<p>This is my schedule:
Analysis I (Rigorous and proof version of Calculus) for those not familiar with the course.
Linear algebra I (regular, not honors).
Honors general Chem I (the chemistry taken by chem, physical chem, and chemical physics majors. There is a different more general one for other science students which is less rigorous).
Honors physics I (in-depth physics designed only for physics and mathematical physics majors only, not the general one taken by other science students). In fact, it is not required for the physics and many physics majors take the less rigorous one. Unfortunately, it is a requirement for mathematical physics.
Intro to Computer programming I (Fun class and the work is minimal and maintainable). </p>
<p>Aside from computer programming, all my other classes have a workload that is either equal to or greater than ALL of my high school classes combined. Usually, I only worked 4 hours a day when I started, but professors just keep assigning twice as many problem sets+readings as the previous week and have nearly doubled my time studying (6-7 hours, 8 on occasion). Not only that, but since most of professors have very thick accents and can't teach that well. They skim an important concept, give a very very trivial and obscure example, and give problem sets with very difficult questions. Most of the time, I am relearning concepts from the textbook and only then do certain things click rather than vice-versa. </p>
<p>As a result, I am just barely getting by in computer programming, analysis, and physics by some miracle. As for Linear algebra, I am about a week behind thanks to getting the textbook late for various reasons and I am so far behind in chem that I have considered dropping it. Meanwhile, most of my classmates seemed to be so carefree and haven't even realized there are assigned problem sets in my analysis and linear algebra classes, as they are only recommended and not marked. Many have not even started on any readings. For some reason, I think quite a few of them will do well in the class. Any tips on surviving this madness? Would love to hear especially from science students (physics and math students' advice would be appreciated even more). Just writing this feels like I wasted precious time that could have been spent catching up on linear algebra and chem.</p>
<p>The problem is that you are trying to cram too many honor + hard-version courses even if it’s the regular version, I’d say that one heavy load.</p>
<p>I’d suggest you view the webcast of MIT/Berkeley for General Chem if you are behind, it actually helped me last semester when I was behind in physics. For linear algebra (I’m taking it right now), “Schaumn Outline of LA” is quite useful, and I even use it more often than my textbook. For the programming class, since you said it’s doable and fun, I’d suggest doing its homework and assignment on the weekend, leaving weekdays for the 4 hardcore science classes</p>
<p>In most of my math, physics and computer science classes I can get away with not doing the assigned reading. (Almost no one does them, really.) Think of your science textbooks more like a reference and less like a novel that needs to be read from cover to cover.</p>
<p>However, I absolutely need to work through problems to digest the material. Otherwise I will trick myself into believing that I understand much more than I really do.</p>
<p>The Intro to Chemistry series by Jonathan Bergmann & Aaron Sams was recommended to me by my Chem prof, he was right the series really breaks down topics that I should have already known and helped me with learn new chem concepts. Many time students in the sciences have forgotten core concepts that profs expect them to know, or their prereqs did not mesh well with the profs teaching strategy. These videos give you a level playing field and though they are a little goofy and some are unnecessarily tedious, they are free on Youtube and have helped many people pass General Chemistry.</p>
<p>Thanks for the helpful comments, everyone. </p>
<p>I just wanted to know if it would be a good idea to do the MITopencourseware for Linear algebra I and then try to work through my problem sets and keeping up with readings of my text every now and then? Would that be a good idea or is it rather a recipe for disaster? Unfortunately, I don’t have a full tenured professor teaching me linear algebra like I do with my analysis class (just a TA). </p>
<p>Bad idea or good idea? I would love to experiment, but I can’t afford to at this point so it is either a hit or miss.</p>
<p>Problems assigned from the textbook I copy from the instructor’s solutions. Homework’s are usually only 5-10% of an overall grade, so if I can’t find the solutions or have to cherry pick easy problems to actually do, then the point loss is negligible.</p>
<p>Readings I procrastinate until a few days before the test.</p>
<p>Lectures I generally pay vague attention in. You can learn everything from the textbook for most classes anyways and chances are you’re going to read the textbook to study, so cut out the middleman and study straight from the textbook.</p>
Is your linear algebra course taught rigorously or primarily computational? If it’s computational, the MIT OpenCourseWare is a great resource!!! Proceed with caution if your course is taught rigorously: watching someone else’s lecture might tempt you to make assumptions on the exam and homework that you didn’t actually prove in class. </p>
<p>
I admire anyone who can learn math from a textbook. I am a graduate student in math now and it still takes me <em>much</em> longer to learn math from a written text than from a presentation.</p>
Problem sets in my math classes aren’t worth a thing, they are just “recommended”. But do you really learn by just copying the instructor’s solutions? I’ve never thought of that.</p>
I’d say it is about half computational and half proofs. The computations are quite straightforward although they can be very tedious, just the proofs that really get me in the class. They are so much more difficult than the proofs my analysis class. </p>
<p>You learn a little bit of the flow. But it’s generally helpful for just knowing what the hell is going on in the class (like what sections/chapters the prof is on). It’s a good idea to study the homework solutions a bit more carefully before the test.</p>
<p>However in my experience professors go out of their way to make exam problems unlike book problems (especially assigned ones), so the value of homework is with a grain of salt.</p>
<p>If your math professor is semi-competent, he will assign proofs for homework that require you to gain some conceptual insight before you can formulate the solution. The real goal of a math assignment is usually not the line-by-line solution (which you could copy from a solution set) but rather the insights you develop to arrive at those solutions. And in my experience, most math professors design their exams in such a way that the exam problems can be solved with the same insights that you gained from your homework problems.</p>
<p>Projectile, it’s interesting that you find real analysis proofs easier than linear algebra proofs. Most elementary real analysis proofs have the property that they are easiest solved through line-by-line reasoning. (You unpack the definitions to find a precise mathematical statement of what you need to prove in epsilon-delta language. Then you might give yourself an epsilon, trace through some algebra to see how it relates to delta, and adjust epsilon to get the delta you need. Yada yada yada.) </p>
<p>Linear algebra requires much more conceptual understanding. It’s excruciatingly difficult to do linear algebra reasoning line by line. It’s often easier to reason on an intuitive level and then translate that intuitive reasoning back into formal mathematics. To do that, you will need to develop a strong conceptual understanding of what the underlying concepts mean and how they interact. </p>
<p>I was in a similar position to you in that my linear algebra course was proof-based and rather poorly taught. While the MIT Linear Algebra lectures are primarily computational, I found them useful to get a better conceptual understanding of what was going on. They won’t teach you how to write a linear algebra proof, but they might present the concepts in a slightly different light which might make it easier for you to reason with them.</p>
<p>And finally, don’t feel too bad if you don’t feel like you are mastering linear algebra on the first try. I didn’t really digest and appreciate it until I started using it in other courses.</p>
Problem sets are helpful, but I don’t think I would learn anything by looking up the answers. This may be helpful for pure computational classes (regular calculus) where proofs are never used, but not at all with proof-y classes according to my prof. Even though it takes hours for me to get through just a few analysis problem sets, I’ve learned so much more than I would by taking a regular calc class and just memorizing algorithms or “tricks” and forgetting them after the final. </p>
<p>Also, my profs doesn’t post the solutions to the problem sets after asking them. They just don’t have the time.</p>
<p>B@rium, thank you for all that. It is quite helpful to hear from a math student that is on the “other side”. I just switched classes today and my new prof (he’s actually the course coordinator) seems much more competent and less robotic than the other math profs. </p>
<p>Definitely agree. With my analysis class, although the proofs are quite intimidating, there does seem to be some sort of systematic approach to effectively proving by applying theorems or looking for a “contradiction”. But with linear algebra, it seems that they can use different proofs and theorems for the same question. </p>
<p>And yes, after only watching 1 lecture of Gilbert Strang on my ipod while commuting, I can say that quite a few concepts instantly clicked. For example, I wasn’t always too sure on the conceptual difference of an infinitely many, unique, or no solution linear system. Because of this, I struggled with non-singular/invertible and singular/non-invertible matrices until I watched that lecture. He really is a competent professor and it would have been great if he taught a more proof-based version (or if it was taught, it was uploaded by MIT). </p>
<p>I sure hope so. Both linear algebra I and II are prerequisites for an introductory to quantum physics class I am planning to take in second year, so I can’t wait to see how linear algebra applies to physics. Which other courses did you find your knowledge of linear algebra useful, if you don’t mind me asking (aside from the obvious multivariable/vector calculus)? As a mathematical physics major, I will need to take topology and differential geometry along with 3 other upper year math courses (most likely set theory, complex analysis, real analysis).</p>
<p>I am glad to hear that things are going better for you now! Take care not to burn out and crash.</p>
<p>Within mathematics, linear algebra is the backbone of anything higher-dimensional and “sufficiently tame”: multivariable calculus, differential geometry, differential topology, functional analysis, even statistics! I also used linear algebra extensively in my computer graphics and machine learning courses. </p>
<p>One word of caution since I see topology on your list: a first course in point-set topology looks like a lot of abstract formalism just for the sake of being abstract. And that’s even true to some extend: point-set topology primarily establishes the language used in the field without without developing the machinery to do anything interesting. If that bothers you, please take a second more advanced topology course and you’ll see what it’s used for. Just please don’t fall into the trap of discounting an entire field on the basis of an intro course!</p>
<p>My new prof is awesome, simply just awesome. He’s quite young relative to the typical age for math professors, but he explains the subject in clarity and is much more approachable. Now, if only he taught analysis. </p>
<p>Thanks for the well wishes, <a href=“mailto:B@rium”>B@rium</a>. I don’t think I’ll burn out (even though all I do is study, sleep, and eat), I love what I am studying and learning. </p>
<p>Interesting. You took computer graphics and machine learning classes? I thought you were a pure math major?</p>
<p>What is your research/specialization in, if you don’t mind me asking? Not too many times do you get to talk to math grad students in an informal setting like CC.</p>
<p>As a maths/physics double major (ish), I find that when I get overwhelmed with everything, I try to take small chunks. By Monday, do problems from lectures 1 and 2 of Lie Groups. On Tuesday, do the first problems for quantum theory. When I break it down to small bits, it seems much more manageable than when I think “Oh god, I have problem sets from Hilbert Spaces, Topology, RQFT, Quantum Theory and Quantum Physics, plus an assignment for Lie Groups! How can I get all of it done?”</p>
<p>If you find you’re spending way too long to master a certain concept/do a certain problem, move on and try something else. I often find that by moving onto other things, I subconsciously think about a problem I was stuck on, and I realise the obvious solution during other work, or when I’m doing something completely unrelated.</p>
<p>The worst thing is to become so stressed out that you don’t do anything at all because you’re panicking about having so much work.</p>
even if it’s the regular version, I’d say that one heavy load.</p>