<p>I am a rising senior who is interested in math. I have a 4.0 in math and science at my school, but it really is not challenging and am going to end up only having learned BC Calc, though we will learn infinite series and stokes theorem. I am on the fastest math track at my school, but it doesnt move as quickly as i can learn.</p>
<p>I have done really well on math contests and get combined scores of 200-220 on the AMC+AIME (qualified for the USAMO once) and generally impress people with my creativity to compensate with my lack of knowledge of more advanced math.
btw, my SAT/ACT scores are 2380/35 and my SAT II scores are 800,800,800 and will not be applying for financial assistance.</p>
<p>Because I am starting with a relatively low point in the amount of math I know, I am looking for schools where I can learn at a faster pace than normal, even though I do not know that much math. I know that the professors at williams have won an astonishing number of teaching awards and it is considered to be the best LAC math program. But i was checking the site and it looks like everyone is lumped in together (as in that whether you get a 3 on BC calc or a 5 you are in math 106). Normally I wouldn't even look at a LAC for math, but I thought that if there was one place that might help students move closer to their real learning pace, it would be Williams with the obviously great math professors, tutorials, and undergrad focus. Does anyone know of someone doing something like this? It is my eventual goal to get a phd in math.</p>
<p>I don't know much about the math courses, but I can think of why everyone is lumped together in Math 106. I know quite a few non-math majors that are taking 106, but the school is small, so there isn't a major-specific class. Beyond 106, I don't see that many non-majors taking upper-level courses.</p>
<p>Williams doesn't offer anything like Harvard's Math 55, if that's what you're asking about. There's no concept of an "honors" or "accelerated" class at Williams, although professors are always willing to work with you if you find a class insufficiently challenging. Also, to encourage a broad education, Williams won't let you take more than two courses with the same prefix during your freshman year, which essentially limits you to two or three math classes (some math classes are cross-listed as physics or compsci, but those are probably not the classes you'd want to be taking). It's not a great place if you want to do math to the utter exclusion of everything else, although you can definitely do a whole lot of math over four years at Williams.</p>
<p>If you really want to leap ahead in math at Williams, or any other school, I would suggest trying to get Calc III and Linear Algebra out of the way ahead of time. Obviously your high school won't offer them, but it's worth trying to take those classes at a local university during your senior year, since otherwise you'll be taking them freshman year at Williams. If you have those prerequisites, you'd be able to jump straight into 300-level math (real analysis and abstract algebra) when you get to Williams, and then you can spend the next three years taking whatever high-level electives you like. It's definitely not necessary to have those classes as background before doing math at Williams - most kids don't - but if you're worried about the pace of your math education it might be something you'd want to look into.</p>
<p>I know this was thirty years ago, but does anyone know how the williams math dept was in the late 70s compared to now (accounting for the improvement in everyone else too)? I only ask because i was looking at field medalists and saw that curtis mcmullen went williams undergrad and harvard grad.</p>
<p>I only saw the grad results for the class of 2008, but which schools do the most williams math majors go for phd studies?</p>
<p>Also, i think that jeke's idea is great and if i wanted to teach myself multivariable calc and/or linear algebra, does anyone have any recommended textbooks that are good for do it yourself?</p>
<p>he's not suggesting you teach yourself. he's suggesting that you take calc3 or linear algebra at a local university or community college.
for whatever it's worth, i took calculus I and II as community college classes in my senior year and i'm taking math 251 Discrete Math in my first semester.
Knowing what I know about LAC's, if you really wanna focus on math without much regard to anything else, Williams isn't the place for you. They always emphasize educational well-roundedness and will more likely than not limit you from exclusively studying math (as jeke mentioned).
And you could always email people in the Math dept. and ask any questions; that's what I did when I was applying and it helped quite a bit.</p>
<p>For multivariable calc - I think the book used here is Edwards and Penney. You can always go to the Water Street Books website to see which books are in use for the class. Linear Algebra has been Leon (7e) for a while, though I don't know if that's changing next year. Great book though.</p>
<p>Working your way through mutivariable calc (during a summer or with some supervision) can be done with enough motivation. If at least you can start with linear algebra in your first semester, then the doors are open to all the rest of the math available (you should immediately take Real Analysis in your spring semester as that is a pre-req for most upper levs). You can also take Discrete Math first semester without even taking 106.</p>
<p>In spite of the divisional requirements, it's possible to take a great deal of math here. You can spend your entire junior and senior years doing only math if you get your requirements out of the way early - (first and sophomore years).</p>
<p>For Linear Algebra, I highly reccomend "Elementary Linear Algebra" by Anton (you can find it on Amazon). I used this textbook last year as a senior in a class offered by my HS and found it very helpful and well written (since the teacher was not the best at explaining things). I think you could very successfully teach yourself alot of linear algebra with this book with or without instruction. Good luck.</p>