<p>Even though I am getting really ahead of myself, I'd still like to know what are the prerequisites for Harvard's Math 55. More specifically, how does one get such a background?</p>
<p>I've read on a Math department that background in multivariable calculus and linear algebra is needed, as well as being familiar with proofs. I am only familiar with the last one.</p>
<p>I do not know how similar is this test in terms of "difficulty" (if we ignore the fact that it is single variable calculus), but it is considered to be pretty damn hard - it is aimed to top 5% a level math students and only about half of the students are able to fulfill Cambridge's offer. </p>
<p>Hence, I would like to ask - what would be the way to extend my math knowledge beyond this point? Are such topics still "easy" to learn from textbooks, without any "lecturing" or "tutoring"? Or should I give MIT's OpenCourseware a try?</p>
<p>And yes indeed, I am aware that only about ~10 students a year complete Math 55 and that the vast majority of them are IMO medalists, but I would still like to give it a try - as I consider myself pretty decent in math. </p>
<p>Rising sophomore here. Although I’m not a math major, I did take Math 23a and Math 23b last year and 2 of my dormmates took Math55 so I have a general idea of the things they teach in that class. Or actually, as my friend put it, the curriculum was quite arbitrary, depending on what the course head (Schmid) felt like teaching. Some topics that I remember off the top of my head include Galois theory, p-adic analysis, and algebraic topology (I think this was for Math55a). If you’re a math junkie though you should do well in the class (the curve is ridiculous such that almost everyone gets at least a B), but I know of international students who’ve taken 2-3 years of university maths to struggle 15-20 hours per week on the problem sets.</p>
<p>I’m another rising sophomore, math concentrator. Icedcoffeee is right: the professor will make the course their own, so it’s somewhat meaningless to discuss exactly what will be covered. It’s also somewhat meaningless to talk about “prerequisites” in the sense of any particular material - you could conceivably take the class without knowing any multivariable calculus or linear algebra beforehand. If you’re interested in taking the class, I’d recommend getting as much proof-writing experience as you can; this is much more important than any kind of coursework.</p>
<p>On the other hand, having some sort of linear algebra background can’t hurt, although I’m personally not a fan of Strang’s 18.06 posted above (way too matrix-centric).</p>
<p>Just out of curiosity, are you considering studying math?</p>
<p>Thanks for the replies. Seems like I will give MIT’s OC a shot.</p>
<p>@10522504: Everything you said, is quite obviously, true. I know that the syllabus depends on a professor, but as you have said, having a background in lineal algebra and multivariable calculus can only help. </p>
<p>And yes, I am pretty much decided that I want to study math, maybe with a CS minor. Also considering physics, but I will see about that, too soon to tell :)</p>
<p>@Icedcoffeee: If I may ask, how does being an international student relate to the ability to do Math 55? Apart from having different syllabuses all over the world, I can’t see any difficulties or disadvantages. I am following the UK’s curriculum, which is somehow considered much more rigorous than those of other countries. Further mathematics covers matrices, polar coordinates, first and second order differential equations and that sort of stuff. Nevertheless, isn’t 15-20 hours the usual, or even exceptional time for completion of problem sets?</p>
<p>Again, getting ahead of myself; I would sacrifice a B or even a C in Math 55 for the opportunity to take graduate level math after finishing the class.</p>