<p>etondad, +1</p>
<p>i’m a bit confused, etondad. you said your son had the same choices, but how did he have the same choices? in recent posts of yours, you say that your son applied to yale, but didn’t get in. and you said you went to yale, so you’re familiar with it…</p>
<p>I went to Yale, as did my father and his father and my uncles–I saw my first Game when I was 6 I think, and Blue was everywhere in my house growing up-- so no surprise that my eldest son (the other boy is in grammar school still) applied to Yale, </p>
<p>In the end : He was accepted to three of his four schools: Chi, Harvard and Caltech…he got in everywhere but Yale–which flat out rejected him. However, I knew he applied to Yale for me and his grandfather–not for himself. Aside from my fond memories, I thought that with his strong interest in music composition that with YSM, he would do well there–not because of math–which I knew was weak–</p>
<p>In the end he chose Harvard bc–caltech --although they tried to create a way for him to get composition training (he loved caltech as a community), couldn’t do it–the music at Chi and Harvard was a “push” but math (now one of his two soon to be declared concentrations along with music) was better at Harvard. He also felt “at home” at Harvard.</p>
<p>Now, does the history make sense? </p>
<p>I am glad, in retrospect that he didn’t get into Yale bc he might have gone to keep up the family tradition, but it wouldn’t have been right–and the admissions committee probably saw that the fit wasn’t right either.</p>
<p>Math at Yale when I was there was horrible–Lang’s textbook is all I need mention to anyone who had to endure it or him–and other than Mandelbrot no longer in the department no mathematician of note–a number of my colleagues are professional mathematicians and it occasionally comes up as to why Yale just can’t put together a good math department, after all, almost all the rest of the College’s departments are at or near the top of their fields–but not math. </p>
<p>Yale’s team hasn’t placed highly in decades of the Putman (Williams College was markedly better this year) and the department’s grad students don’t fair particularly well in job placement. However, applied fields such as Finance at SOM are top flight-- but finance is NOT pure math.</p>
<p>Etondad,</p>
<p>I haven’t used any advanced textbook by Lang but I have skimmed through his text “Basic Mathematics” and I found his style of writing quite informal but didn’t notice anything that might be as off putting as you (and another post in the first page, I believe) seem to describe. What is so wrong with it?</p>
<p>How did things work out for you after Yale? Are you still doing math-related work?</p>
<p>Did your son study (proof-based) calculus of single and multiple variables before starting Math 55? If yes, was it independent study or did he take the course at another college while in high school? I just wanted to know some more about the background of students enrolling in the class.</p>
<p>My son took math 55 recently. Beyond calculus, he took a course in multivariable calculus, a course in differential equations, and a year-long analysis course at a local university (using Marsden, not Rudin). He self-studied some linear algebra over the summer before Harvard.</p>
<p>He chose between MIT and Harvard. He felt that in class, the MIT students were just going through the motions, while the Harvard students were actively involved. He also got into CalTech, but his interests are broader than math and science so Harvard was a much better opportunity.</p>
<p>He did multivariable in school as well as linear algebra. He was in BMO track and so has done proofs since what would have been the equivalent of 8th grade. He self studied abstract algebra and some analysis before he came to campus. </p>
<p>The course as one writer put it–is like drinking from a fire-hose. It isn’t that the concepts are hugely different than other courses in those field (although, according to S 2 out of the last 3 Psets had a problem on it that stumped the entire class–even collaborating) it is just they move at break-neck speed. I wonder if someone tried to take the class without strong preparation if they would stick it out-- not because of candle-power, but because there is no time to waste–not a moment.</p>
<p>It is down to the last few weeks of the year and the class, I can tell from him and his friends, is burning out and limping to the finish line. Siu is an analyst and so the rigour this semester has been amp’ed up from first semester and they are all exhausted. When I asked him how he is doing he says that right now he is in sleep depravation mode and in pain, but once the course is over he will be sad, because no other course–even if the material is far more challenging–will ever push him to his limits like this course has.</p>
<p>So the two things before trying 55-- preparation–esp in proof work, and lots of “wanna” bc it does become obsessional. It is interesting that a number of his friends are going to stay in math, but are taking about allied work–finance, applied math, physics.</p>
<p>As for me-- I wear a number of hats, I am an academic MD now in psychoanalysis, but I also have done and do some finance work (using some quant modeling for options work). But I haven’t published in this area-- however, a number of the people with whom I collaborate, have. I advise at one of the Houses, and a number of colleagues there are in the math department. </p>
<p>You are the first person to have said/written nice things about Lang’s book. But I have to admit it has been decades since I used that book. I shudder in remembrance.</p>
<p>Imntwo - woah, great preparation there. As for MIT - I have to say I’m a little surprised by that. Did he sit in the “honours/with theory” variant of a course that was post-differential equations? (less likely to have non-math majors in them)</p>
<p>BMO? I take it your son went to Eton as well and his study of multivariable calc was from A2 Further Maths? All I have right now is A-Level Maths, which goes a little further than the UK boards, meaning I might have covered a little more in statistics, mechanics than is usually found in S1/M1 and perhaps a chapter or two from FP1. Nothing fancy. I considered taking Further Maths on my own but decided against it, thinking it would frustrate me to no end to take yet another “mathematical methods” like course. How did your son bare with that, as someone who is interested in university mathematics?
I also suck at Olympiad math, so my plan is to get myself used to proofs and buy Spivak’s book (Calculus - not the manifolds one, of course!) for me to start this coming summer.</p>
<p>Sounds like a cracking course. </p>
<p>If you don’t mind me asking, how did your son get interested in math? My dad used to teach high school math but he never tried to influence me to even like it. Me getting into math/applied math was something that happened on its own and I went from the guy who “did the bare minimum” to being whatever is I am right now. I don’t think “passionate” is the best term, seeing as I wouldn’t cry or feel pain if I somehow wasn’t able to do or learn some new math. I do have strong feelings for the subject but they’re not to that extreme. Heck, I think I actually prefer the applied side of things more…</p>
<p>Do note that I haven’t actually used the book and only skimmed through it. Maybe his style can be a nuisance when one is trying to learn more advanced topics.</p>
<p>There were only so many courses taught at times when he could take them. It was more than honors calculus - some students took it to fulfill an analysis requirement. Multivariable and DiffEQ were taught in his school.</p>
<p>He was taking grade-level math until 7th grade, and I supplemented. But halfway through eighth grade he really accelerated.</p>
<p>Sombre: Yes, he did Further Maths. Eton also had a Math Society in which they worked on advanced topics and had invited speakers --mostly from Trinity Cambridge. He found the A2 a papers to be a big help, but without the work in proofs from the BMO and UKMT he would have been lost (Further Maths, is not a proof based curriculum). Also the abstract algebra, topology and analysis he needed, he had to self teach.</p>
<p>If you could do Spivak’s manifolds book you could skip 55 altogether!!!</p>
<p>I have no idea how he became interested in maths, he always was–from a toddler, he found the whole idea of zero to be the most fascinating concept–he would tell anyone unfortunate enough to visit all about the “something which is nothing.” It most certainly did NOT come from his parents. He was fortunate that at Eton he had several beaks (most esp, Simon Dean–a/k/a “Deano”) who were not satisfied in teaching the top set the curriculum (in fact my S told me that each “half” Dean would point to the corner of the room and tell the boys that the textbooks and worksheets were there for the term, and as far as he was concerned he had done his duty in “handing them out” and they would spend the rest of term working on whatever he and they wanted–The class would return to the neglected books for the last week or so, just to make certain that there wasn’t any concepts with which some boy had issues.)</p>
<p>^
If one is interested enough, has good guidance and even average intelligence (not going to argue over what intelligence is but just assume a moderately intelligent person, nothing exceptional), one can get on with their work very quickly. Algebra I, II, Trigonometry, Geometry and Pre-Calculus don’t need four years to be completed. Sure, there should be some time to let the material sink in but if one can pick them up fast enough, there’s no need to linger on. One will be using algebra and trig almost everywhere. :-)</p>
<p>I find it fascinating that they have courses up until differential equations in his high school. By what kind of teachers are these taught? (do they have master’s degrees in math/science/engineering?)
We do cover differential equations in the A-Level but it’s at a rather rudimentary, as opposed to college level. No proofs.</p>
<p>^ MAs, PhDs and DPhils in pure maths (I think one has her degree in statistics…). </p>
<p>This liberty with the curriculum is for the top set-- there are I believe eight different Divs per year–the rest basically cover the set out curriculum–what Deano does isn’t looked on upon with official favor but the boys do well in the papers so he is allowed to teach that way.</p>
<p>Also there are the Oxbridge classes for those who might want to prepare for interviews–basically proofs.</p>
<p>If I ever get kids who somehow find themselves interested in science, I’m definitely gonna have them apply to a school like Eton (sure there’s others)…that is of course, if I don’t make my own school. That’s one of the reasons I’m applying to the States.</p>
<p>I really like the way they do things. I was looking at their weekly time table a few months back and the fact that they took time out for sports*, some of which originated from the school itself, and that things were so well structured seemed pretty great. I’m not one for longer lessons, as I do the bulk of my work individually, but that aside, it all looks great. </p>
<p><em>A-Level schools tend to just be grade-focused. The better schools on % of A</em>s/As achieved and the rest, with pass rate.</p>
<p>So true. Algebra through precalc took six months. Calculus took longer - about nine months, but we were very thorough.</p>
<p>His high school was a large magnet school, and there were more than 50 students each year who were ready for multi and diffeq. I’m not sure what the education of the teachers was, but they taught a rigorous, university-honors-level class. I think one teacher was a PhD, and the other left teaching to go back for his PhD.</p>
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<p>I totally agree with you guys. And it’s really annoying when people get all prudish about letting kids getting advanced at math, as if it should take 6 years to learn how to add, subtract, multiply, and divide. </p>
<p>For people that can do math, it doesn’t make any sense to take that long to learn those skills and then cram number theory, group theory, analysis, topology, linear algebra, differential equations, etc. in 4 years in college.</p>
<p>It is much easier to learn stuff at a more even pace.</p>
<p>CalTech is a great place for math & sciences obviously and it’s hard to turn it down. This is one of the difficult choices our son had to make among others, and he is at Yale. Yale is attracting some really strong Math/Science kids lately, and your son will be able to find challenging Math courses and excellent peers at Yale. </p>
<p>Too much is made out of grad school rankings, IMHO. When he is comparing schools this good, he should safely toss rankings in the nearest trash bin and pick one he feels like would be the best overall environment for him for the next 4 years! Congrats and best wishes.</p>
<p>Imntwo: That sounds great. How was your son introduced to proofs in mathematics? Was he doing Olympiad mathematics as well? My mathematics background is good enough to get me through A-Level maths but I definitely don’t have the preparation to succeed at Olympiad exercises. I don’t particularly enjoy competition/recreation mathematics either, so I suppose it’s not much of a problem. Having said that, I haven’t really tried hard. Anyway, I would just be interested in knowing how he prepared for the “honours level college courses”. </p>
<p>Collegealum314: One should take it into account that “mathematical maturity”/“mathematical thinking” is a skill that takes a while to develop and while I agree that coursework in college looks like it goes too quickly, it certainly is less overwhelming than working at that same pace would be when one has just started learning mathematics! I’ve seen discussions where people said that even in graduate school, classes were done at too quick a pace and while achieving A-grades was/is indeed possible, there is not much time to let the material sink in and gain a deeper understanding of it. </p>
<p>I do understand your where you’re coming from though, seeing as I spent many years bored in my classes and resorted to other things to occupy my mind, like writing and girls. Sometimes, writing about girls but that was when I was younger. (haha)</p>
<p>Parent2015: This is quite old a thread and it is likely that the OP’s child is already attending college.</p>
<p>A combination of learning proofs the whole way through calculs, plus working olympiad problems and reading the solutions, plus the high school multi and diffeq courses that didn’t skimp on proofs, plus artofproblemsolving.com’s WOOT course. But basically, I inculcated his belief that if you couldn’t prove it, you didn’t know it.</p>
<p>Parent2015, it would be terrific if Yale was able to get its math program up to the rest of its offerings. It hasn’t for a while had much problem in the “wet” sciences, but it has had trouble in the “dry”–physics and math-- if this could be balanced out that would be great for Eli.</p>
<p>@etondad: My message is about Math, Phys, & hard sciences. I have a feeling that the classes for majors in these areas are actually quite good, and the shortcomings, if any, maybe in the more intro classes for non-majors or those entering Yale with less math & science prep. I truly believe Yale is a fine choice for undergraduate education in these majors. OP will find both challenging courses and excellent peers.</p>