<p>How are these classes? </p>
<p>Math 53 Multivariable Calculus</p>
<p>Math 104 Intro to Analysis</p>
<p>Math 110 Linear Algebra</p>
<p>Math 113 Intro to Abstract Algebra</p>
<p>Math 115 Number Theory</p>
<p>Any previous experiences about their difficulty etc.</p>
<p>Are there any high schoolers who have taken these courses?</p>
<p>It depends on your professor + how deep you go into the given class entirely. I think all of them may be mastered with consistent effort. I had looked at several of these before coming into college – it really depends on your maturity level. If you’re not ready for them, they’ll be a waste of your time to take the classes (you might as well spend the time reading them carefully on your own time).</p>
<p>Which college level math courses did you take while you were still in high school?</p>
<p>Didn’t take most of them – mainly read the textbooks on my own, actually. Personally I think this might be a better idea for you. You want to absorb what you study very well, and I think forcing yourself into classes at an early stage may not be the best way to absorb the material. </p>
<p>But for instance, stuff like linear algebra, analysis, multivariable calculus, differential equations, etc, etc, I certainly had a bunch of exposure to in high school.</p>
<p>Ya, I have already taken a lower division Linear Algebra course at a local community college, and I think the upper division Linear Algebra class will be a great supplement to build on top of the stuff I have already learned.</p>
<p>My primary choice for the summer ideally would be to attend Ross Program/PROMYS, but given the selective admission process, I doubt I will get in, so these classes are essentially my backup plan.</p>
<p>That’s a good plan, I agree – it’ll be a good supplement certainly. I would recommend starting off with the upper division linear algebra course certainly. My personal opinion is that undergraduate analysis is a little boring!! But that shouldn’t influence you. I still think linear algebra is the best first exposure to upper division stuff. I’d go through that entirely before touching abstract algebra, though – not because it’s a prerequisite, but because while you can make it through abstract algebra with less background, the best thing is to develop the requisite maturity, and then learn it <em>very</em> well the first time you do it. </p>
<p>In short, I’d recommend that you take Math 110 and spend lots of time solving all the problems you can in your textbook, more than what’s assigned.</p>
<p>And that alone would be better than going to Ross/PROMYS?</p>
<p>Well, it depends. What are your goals? What’d you like to major in, and with what goal? </p>
<p>What is the Ross thing? Not familiar.</p>
<p>I am planning to major in Math/Physics. Ross Program and PROMYS are two Number Theory summer programs that are quite prestigious.</p>
<p>So in the end, would I benefit more from an intense summer working with others/learning Number Theory, or would I benefit by taking math classes at Berkeley?</p>
<p>Well…that’s a personal decision. My own view? Do what is most appealing to you. I don’t think either will really significantly change your path. </p>
<p>See, classes are classes – they’re something you’ll do at some point. If your summer programs are so fun, I’d not pass up that chance.</p>
<p>I took MAT 55, Discrete Mathematics, as a highschooler at Cal. I will be going to Princeton next year. I don’t know if Discrete Math makes a big difference on your transcript, but it certainly opened my mind. I will be taking Analysis this summer. If you have previous experience in mathematics, you should take Analysis. I took 55, because I didn’t really know much of pure mathematics and I was also rejected from Stanford’s Math Camp. 55 opens your mind to a wide range of mathematical topics (not too specific like Analysis) so that you can find a topic you like and broadly explore it by yourself, during all the free time you have in the summer! I did something along those lines and that’s why I recommend 55, as it is a good experience and isn’t too hard to get an A. By all means, if you have the mathematical ability and drive, take Analysis.</p>
<p>^ Did taking those classes have any effect on your going to Princeton?</p>
<p>I am planning on taking 53, 110, and 115</p>
<p>Analysis seems nice, but it might overdo it for me</p>
<p>^^ That sounds a good list. However, please take this over 2 years. Summer schedules are ultra compressed, and even 2 courses is too much homework, and frankly I don’t think you’ll absorb it as well. If you really want to flirt with the material in all these books, I’d recommend reading it by yourself. Maybe focus on one class over summer and then pick up the textbooks for the others if you’re interested.</p>
<p>Trust me, <em>probably</em> taking these classes will not have a huge effect on getting you into Princeton or whatever. Focus on your essays, etc, more.</p>
<p>Your intent in taking these classes is not supposed to be getting into Princeton. Thinking about it, it seems like the topic is completely irrelevant. Princeton doesn’t care (to the extent that it will admit you) if you took college classes or not, it cares about your “quality of though”, which you can demonstrate (and should do so) via other means, such as your own individual research onto a particulr mathematics topic or doing well in mathematics competitions, etc. I’ve met people who’ve taken many upper division math classes at Princeton and were still not accepted. There’s no shortcut in just taking classes and getting into college, rather it is about reflection and utilization of that knowledge (which you will hopefully show in your essays and extracurriculars, etc etc). But to do that, you don’t necessarily have to even take a math class, you can just study by yourself, unless you need to take a math class to structure yourself to learn the material…</p>
<p>I learned discrete mathematics because I wanted to gain a new view of pure mathematics as I decided to spend my summer at Berkeley doing my own research onto the foundations of quantum mechanics and exploring the nature of logic. Now, this wasn’t necessarily done through a camp or any prestigious or organized summer program. It was merely me in the Berkeley library, furthering my inquiries, while taking a math class and helping teach a philosophy class.</p>
<p>Thanks for that advice. I mainly want to take 110 to learn more about Linear Algebra, while 53 and 115 are for extra topics in math I want to be exposed to.</p>
<p>Hopefully 110 will not be too difficult as I have already taken a lower division Linear Algebra course.</p>
<p>I also want to do some independent research, and I think doing these summer classes will allow me to get some ideas about what type of research.</p>
<p>But if I get accepted to the Ross Program or PROMYS, which are two excellent Number Theory summer programs, I will rather go there than take summer classes, because its more focused.</p>