<p>abstract algebra is such a pain in the a55. Either that, or the professor is making it worse than it's meant to be. All we did in abstract algebra was putting together formal definitions and proving stupid things, like the distributive law on set S or something like that.</p>
<p>It was really boring, and the margin for error in this class was very small. I'm looking to get a B if I don't f-up the final.</p>
<p>I liked linear algebra, the non-theoretical parts of it are somewhat useful and interesting. I heard real analysis is more interesting, but harder than abstract algebra. Can someone tell me about real analysis?</p>
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<p>Likely untrue if your algebra course is taught properly…which it seems yours wasn’t, from your description. Basic real analysis tends to justify the theorems in calculus, and then possibly go into more advanced integration theory via which functions which are not Riemann integrable can still be integrated in a certain reasonable sense. This is a formalization of the theory of measuring sets, which is useful because it can be applied in the context of the measure being a probability measure.</p>
<p>I didn’t quite get most of that. But here’s the description they gave me at our college website “A careful development of calculus of functions of a real variable: limits, continuity, differentiation, integration, series.” I take it that this class involves more application and less proofs than abstract algebra?</p>
<p>My math professor for abstract algebra was an English dude. He graduated from U Cambridge in the 70s and wrote a ton of math papers involving proofs. He also wrote his own abstract algebra text book, which we use in class. The guy’s a math freak, but he could’ve made the class more interesting by showing more clear examples than assuming that we’re all math majors.</p>
<p>Real Analysis is all about proofs. You basically learn calculus again but this time you have to prove every step along the way.</p>
<p>Real Analysis and Abstract Algebra are the two core classes or core sequences for the math major. They introduce the basic definitions, tools and results that will be used all over the place in more advanced courses. As such they can seem a bit boring, dry, tedious and completely irrelevant until you get to the higher-level courses. (Unfortunately, students who stop taking math after real analysis and abstract algebra leave the field thinking that math is all abstract nonsense.)</p>
<p>What b@r!um said - real analysis is probably the most proofs-based class there is, period. Most other classes teach you some new interesting facts and hopefully how to use them in context of examples, but many of these “interesting things” you consider in the first real analysis course can actually be guessed or reasonably dealt with using a good calculus foundation. The whole idea is to get really good at formally writing out proofs, even when your intuition says the answer is quite easily found. </p>
<p>However, what some people find really fun about real analysis is the very fact that it is a more intuitive subject to them simply because you picture how close things are getting, picture how functions can behave, etc…and then translate this intuition into formal writing.</p>
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<p>You may have a possibly valid complaint, but for the wrong reason. Abstract algebra is a class for math majors. Anyone else who tries to take it should not expect a different treatment, as it will likely be useless to them as professionals unless they learn it the way a math major would, because a silly examples-based course may help you think the subject is cool, but not tell you how to think about it properly when you actively engage in the material. </p>
<p>Examples should exist to help motivate the theory, but I think a few illustrative ones is all it should take for one to understand the importance. If you’re interested in applying algebra or analysis, you have to learn the theory really well first, else you won’t be able to deal with nontrivial examples because you won’t have enough machinery to attack it with. Simple examples can be attacked with weak-sauce theory, but the whole point of this general nonsense is that it’s useful in more contexts than would ever be immediately apparent.</p>
<p>"Simple examples can be attacked with weak-sauce theory, but the whole point of this general nonsense is that it’s useful in more contexts than would ever be immediately apparent. "</p>
<p>Those courses are useless for people who don’t plan to become college professors or mathematicians. My suggestion to the OP is: take the courses but don’t worry if you are left feeling like you got nothing useful out of them, because for most people there really isn’t anything useful to be gotten out of those courses.</p>
<p>I’m an engineering major thinking about grad school. I think I’ve already completed my minor, which goes up to abstract algebra. There is this one course called intro to proofs, but I think I can get it waved, since it was just a prerequisite to linear algebra and abstract algebra.</p>
<p>Is real analysis useful for grad school? Is it beneficial for me to take it? What other math classes do I need to take to prepare for grad school, like statistical mathematics maybe?</p>