<p>I'm planning on taking math 508 and was wondering if anyone has taken it already and can provide some feedback or insight into its difficulty.</p>
<p>I honestly don’t know why they have these two different courses instead of just one. I looked at the exercises of 508 and it seems like just any typical course based on Rudin’s Principles of Mathematical Analysis. If you’re ready to study Rudin, then you’re ready for 508. The only difference seems to be that they have no “trivial” problems on 508. This is a problem only if you have troubles understanding what a theorem or definition says and you need simple problems to clarify their meaning. Thus, it seems that 508 assumes that you understand a definition or theorem by reading it and then assigns problems where you need to apply them. However, this is easily fixed by just looking at problem sets from previous problem sets of 360 that cover the same topic.</p>
<p>I would also assume that 508 has a much smaller class size and in general stronger students, so you would have the benefit of having better class discussions. The exam problems were pretty much the same level than I had in my 2nd year honors course, so they’re not too hard.</p>
<p>Disclaimer: I’m not a Penn student. I’m starting in the Ph.D. program in September.</p>
<p>I talked to Professor Gluck (math advisor) about those two classes earlier. He basically said that 508 might move a little faster and expect you to be a little more sophisticated with math. He recommended to me to sit in on both classes and see how they felt because a lot of it is clicking with the professor than the material.</p>
<p>Venkat, does this mean u will also be taking real analysis in the fall of 2009? how do u recommend on preparing for it in the remaining time we have left this summer? i’m worried because i am a math major and will be taking at least 3 upperlevel math classes plus others.</p>
<p>The best preparation for such a class is to just start reading Rudin before class starts. Any book on topology like Munkres is going to help too and Munkres might even be a bit more verbose on the material relating to metric spaces which Rudin covers in chapter 2.</p>
<p>In a class on analysis you’re also going to need almost every possible inequality out there. A good thing to do is to just hunt for all “standard” inequalities that you’ve come across in your previous courses and make sure you know them. A central theme in analysis is learning to approximate stuff (that’s what you do in epsilon-delta proofs) and that’s where inequalities come in.</p>
<p>^wow, I’m going to fail next semester in 360, i have no idea what you mean by inequalities…</p>
<p>Zero, I am signed up for 360 right now, but might do 508 if I feel like it’s a better fit. I’m not 100% sure on the math major, but we’ll see. To prepare I’m trying to gain some experience writing proofs (didn’t take the freshman seminars) and maybe skim over some of the textbook which I borrowed from a friend. Gluck told me to just relax and that we shouldn’t need any special preparation. From talking to my friends who took 360 it seems like a lot of it is working through the problems and getting it to “click”.</p>
<p>really? we dont need to prepare? im like reading all this random stuff on intro to analysis and proof writing because im so afraid the class is gonna be super fast >< i guess i should talk to a professor like Gluck as well. Is he on campus this summer?</p>
<p>Basically I mean stuff like Bernoulli’s inequality etc. which are good to have wired into your brain when the class starts. Your friend is right about the fact that you need to get the stuff to “click”. Basic analysis is actually really simple, because almost all proofs use exactly the same ideas. In this regard the best possible preparation you could possible have is to use the weeks left to just study Rudin and do a few exercises in chapter 2.</p>
<p>If you want a more gentle introduction to real analysis before the class starts, you can take a look at Ross’ Elementary Analysis. It’s a dumbed down version of Rudin and should be suitable for self-study.</p>
<p>eof, can you list all the inequalities we should know? I really really really need an A in this class to make up for my lackluster performance in Math 114 and 240.</p>
<p>I think pretty much anything you might need is going to be covered during the course, but I was mainly meaning that you need to know how to apply them. It can often be quite tricky to know when to apply an inequality and that usually comes with experience of doing problems.</p>
<p>Most importantly you’re going to spend a whole course applying the triangle inequality to bunch of things. Thus, if you have any problems with absolute values, then you should look into some old calculus books and do problems relating to absolute values (usually in the prerequisites chapter). For a list of nice inequalities that everyone should know, the following is a good start (but I doubt you’ll going need more than half during your course):</p>
<ul>
<li>Triangle</li>
<li>Bernoulli</li>
<li>Cauchy-Schwarz</li>
<li>Jensen</li>
<li>Arithmetic-Geometric mean</li>
<li>Young</li>
</ul>
<p>There’s actually a really good book on inequalities written by a Penn professor:</p>
<p>[Cauchy-Schwarz</a> Master Class: Introduction to the Art of Inequalities](<a href=“http://www-stat.wharton.upenn.edu/~steele/Publications/Books/CSMC/CSMC_index.html]Cauchy-Schwarz”>Cauchy-Schwarz Master Class: Introduction to the Art of Inequalities --- Links to Reviews, Sample Chapters, Typos, Original Sources)</p>