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#6
Feb2606, 10:28 AM

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It also depends on your "personality". Some analysts loathe discrete mathematics and would gladly not learn anything about it, and vice versa.



#7
Feb2706, 08:06 PM

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Here's a related question: what is the mathematics that depends on the most other mathematics?



#8
Feb2706, 08:27 PM

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I've had a batch of math classes, and so far, the most difficult IMO is differential equations. Lots of plugandchunk, and that's the problem for me: most of the time I don't know where to plug things.



#9
Feb2706, 10:15 PM

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It all depends on what you like. If you truly hate it, well certainly it's going to become difficult after awhile. You'll never give it some thought because you hate it. 


#10
Feb2706, 10:34 PM

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difficulty is relative to the individual. for me analysis is the most difficult and the easiest is geometry topology, and in between is algebra.
but complex analysis is to me easier than real analysis. and so on... 


#11
Feb2706, 11:05 PM

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I've been asking for a good book for awhile now. Something that is not too rigorous though. Sure, I might do well in the course, but that means nothing to me if I don't know what's going on. We don't have a textbook in our class, and we seem to be jumping all over the place. A nice thorough textbook would be what I'm looking for. I want a good one. I've seen free ones and cheap ones, but there are reasons for them being free and cheap. They aren't very good. 


#12
Feb2806, 12:28 AM

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#13
Feb2806, 01:33 AM

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#14
Feb2806, 07:00 PM

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We jump around in the sense that we don't know where we are going or heading. We didn't have a course outline either, so that doesn't help either. 


#15
Feb2806, 07:31 PM

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Math/formal logic=by the far hardest math course I have ever taken. You really have to think way far outside of the box to follow what is going on in math logic. Proving godel's theorems and learning recursion theory was the most challenging thing I have ever learned in my entire life. Next to logic, learning about Hilbert Spaces was also very hard, but not as bad as logic.



#16
Feb2806, 10:37 PM

P: 166

Speaking from what little I have done, I found algebra hard, specifically just logrithms. Took me weeks to realize how change of base worked....well not really but you get the idea. I just finished roots of complex numbers using DeMoivre's Theorem (begining trig).
Speaking from what I have heard, everyone says Cal II is a (certain inappropriate word that starts with a capital "B"). All I hear is 'Cal III is some much easier than Cal II, what a "B" it was'. 


#17
Mar106, 09:50 AM

P: 304

Cal III is easier mainly because by the time you get there, you are used to integration and differentiation. Cal III doesn't teach anything conceptually new, unlike cal 1 and 2.



#18
Mar106, 10:11 AM

P: 15

The most difficult maths is the one you haven't learn and you are not going to learn...so, learn more practise more, and all will be clear...



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