<p>The difference between Math 55 and Math 25 is described as follows:</p>
<p>Math 55 is for students who are familiar with writing proofs. Math 25 introduces students to proof-writing.</p>
<p>My impression, looking at the syllabus of each course as much as I can by Web browsing, is that Math 55 moves VERY RAPIDLY into rather abstract topics of topology and abstract algebra. In almost all other universities in the United States, the same topics are first covered in upper division courses strictly for strong math majors. I heard from a Math 25 student of a few years ago about an eastern European student who actually first learned to integrate as integration is taught through the “little Rudin” textbook most years in Math 55, but most Math 55 students have a very solid background in multivariable calculus and linear algebra (the nominal subject matter of the course) and a very rare level of experience in writing mathematical proofs AND a rather abstract turn of mind. Math 25 indeed serves as a good middle ground for well prepared students who still want to learn a lot of new material in their first year at Harvard but perhaps don’t want to be as dedicated to math 24/7 as the Math 55 students often have to be.</p>
<p>Tokenadult, I sent you a PM.</p>
<p>Math 25 is a great class but it’s not really an introduction to proofs,
it uses little Rudin, and assumes a little knowledge of abstract algebra, so it is pretty tough w/o some prior exposure to abstract math via summer programs or college classes. Students with a 5 on BC calc and a “turn the crank” multivariable class usually find Math 25 too tough and drop down to Math 23, which is more of a “first exposure to proofs” sort of class.</p>
<p>Regarding Math 23 and the OP’s original question regarding difficulty of Harvard math courses compared to BC calculus – My daughter is in math 23 having only had BC calculus in high school. She would say math 23 is more difficult than BC calculus in the sense that 23 is a lot more work outside of class, but it is not the mind-stretchingly difficult of math 55 or even 25. Also, one thing she has found in that class is that there are some students even in 23 who have previously had a multivariable class. That difference in preparation obviously makes it harder for those with the weaker backgrounds.</p>
<p>And as an aside, the practice of freshmen repeating some of what they’ve studied before college seems to be a factor in most of her classes. Her beginning foreign language class includes students who’ve had a year or two of prior preparation, and her economics class includes students who’ve studied economics in high school. Again, that difference in preparation makes it more difficult for those who haven’t had the previous exposure to the subject matter, and it may place them lower on the curve from a grading standpoint, at least in this first semester.</p>
<p>“What do you mean? Do you mean the pedagogy was variable, period? Or that it actually worked for some students (who needed teaching and didn’t know the stuff already) but not for you? Or did these bright students not need any pedagogy at all, so their success does not testify to the quality of pedagogy?
I am applying to college to study math, and naturally I am concerned about what the experience is like for math majors…so, seriously, is the most advanced first year math class (math 55) divided into two groups of students who either don’t get anything from the pedagogy because they don’t need it or don’t get anything from the pedagogy and consequently fall behind?”</p>
<p>Twochickens:</p>
<p>Well, the quality of the teaching itself was variable. Some teachers were very skilled at conveying in an intuitive way what the math meant, others weren’t and just went through the symbolic manipulation without fostering a lot of understanding. (Some had impenetrable accents or handwriting, but that’s another story.) An example of the former type of teacher would be Richard Feynman, whom I never had but who was legendary for his ability to make the most abstruse concepts graspable. </p>
<p>I don’t think there’s anybody who “doesn’t need” teaching in Math 55. Maybe the rare genius like Ramanujan, but nobody my year and I knew some pretty clever people.</p>
<p>And as to your last question, bear in mind that I took Math 55 in the 70s. I have no idea who teaches it now (though I see they still use Spivak’s little book on calclus of manifolds). If you do take it, though, I strongly recommend that you get into or form a study group. If I had had the sense to do that, I’m sure I would have gotten a lot more out of it.</p>
<p>Ok, thanks for the reply johnshade</p>
<p>Math 55 article in the Crimson:
<a href=“http://www.thecrimson.com/article.aspx?ref=516216[/url]”>http://www.thecrimson.com/article.aspx?ref=516216</a></p>
<p>Wow! </p>
<p>It’s interesting that the Crimson reported noted the class composition this year: “45 percent Jewish, 18 percent Asian, 100 percent male.”</p>
<p>Last year’s class of 21 (?) had 3-4 women. This year’s class is smaller, I think.</p>
<p>The Crimson article reports that in the 17 academic years since 1990, only 17 women have taken math 55. That works out to an average of exactly one per year.</p>
<p>Academic year 2004-05 may have been the high water mark for the proportion of women enrolled–4 women out of 12 students in the fall term. </p>
<p>Ironically, during the middle of that academic year, President Summers made his now notorious remarks about women.</p>
<p>That was also ironically the year that two out of Harvard’s three highest scorers on the Putnam were women.</p>
<p>Also, I was struck by this quote in the Crimson article:</p>
<p>
</p>
<p>If you are a woman who happens to be taking the class when there are no other women in the class, you might find it offputting if the rest of the study group forms this sort of “fraternity.”</p>
<p>Haha, one of the kids mentioned in that Math 55 article used to stomp our school’s math team singlehandedly. He basically did all the work on team tests and still managed to beat us by significant margins.</p>
<p>my math class starts in the morning. and i hate morning classes</p>
<p>marite - Thanks for the Crimson Article on Math 55. I loved it and sent it to cookieson. His response, “That’s crazy. Leave it to Harvard to alienate the math nerds even more from the student body. Princeton lets math nerds have a social life.” They also have an Honors Linear ALgebra class that the top freshman take, but there are also upper classman in the class. There is also a very high dop out rate, but it’s not nearly as intense or time consuming as Math 55.</p>
<p>I don’t think the pedagogical concern with math 55 is so much nerdyness as balance. Obviously the aim should be to challenge these kids at the top of their ability but they should still have enough time and energy left over to do other “nerdy” things like lit-hum, Physics 16, two or three languages and music. But perhaps I am showing my U Chicago bias too clearly.</p>
<p>How about some information about Math 25 as an alternative to students who just haven’t had the background necessary for Math 55? I’m hoping to take that if I get in. I’ve got a little practice with proof-writing and should gave mv cal, linear algebra, and diff eq under my belt by the time I matriculate next year. Is that just the nominal background (the site says “A previous knowledge of proofs, linear algebra, or multivariable calculus is helpful, but not necessary”)?</p>
<p>The math placement test is not useful in identifying which level of Calculus beyond AP a student should take, but there is a freshman orientation session, staffed by veterans of Math 25 and 55, that is supposed to be very helpful. But it does not prevent 50+ students from trying out Math 55 then dropping down to Math 25. Also, a number of students who took Math 25 do drop down to Math 23. It’s all okay.</p>
<p>Depending on what you mean by “a little practice with proof wiritng” your background is probably at or just below the median for Matgh 25. Like Marite says, the best way to find out which class you like is from placement meetings and going to the first few weeks of class, but in the meantime you can also take a look at this fall’s problem sets at <a href=“my.harvard”>my.harvard;
<p>Pardon my ignorance, but is this Math 55 class a freshman class? (if not, what is it?)</p>
<p>And since I’ve been told that it crams pretty much 4 years of math into… 1 (or 2?) semesters, are you credited with all the math you need? I guess it depends on your major, so my question would be for economics concentration. </p>
<p>Also, how many hours of lecture is this class per week? And are there any TA run study sessions, etc?
(on that note, on average, how many hours of lecture can you expect for any class in college?)</p>
<p>I’m still a HS senior, so I really don’t know much about classes and credits needed in college… I’m just wondering, as this super-hard math class intrigues the coke-bottle glasses geek in me. ^^</p>