<p>So I'm considering declaring a math major as a my second major ( my first one is econ). I'm going through my schedule for next semester, and I have math 360 registered, but I'm not sure as to whether I want to continue taking these courses ( and so I'm not sure whether math is my thing). I finished up math 104-241 and did well in all (all A's except for an A- in 104 lol). But from what I've seen online and talked to people, the rest of these courses are all proof based. I detest proofs and have little experience/ability with them. I like calculating random stuff, as we have done in the past calc courses. But I do understand that math is based on proofs. So...if I hate proofs, should I even consider going on? Otherwise I'll just do econ and take random math/stat courses I'm interested in. what do you guys think?</p>
<p>seriously 28 views and 0 answers??? I really need help dudes.</p>
<p>yeah, proof based courses are a stretch for everyone so don’t worry. The main thing is to start small. Try to get a somewhat gentle introduction to probability/real analysis. A lot of that is set theory so I would start by watching some of the real analysis online lectures in the University of Chicago fin math program. Dr. Fefferman is awesome and it gives you a real sense of higher math. If you got A’s in the calculus sequence, you’re a talented student and can do well in more abstract classes with consistent effort (struggling through homework is key).</p>
<p>My advice is to try to find a friend or friends you can go through 360/361/370/371 with. It will make homeworks and studying for exams a lot less painful. One of the advantages of higher math at Penn is that a fair amount of the exams will be take homes so that removes the time pressure for the most part.</p>
<p>The initial investment in 360 and 370 is tough no doubt. If possible, I would only do one course in the first semester and take 312/412 before 370.</p>
<p>thanks for your response.</p>
<p>My main worry is whether or not I am actually interested in taking these courses (and so continuing with my math studies). I was going over a math 360 test and, honestly, I wasn’t attracted to the material. I mean, I enjoy solving integrals and problems, but I’m not that interested in first principles and writing out proofs. So I’m not sure whether this course is for me or not.</p>
<p>Megaman, I’m in the same boat as you. I’m doing econ and taking 360 next semester. Not sure if the math major will pan out, but might as well give it a go.</p>
<p>Doesn’t sound like you’re interested in knowing why math works, or where it comes from, so I’d say no. But the only way in which you can really tell is to try.</p>
<p>A math major is about the proof-based courses. Short answer: if you’re not interested in proofs, stay away from the major.</p>
<p>I would push you to consider it a bit more, however. You never really know until you’ve had some experience with the material that you won’t like it. Start out taking the course - stick with it at least until the drop deadline, and decide whether you like it. Just because you take one course, it doesn’t mean you need to take them all.</p>
<p>I will say that many people go through this experience, where they enjoy doing the math 104-241 track, but dislike the real math courses. It’s normal.</p>
<p>Ok, I’m an incoming Ph.D. student at Penn, so this is my take. I am actually pretty surprised that you haven’t taken proof based math yet. As a student from Europe our first math course as a freshman was already proof based analysis… Most people I know really enjoy proofs once they learn to do them while some people never learn and always hate them. However, most people who never learn how to do them, just don’t put in the required effort. I think the first step is reaching a level where you can say with 100% certainty that a proof you have written is correct without requiring anyone to grade it. At that point a problem is reduced to actually finding a proof instead of wondering if you’re done or not.</p>
<p>So, do you hate proofs or don’t you know how to do them? If it’s the latter, then it just boils down to learning how to do them. Many people also “skip” proofs in lower level courses thinking that you don’t need them and this just exacerbates the problem. Doing proofs is for most people a skill that needs to be acquired. There are, however, a few books that covers the topic on how to prove things i.e. the logic behind mathematical proofs. The following is supposed to be good:</p>
<p>Daniel Velleman, How to Prove It: A Structured Approach</p>
<p>Second, many people study math in the wrong way. If you’re just used to looking at proofs and just realizing that they work, then you’re probably not learning them. Most people don’t realize that learning the proofs is equally important as learning the results! I follow a system pretty much like this.</p>
<ol>
<li><p>I write down every single lemma, theorem etc. on my computer (i.e. copy the book), but leave out proofs.</p></li>
<li><p>I make sure that I can prove every single statement in this document without looking at the text.</p></li>
</ol>
<p>The way I have accomplishes (2) without wasting too much time has been using a flash card system where you can assign scores to cards where each card contains one theorem or lemma. You can then score the card based on how easily you could prove it and the higher the score the more time it’ll take before it will show you the card again. The program I’ve used for this is called Mnemosyne and is open source.</p>
<p>I noticed that math 360 has been using Marsden’s text. I suppose it’s pretty similar to Rudin which I used myself. I’ve heard lots of good things said about the following text:</p>
<p>Ross, Elementary Analysis: The Theory of Calculus</p>
<p>It’s supposed to very gently introduce the idea how you make a rigorous proof in analysis. It also has solutions to exercises which helps studying it by your own. If you are afraid of math 360, I would recommend looking at these two books over the summer and doing as many exercises as you can from Ross.</p>