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My 2 cents: The author presumably goes to Princeton - the ivy league is in general a tough place to "start learning" things, especially STEM. Few of the staff w

My 2 cents: The author presumably goes to Princeton - the ivy league is in general a tough place to "start learning" things, especially STEM. Few of the staff would teach you the basics of anything, mostly because you are attending a research college, where teaching is the professors' side gig. I went to an ivy league school, and a large portion of the people in the CS program did competitive programming/knew number theory and discrete math from high school etc. All the problems we got as homework were really intense - I'd consistently do more than 60-70 hours of studying outside of classes to keep up. Mind you, for me CS was/is like crack - I feel like I'd have put in even more time if I didn't need to sleep or want to hang out with my friends. There are some intro classes, of course, but the quality of those varies a lot. Edit: I don't mean to discourage people with this post. I was actually one of the few people who didn't have much of a CS/quanty background in my CS classes. My advisor told me to have a backup major in case I fail the tougher required classes, but I made it through.

Waterluvian 5y ago
I went to the University of Waterloo and took a "Intro to CS for non-math students" course. The thing was designed and taught by CS faculty, so naturally they taught you the basics of programming using math. I spent more time re-learning high school math than actually learning programming. And not because it was directly related, but because some lessons were like, "write a function in Java that factors a quadratic." So 90% of that tutorial was me re-learning what the heck a quadratic is and how to factor it. The experience really sucked and I gave up on university programming courses and just started learning it all practically and on my own terms. Edit: Enjoy this wonderfully styled course page: https://student.cs.uwaterloo.ca/~cs125/S08/Resources/Admin/CourseOutline.shtml https://student.cs.uwaterloo.ca/~cs125/S08/Resources/Admin/C...
- artificial 5y ago
  I like learning files and sockets once the syntax is a familiar and then branching out to error handling followed by more advanced topics and then circling back around to testing. Project based learning resonates best with me, hands on cements knowledge rather than pure theory.
- kamaal 5y ago
  The real question is in asking, what are you going to use the programming language to build? If you are going into a Math heavy domain, you are going to use a programming language to solve math problems, and hence involves learning Math. This the same problem, with whiteboard leetcode style problems in interviews. Most people fail to understand why they have to put in months to years of practice into a domain to which doesn't concern with their everyday work. On the other hand there is tremendous shortage of people with skills for real world problems and applications.
  - Waterluvian 5y ago
    Yeah. I've been writing code as a job for a decade now and have never needed to factor a quadratic equation. I really just needed a course that helped me get introduced to programming (which I ended up using a LOT in the domain I went to school for: geography and remote sensing). (Every time I write something like this I immediately feel defensive about being an impostor. Someone saying, "how can you not know that? You should know that. You must not be doing _real programming_.)
    - mlyle 5y ago
      > Yeah. I've been writing code as a job for a decade now and have never needed to factor a quadratic equation. A lot of people never touch algebra again. Some of us end up touching it a lot. This is a bit of a tricky thing, in that: - A whole lot of practitioners have very limited continuous math and deep CS needs, so some of these requirements are artificial barriers to some extent for many jobs. - But is it reasonable to give them CS degrees without at least basic competence? - Plus, part of the point of a university education is to round-out students and expose them to many things...
      - Waterluvian 5y ago
        To be clear, this course was exclusively "CS for NON CS/math majors." If you were in CS, you were not allowed to take it. They also offer a lot of "math for non mathies" courses, which would have been a great place to teach quadratics.
- criddell 5y ago
  I think you also need to consider just what is meant by “computer science”. Is it programming? My daughter is studying comp. sci. right now and there seems to be a ridiculous amount of math and math proofs and very little programming in her program (she’s still in her first year). The spend a considerable amount of time proving stuff using big-O (and theta and omicron etc…) and surprisingly little time applying those ideas. I think what you wanted (and what should be offered to everybody) is a course designed to teach programming and programming concepts.
  - weaksauce 5y ago
    computer science is not programming though it often involves doing that. it's a math degree with many different topics all related to computing and math. So yeah if they wanted to learn how to program java that's a completely different track. they generally don't teach you much programming or other practical things at a university track. you need to know it but it's ancillary to the degree.
    - l33t2328 5y ago
      A computer science degree isn’t a math degree any more than a physics or chemistry degree is a math degree. Classes like Computer Organization, Operating Systems, Networking, Databases, Software Engineering Fundamentals, the first year programming sequence, etc. could hardly be considered math courses.
      - deleted 5y ago
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      - thorajeu83 5y ago
      - weaksauce 5y ago
        > Classes like Computer Organization, Operating Systems, Networking, Databases, Software Engineering Fundamentals, the first year programming sequence, etc. could hardly be considered math courses. so a math degree has to have every single course be a math course? do they not take literature? Networking had me prove the theoretical limit of networks using calculus and other things, databases had us using relational algebra and other proofs... it certainly wasn't `select * from users;` kinda course. it's a math degree at least at my university and most reputable ones it is. are all classes 100% pure math? no of course not but the emphasis is math.
- strangemonad 5y ago
  Long story short, if you want to do something off the beaten path, you need to get to know some of the faculty. I also went to Waterloo but as a cs undergrad. I was also a student rep on the undergrad curriculum committee (this was all some years ago). You’ll notice that all the non Math / CS major classes are completely different offerings. Non math majors can only take those “other” cs classes and likewise math majors can’t take them and must take the classes intended for CS students. Unless things have changed, very few faculty tech these non cs major CS classes (mostly sectional lecturers). My overall impression (at the time) was that these classes weren’t that great. They mostly taught you to program (in Java) but exercises were grounded heavily in math problems but didn’t really teach math. If you really want to get a good sense of “computer science” (the discipline) rather than just learn to program, I’d try and get to know the profs that teach 135 and see if you can get a specific override exception. You could possibly do the same for 136. Going deeper down the cs course tree is a bit harder. Part of the challenge is the depth and pacing you want to offer majors doesn’t always align with the broader overview non majors are looking for. Eg you might want a single course covering algorithms and data structures rather than 3-4 courses and you might not care about the math involved to prove amortized costs. If you want to go beyond 135/136 there are a few possible paths that come to mind and involve finding cross appointed faculty and seeing if they might sponsor you for an override into their class offering. If you’re in psych, the cog Sci route would get you to know people who are cross appointed with AI folks, arts used to have cross appointed faculty with the computer graphics lab (Craig Kaplan is a friendly face in the CGL). Physics obviously has overlap with the quantum computing lab. I don’t know any of current the undergrad ce advisors but J.P. Pretti might be able to point you in the right direction
  - mcguire 5y ago
    Roughly the same was true at UT Austin when I was there. They introduced CS-for-non-majors classes, but I don't know anyone who would have touched them with a 10-foot pole.
- fredophile 5y ago
  I can't say I'm too surprised. Waterloo is unusual in that they offer a Bachelors in Math in addition to the more standard B.Sc. and B.A degrees. Computer Science majors there graduate with a B.Math.
  - alibero 5y ago
    Waterloo also offers a BCS which has fewer math requirements than the BMath: https://cs.uwaterloo.ca/current-undergraduate-students/majors#BCSvsBMathCS https://cs.uwaterloo.ca/current-undergraduate-students/major... The BMath option is only required if you want to have a double major in CS and a different area of math. Otherwise the BCS is strictly more flexible: you have 5 fewer math courses and 5 more electives (which you may use to take math courses if you really want to). From my experience most people are graduating with BCS unless they really like math.
    - fredophile 5y ago
      Interesting. At the time I was picking universities that wasn't an option they offered.
- ww520 5y ago
  That’s what programming is. Programming is applying computerized solutions to different problem domains. To make a successful problem, you have to learn about the targeted domain and sometimes become an expert in it. In this case the problem domain is quadratic factoring.
  - colinmhayes 5y ago
    This isn't helpful for say econ majors who want to build econometric models though. The class sounds like it is specifically for non cs majors so it doesn't really make sense to get into theory that might not apply to their studies.
    - ww520 5y ago
      Right. Sometimes we are forced to go outside of our comfort zone. A software engineer might not care much about insurance actuary, bank money transfer, railroad signal rules, or econ supply/demand curves. But when the job calls for creating programs to do those areas, he better learns those fast, on the fly. That class taught an important reality of software development. You have to be willing to learn something you're not familiar to get the job done, and how well you understand the problem domain directly affects how well the program is developed. So the class was not tailored for the econ major, but at the college level, students need to learn that no one is going to hand a solution on a silver platter for your problem.
- alasr 5y ago
  IMHO CS, software engineering and computer programming are very different but closely related fields. Each field focus and work on different (but complementary) set of activities in order to efficiently solve a computation-based automation problems. Based on the scale and complexity level of software artifacts, you'll see an individual, a small team or very large team are working on a given challenge/problem[1]. CS is, with mathematics as its foundation, focused more on the abstract and computational aspects[2] of a computational problems/challenges. As expected, CS solutions are usually very generic and independent of any specific programming language, it presents its solution in abstract forms and along with some code (written in some programming language). From CS's point of view, the coding part of its solution is primarily[3] for demonstrating that the solution of a specified problem is computable and efficient (for some practical purpose) and can be verified independently if needed. Now, computer programming languages are just one of the tools which helps us write those codes to "communicate" our solutions to computers and fellow programmers (who, as part of the team, need to understand in order to help developing and maintaining the software program). And, there're other alternative programming languages available which practically does the same job (though some of them are more appropriate and suitable than others, due to reasons/concerns outside the scope of a particular programming language[4]). Having said all the above, I think I understand the core of the problem(s) you (and students in similar position as you) described here, in your post. I think I've faced similar challenges while trying to understand some non-CS course (for example, accounting and finance). Being new to any field of STEM/business/..., it's easy to get pulled into non-important areas of studies instead of focusing on the core ideas/concepts of the course. And I believe it's always course instructor primary responsibility making sure that core concepts/ideas are made very clear at the course and individual lectures level and, similarly, corresponding supporting concepts/activities which make up the course and its core concepts. NOTE: I've few more thoughts on the subject; however, I think, my current post is already getting too long so I stop this post, at this point. --- [1] - Btw, as you may already know, team size alone doesn't indicate that they're working on a easy or difficult problem. Sometimes it's just a consequence of some financing/time constraints or inefficient team management. [2] - For example; data model, data structure and algorithm. [3] - Other benefits are secondary and can be considered as bonus. [3] - Reasons/concerns related to either CS or software engineering.
- ska 5y ago
  A couple of things worth considering 1) CS::software development is a bit like physics::mechanical engineering 2) CS at waterloo definitely skews to the cs-is-part-of-applied-math thinking in many ways. Other university CS programs are very different. I'm not saying a "practical programming for non math/cs types" course isn't a good idea, just that really isn't what you signed up for.
- inetsee 5y ago
  "Enjoy this wonderfully styled course page" I have the Tranquility! extension on my browser, which turns that web page into something quite readable. The web page as it is is the complete opposite of something readable. https://addons.mozilla.org/en-US/firefox/addon/tranquility-1/ https://addons.mozilla.org/en-US/firefox/addon/tranquility-1...
- 908B64B197 5y ago
  > The thing was designed and taught by CS faculty, so naturally they taught you the basics of programming using math. I would have honestly made the same assumption that students interested in programming would have no problem with high school level math. Maybe an intro course aimed toward the business school wouldn’t be as math-heavy? 6.001 was notorious for starting out with examples from calculous and required some proof reading. But it wasn’t aimed at anyone. It’s tougher to enroll in 6.001 than most other intro courses.
ianai 5y ago
True, but linear algebra being the crux of so many disciplines the linear algebra course should be especially emphasized and clear. It's not the place to throw random hurdles. It's the place to get this information into the students' brains 100% so they can leverage that knowledge correctly later. More of a foundational course in that sense. Like if you were pushing out liberal arts majors without any grammar courses. Edit- Now, the course says it's for students considering a major in STEM. I wonder if the business side of the college means to say: "Students who got into Princeton ostensibly to study some area outside of STEM but who are now thinking of going into STEM. They may take this course then add to our STEM student roster by switching majors and we don't want that for business reasons. So here's a course that will push back all but the students who have a good case to be in STEM."
- ghaff 5y ago
  >Like if you were pushing out liberal arts majors without any grammar courses. I would expect very few liberal arts majors (who aren't majoring in linguistics) would take a grammar course. Linear algebra is actually sort of interesting. Before computers were commonplace I'm not sure how widely taught linear algebra was. I certainly never took it but was admittedly not a CS/EE major. I do remember a robotics course I took in grad school that involved doing these ugly matrix operations by hand. (No Matlab.)
nojito 5y ago
This is true but the class the author was taking was not required for Math majors.
mlyle 5y ago
> My 2 cents: The author presumably goes to Princeton - the ivy league is in general a tough place to "start learning" things, especially STEM. Few of the staff would teach you the basics of anything, mostly because you are attending a research college, where teaching is the professors' side gig. Still, it seems there's bits of departmental strategy that are a bit kooky. Why provide practice problems (not for credit, it seems), and then never share solutions? What is the point in the student practicing without feedback about correctness? Wrong practice is just as likely as right practice.
- nicoburns 5y ago
  In my experience this attitude is extremely widespread amongst university departments. I think it's a simple combination of elitism and poor training in pedagogy (unlike school teachers, university lecturers typically undergo no mandatory training in teaching).
  - busterarm 5y ago
    When the author described this specific math class as a required math class for Engineering majors and not math majors, I spotted it for exactly what it is: a weedout course. It's intentional.
    - speed_spread 5y ago
      Aka Institutional Gatekeeping.
- bertr4nd 5y ago
  Possibly the concern with sharing answers is that students could memorize the form of likely exam questions without deeply understanding the material? But that risk exists simply by sharing the questions so I’m not sure I find that argument persuasive. I’ve always been rather disappointed by the lack of solutions in math books. I mean, on the one hand, it’s a great feeling to crack a difficult problem unaided, and there’s something to be said for building the intellectual discipline one needs to attack a problem with no easy answer. But also, there are some problems that I never manage to solve because I “time out,” and it’s possible that as a result I’ve missed the opportunity to learn techniques that will be useful in the future.
lordleft 5y ago
I also went to an ivy and echo this comment. The math classes were geared towards people who had considerable expertise / interest in mathematics to begin with, which didn't help someone like me who didn't have that expertise. While I think that academic settings that cater to advanced students are worth cultivating, I don't think intro or require math sequences are the places to do that.
- hnmullany 5y ago
  Also went to an ivy and found the "math for non-majors" to be pretty well taught & very manageable - although I did have pretty solid high school math. I did not have the same experience with my first physics for majors course - which was taught by a guy who talked into the blackboard and spent the entire class writing on the board in a fugue. Made me switch majors.
- brimble 5y ago
  I'm torn because on the one hand I don't know how someone who hadn't already been programming for years, or at least been a big computer nerd and tinkerer, could have gotten through even the relatively weak CS program that I did. I gather math is similar. On the other hand, I don't think anyone expects to start learning, say, music, in college, and major in it, having had nothing but maybe a couple required and non-rigorous music classes all of k-12, and not being able to do much more than squeak out "Mary Had a Little Lamb" on a clarinet. Their first class will be them in a room of 19 others who have all been playing at least one instrument since they were 5, played in jazz band in high school and picked up tons of music theory, had extracurricular instructors and tutors for years, et c. Of course that's not going to go well. Maybe colleges should just be more up-front about that, with other majors. OTOH I don't think social science classes do this. They seem to assume no more than that you weren't asleep during your high school social science classes. They do expect you to come in writing at at least a 12th grade level, which is sometimes... optimistic. But not much else.
  - ghaff 5y ago
    CS/programming (yes, I know they're not the same thing) is something of an odd beast at many top schools. I took MIT's intro MOOC a while back. And the idea that I could pass that, alongside other coursework, never having done any real programming boggles the mind. Yet, no other engineering major has that degree of informal prerequisite. And, yes, it's pretty much like the arts. (As a side note, I did take an Intro to Music class in college. Of course, I discover it's taught by a rather well-known choral director so the class is filled with people who were quite practiced in music and said choral was happy to teach to that level. I actually got something out of it but a lot was also over my head.) (As another side note, way back when I took intro to programming--or whatever it was called--for non-CS majors. This was back before PCs were widespread and I'm sure anyone here would find it ludicrously elementary for even an intro course at a good university.)
mannykannot 5y ago
I agree that one should expect challenging classes at Princeton, but it seems quite a few students struggled with this course, and I would guess the majority of those were STEM-oriented. On the other hand, you cannot conclude from one case that math teaching is broken.
tandymodel100 5y ago
spicymaki 5y ago
Here is my take: This class seems to be a filter class. A class designed to sift out students that would not cut it in a engineering/science curriculum. They are not designed for students to learn, they are designed as a barrier. That in itself is fine if it happens early enough so students can regroup and reevaluate what to do next with their lives. What I don't like about this is that there is a mismatch between what colleges are saying they want to do and what they are actually doing. They should actually state that in the name and description of the course. I wish schools would be transparent so they don't waste the money and time of the students. This won't happen of course, we will just continue the kabuki dance.
- xxpor 5y ago
  Yes exactly. I didn't go to an Ivy League, but it was still pretty good. The 100 level big classes were waaaaay harder than classes for the actual major. Lots of dumb problem sets that were huge just to be huge. Lots of time writing lab reports with error calculations etc. The one hack I figured out was that if you didn't include an error calculation in your lab report, they only took off 1 point. Given it took 20+ minutes to write it up in the format they wanted using the Word equation editor (this was before I knew Latex), the -1 was absolutely worth it. I never, ever, had to spend 60-70 hours a week outside of class doing work though. That's insane.
- pevey 5y ago
  That is often given as an excuse for this common experience, but it is not really intended. Top schools are assessed on their graduation rates. It is part of the rankings they are obsessed with. It serves no one--students or schools--for students to be weeded out in these intro courses. The truth is just that even top schools in the US (and I suspect, ESPECIALLY top schools, more so than middle-tier schools) are really, really bad at teaching STEM, even to students very interested in learning. I still have clear memories 20 years later of my awful Calc 3 (multivariate) class. In one lecture, the prof spent the entire time on one problem on the chalkboard. He never looked at his notes. At the very end, he looked at his notes and then at the solution on the board and then back at his notes...and stuttered that the solution on the board was incorrect. Somewhere along the way he made a mistake. "But you get the idea," he said. No, we didn't. Just awful. We were completely on our own. All this guy cared about was his research. We were a distraction to him.
Ar-Curunir 5y ago
My 2 cents, as somebody who did CS at UC Berkeley: it doesn't have to be that way. At Berkeley we have gentler intro courses that you can take to learn the basics of (e.g.) CS and Astronomy. These courses (CS10 and Astro C10) are award-winning. There's no reason one couldn't do, e.g., "The Beauty and Joy of Number Theory" or "The Wonders of Linear Algebra".
- whimsicalism 5y ago
  If you are just learning results and not proofs, I wouldn't really call that a "math" course. If you are learning proofs, it is going to be a bit of a slog in the way that CS50, etc. can avoid.
  - munchbunny 5y ago
    In my experience, if there's one thing missing in math pedagogy, it's that none of the math classes teach you how to think through and write proofs. I was personally fortunate that my high school math teachers made an effort, but that's not that common. It'd be like if the first time you encountered the concept of an "essay" was when you took a history course in college. You'd have a rough time just understanding how to do the homework.
    - zozbot234 5y ago
      > it's that none of the math classes teach you how to think through and write proofs. Formal logic is usually introduced in calculus and discrete math courses. Arguably though it could stand on its own especially if it was taught using modern computer proof assistants, which make the "structuring" of even fairly complex proofs very clear.
    - deleted 5y ago
      [deleted]
- buescher 5y ago
  Berkeley is almost an order of magnitude larger than Princeton and so can support a bigger range of courses.
dllthomas 5y ago
I spent 4 years at the local community college in place of highschool before transferring to a proper 4 year school. Wanting to make sure I was where I thought I was in math I checked with the advisors and they told me "Oh, yeah, if you did your lower-division math at Cabrillo you're probably better prepared than if you'd done it here."
uejfiweun 5y ago
So I'm wondering, what exactly are these elite programmers doing now? What companies do they tend to work for? I ask because I went to a "top" school with a small CS department, and I thought it was pretty easy - now I'm at FAANG and not having too hard of a time either. I'm wondering what kinds of opportunities I missed out on by not having a CS program with this level of rigor.
- Mandelmus 5y ago
  My guess would be the dividing line goes between science and engineering. The top level science work requires a lot more (mathematical) rigor than the top level engineering jobs. (I say that as more of an engineering type myself, albeit with a confidently above-average degree of mathsiness.)
- whimsicalism 5y ago
  > I'm wondering what kinds of opportunities I missed out on by not having a CS program with this level of rigor. People over-state the difficulty of things and generalize something being difficult for them to being very hard and difficult to everyone. The smartest people I know from school all went into academia.
  - someguyiguess 5y ago
    That actually explains this whole situation perfectly. I’m making a huge assumption here, but if the people who had no trouble picking up this information, are the same people who end up becoming the professors, they probably teach in a way that does not cater to students who need the instruction and feedback of a professor.
qwrshr 5y ago
I think it depends a lot on the specific school. I'm at an Ivy League school that tries to make its classes accessible even to people without previous experience.
somethoughts 5y ago
Your comment and the OP kind of have parallels to a Malcom Gladwell discussion titled "Why You Shouldn't Go to Harvard [for STEM]" https://www.youtube.com/watch?v=7J-wCHDJYmo https://www.youtube.com/watch?v=7J-wCHDJYmo If I recall the TLDR was if you want to graduate with a STEM degree go to a strong second tier school and be the absolute best there instead.
deleted 5y ago
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whakim 5y ago
Counterpoint: I went to an Ivy League school and studied both computer science and a humanities field. I didn't take an intro CS class until my sophomore year and had no prior experience. It was only because of quality/resources - as well as the tremendous effort to cater to folks with any level of background, including none - of that intro class that I continued on. I wish more intro classes in STEM were like this.
- ghaff 5y ago
  Anecdotally, some schools are making a genuine effort to have a legitimate Intro CS/programming course. As I noted elsewhere, pretty much uniquely among majors outside of the arts, a lot of CS majors are designed in a way that is very unfriendly to people who weren't already hacking on computers a lot.
- tomtheelder 5y ago
  I feel like I know which Ivy you're talking about, and if I'm right that class has been fantastically designed for that purpose. I _hate_ the idea of a barrier class. Most students are already terrified at the idea of studying STEM. Why on earth would we further discourage them?
  - whakim 5y ago
    Yeah - you've probably got the right one. I think the real thing this shows is that if you teach intro classes well (and try really hard to get people from atypical backgrounds to take those intro classes in the first place), students don't drop out the moment the going gets tough because they feel unsupported and assume STEM "isn't for them." (I certainly was in that category and would never have studied computer science if I had had a different introduction to the subject.) The failure to teach many more intro classes this way is all the more acute at Ivy+ institutions because they're not lacking for resources.
raverbashing 5y ago
For real, this is not it. Yes, you can't expect to start from zero at this course. But it seems that they failed at teaching the course. "Filter course" maybe (as another commenter suggests), but my opinion is that it's a BS concept created by the universities. Sure, lots of places have "sink or swim" evaluations. But it is more a product of the universities pride than anything of real value.
kenjackson 5y ago
Unfortunately, this is common at a lot of top schools. The emphasis is less on teaching and more on weeding out. The thing that makes this so disappointing is the end product at the high end isn't much improved. But we miss out on the breadth of teaching across a wide spectrum of people. The example given of not supplying answers to study questions is a classic example. Or asking questions on tests that students have never even remotely seen before (all that's really testing is if students have some tangential information that allows them to connect the dots). Part of the problem is that we rarely (even from elementary through secondary school, much less university) hold teachers accountable for teaching. And I don't mean unreasonably accountable. I'm not trying to fire a bunch of teachers, but I do want teachers to really want kids to learn the material above all else.
- black_puppydog 5y ago
  > the end product at the high end isn't much improved. But we miss out on the breadth of teaching across a wide spectrum of people I think this can't be overstated. It means that these elite schools (where the elite go, and where they are recruited from) largely filter for people who are great when they enter the school, and not much else. Potential for greatness through learning doesn't matter much then, does it? Between the economic filtering for admission and courses like these that will favor students that arrive with a bunch of training you're much more likely to receive of your parents are wealthy, these schools mostly seem to aid the elite at preserving the status quo...
danielmorozoff 5y ago
Having also attended both public and ivy league schools in STEM from undergrad to PhD levels I can say from what I have seen there is a huge lack in mathematics education. This is especially true in the lower undergrad courses where profs see it as a burden to deal with in terms of teaching and the classes devolve into mechanistic / memorization exercises. very few teach students to reason with mathematics mostly prb bc 1 the profs are bad or disinterested teachers or 2 bc the profs have fundamentally other interests and are forced to each elementary classes in subjects they may mot have an affinity for or deep knowledge in- ie functional analysis or prob theory ... Once you get into the later classes math education steeply improves where fundamental questions are investigated and asked. i remember auditing a math physics class with 4 students and a prof al phd students - it was incredible and was totally outside of my area of research. all this to say i think undergrad math education is poorly designed/ incentivized and run in my experience and leads to a huge loss of talent from the practice and art of mathematics.
- jimhefferon 5y ago
  > Having also attended both public and ivy league schools in STEM from undergrad to PhD levels I can say from what I have seen there is a huge lack in mathematics education. I respect your experience. I want to say, though, that I teach at a small liberal arts college and everyone here puts a great deal of energy into teaching. So there is an alternative. > leads to a huge loss of talent from the practice and art of mathematics Yes, it is a terrible thing.
  - danielmorozoff 5y ago
    You bring up a valid and important distinction that i have heard before surrounding liberal arts vs research unis. Having attended the latter, I have no personal experience to compare, but have heard much more positive reviews of liberal arts education from those who studied maths there. Again I believe the incentive structures at teaching universities properly match what students are there to accomplish, whereas at research unis they tend to be muddled.
omershapira 5y ago
When I was at Tel Aviv University, at the time #7 in the world in cited Mathematics works, a TA once told me they were told the method for supporting students is nicknamed "foam": Foam rises to the top. In other words, if they can't figure it out, there's no incentive in helping them, because they're not going to become PhD researchers, not going to create citeable papers, and not going to get the University a budget increase. This meant the university was comfortable with a low grade average, because school in Israel is subsidized - they're not competing for students, and the proportion of people with a BA/BSc in Israel is among the highest in the world. The only thing that mattered is more research, which means more grants, which means more staff, which indirectly means more professors to throw at teaching. In all my time at TAU, I only encountered one Maths professor who wasn't faculty, so it seems the system was working.
bradleyjg 5y ago
Few of the staff would teach you the basics of anything, mostly because you are attending a research college, where teaching is the professors' side gig. Outside of biology and a small handful of other grant driven fields, notably not including math—-the customers of the side gig are paying for everything. The least the people charging such high prices could do is put in a bit of effort.
deeviant 5y ago
> Edit: I don't mean to discourage people with this post. I was actually one of the few people who didn't have much of a CS/quanty background in my CS classes. My advisor told me to have a backup major in case I fail the tougher required classes, but I made it through. Quant background coming out of high school? Good grief.
- munchbunny 5y ago
  Pretty sure they meant math-heavy, not Wall Street quant.
munchbunny 5y ago
My experience, also from an ivy league college, was that the beginner classes were taught well but often lacked rigor. But if you were looking for the level of rigor that introductory courses for dedicated majors would provide, you were going to have a bad time because those were often quite unforgiving. For example, the 100 level math classes mostly did not touch proofs, just calculation. The 200 level math classes were almost exclusively proof based, but they didn't teach you how to write them. Either already knew how or you were going to have to teach yourself the mental framework on the fly. Contrast that with 100 vs. 200 level humanities courses in my college, where there really was a focus on teaching you how to argue points in writing.
- Jtsummers 5y ago
  That's not unique to ivy league schools. Outside of math majors, most math is taught in an "application" approach, especially at the 100 and 200 level. You're taught enough to be able to use it. You can set up your physics problems in a way that uses calculus, and you know enough calculus to compute an answer (and maybe a bit of diff eq, but likely in Physics 1-3 you haven't formally taken differential equations so your skill there is limited). You know enough linear algebra to set up systems of equations and solve problems with it. But you will rarely find 100 and 200 level courses that, beyond a cursory evaluation, cover the fundamental theorems that really define calculus and linear algebra (as a non-major) unless you end up taking a 300 or higher level course. Same with probability and statistics. The 200 prob/stat class teaches you about applications, and enough to use normal and uniform distributions (guaranteed) and maybe a couple more. You can do some limited modeling, but you won't be able to derive various properties of those distributions or other distributions unless you take a 300/400 level stats course. Which, it turns out, is sufficient for the vast majority of engineers and scientists.
dghlsakjg 5y ago
I went to a high school that did not offer competitive programming, number theory or discrete math. I probably wouldn’t have had time since I worked through most of high school Does it stand to reason that I have no business studying CS? What are students who come from a less privileged background to do, self select out of good programs?
- micromacrofoot 5y ago
  > What are students who come from a less privileged background to do, self select out of good programs? In my experience, more or less, yeah... self-select out and get to work as soon as possible. I worked through most of high school and all of college. Almost decided against college entirely (money fears), but I'm glad I changed my mind. There's no way I was going to an Ivy League and studying 40 hours or more a week. Years later and I still can't imagine living for a period of time where I have more than 2 weeks of work off. I've been working since I was 14. I went to a decent school, had decent-ish grades, and tried to get paid to do as much relevant work as possible. I still dream about having the ability to take a few years off to study. Must be incredible.
2muchcoffeeman 5y ago
But not providing answers? I hope the tutes were rigorous.
dan-robertson 5y ago
I didn’t go to university in the US but I aren’t to one of the most prestigious/competitive/highly ranked schools in the country (I recall thinking it was the top but could have been biased; it was perhaps number 2) which feels comparable. There were a few differences from the US: 1. Most people would only take courses from their ‘major’ which they would apply specifically for rather than taking various courses from different departments. There was choice, e.g. science students were all grouped together and could choose from ‘normal math’ and ‘extra math’ with some people (e.g. those interested in physics) encouraged to do the harder course. Another counter example was a classist I vaguely knew who took one of the hardest final-year math courses (it began with ZFC and nonsense like proving that x -> x, and quickly ramped up from there) 2. Generally people were marked on exams and (at least in mathematics) everyone took the same exams and answered questions from their courses. Homework did not count towards final marks and wasn’t even graded. Some thoughts regarding the article or courses at ‘top universities’ 1. For some students it can be good to just get a lot of practice at doing a long chain of operations without making mistakes. This is a common problem from school where most questions don’t have many steps and have lots of checkpoints, e.g. (a) prove trivial step 1. (b) hence do trivial step 2, (c) hence do trivial step 3; rather than something more like ‘solve the problem by figuring out what the 5 steps are and following through without making serious blunders’. Maybe that was part of the point of the course. I don’t think my university would have wasted a course on this point though. We did have some early courses that were partly just building mathematical maturity though. 2. Not getting any answers to exercises is bullshit. Doing the exercise is meant to teach you something, and knowing the answer (or rather the thing you were missing to solve the exercise) feels pretty necessary. Towards the purer end, it’s quite typical that an exercise is basically ‘try to prove this thing that we give you the tools to easily prove in a few chapters’ and (after a time) you are generally expected to be able to work out for yourself if your solutions are correct. But having a good solution can be very helpful. It feels like it is usually good to have students suffer on an exercise for a bit and hopefully solve it before showing them the ‘nice way’ but it is still important to learn the better way to do the thing you figured out. For example, you could blunder around doing some horrid algebra and then be shown an easier way through, or some property you ought to have spotted. [1] 3. The professor (or better, someone who knew what they were doing in small groups) should have gone through the exercises and the answers. (And they would ideally be exercises where you would learn something rather than just doing calculations). The way my courses worked is that people would get given ‘homework’ exercises, attempt them (typically alone) and then some phd student/academic would read the submitted homework and go through the answers with students in small groups of 1 or 2. There would typically be problems that were too hard but whose solutions (or incorrect proof attempts) would be instructive[2]. 4. Possibly they were expected to come to office hours for help but didn’t because they couldn’t work out how to interact with the professor or didn’t realise that that’s what they were meant to do because they were new/from the wrong class. 5. Knowing about matrices is useful and necessary for many other things but it feels like a poor introductory course. I think it’s better to focus on something that is new, mathematical (in the sense of doing proofs not calculations), and doesn’t have many dependencies. Like ‘introduction to some number theory and how to prove things’ or ‘elementary group theory up to the first isomorphism theorem’ or if they already know what integration and differentiation are, maybe ‘analysis with epsilons and deltas from sequences to Riemann integrals’. It’s also possible to have a good course with matrices (see my other comment on this thread) without having a bunch of pointless manipulation of grids of numbers. [1] two examples come to mind: 1. Consider the problem of giving someone a gift such that they get $x after deducting a flat tax rate. You can imagine giving them $x and then topping that up by $(x - tax) and then topping up again summing the geometric series to get the answer, or you can just do x/(1+tax rate). Similarly there’s the problem of the fly going back and forth at constant speed between two trains moving towards each other. 2. The question was ‘find a space X and retractions from X to the annulus and to the Möbius band’ there is an easy visual answer: take a solid torus (S1 x D2), parameterize in R3, and carefully define your functions. But there was also some even easier answer, something like take the product space of the annulus and the Möbius band and the retractions are trivial. It was useful to know how much easier things could be. (Possibly the question was about deformation retracts). [2] An example from an earlier course would be ‘construct a function R->R that takes every value on every interval’. I think I wrote some nonsense like the limit of tan(nx) as n->infty, which at least led to some discussion. The canonical answer is Conway’s base 13 function. A classmate of mine came up with a scheme based on something we’d proved earlier: any convergent but not absolutely convergent series (that is a sequence a_n such that sum_1^n a_i converges as n grows but sum_1^n a_i| does not) can have its terms reordered to make it converge to any value. Other examples could be logic/AOC puzzles about infinitely many prisoners suffering cruel punishments, hard proofs related to the topic, or ‘what is yellow and equivalent to the axiom of choice?’
WalterBright 5y ago
> 60-70 hours At Caltech, the expectation was to spend 2-3 hours studying for every hour of lecture. I found it to be pretty accurate, spending maybe 50 hours a week total. I was never bored :-)
Seattle3503 5y ago
> Few of the staff would teach you the basics of anything, mostly because you are attending a research college, where teaching is the professors' side gig Princeton in particular prides itself on being focused on the undergraduate experience compared to other research universities. Research is (supposed) to be secondary.
kwertyoowiyop 5y ago
> Few of the staff would teach you the basics of anything, mostly because you are attending a research college, where teaching is the professors' side gig. Hopefully they make that clear to all the naive students before they sign up! :-)
porknubbins 5y ago
My experience doing a huge number of MOOCs at Ivys or equivalent level CS programs is that the programming assignments are no harder than other good CS programs, but I assume the grading is more competitive. For example most OS courses make you write a memory allocator, which isn’t easy anywhere but maybe you have to optimize more at Ivies vs just making it work. That said I’ve noticed MIT expects a higher math level than anywhere else, and Stanford leans toward a kindler gentler approach, at least its MOOCs, vs the East coast competitiveness.
am3101 5y ago
I went to Princeton and actually found the "COS" department was excellent at introductory programming. A lot of people took COS 126 (the introductory class—equivalent of AP Computer Science) with no programming background and did fine. There was also a COS 109 class that was way easier that _Brian Kernighan_ (of K&R) taught that was explicitly targeted at humanities majors. https://www.cs.princeton.edu/courses/archive/fall21/cos109/ https://www.cs.princeton.edu/courses/archive/fall21/cos109/ . I think classes beyond COS 126 were _not_ like this and similar to what you describe re: meaningful hours outside of class, but if you are just exploring, 126 probably scratched your itch. I had a very similar impression of non-COS STEM classes while I was at Princeton, however... both course descriptions and other students pretty strongly discouraged me from exploring STEM classes.

Waterluvian 5y ago

I went to the University of Waterloo and took a "Intro to CS for non-math students" course. The thing was designed and taught by CS faculty, so naturally they taught you the basics of programming using math. I spent more time re-learning high school math than actually learning programming. And not because it was directly related, but because some lessons were like, "write a function in Java that factors a quadratic." So 90% of that tutorial was me re-learning what the heck a quadratic is and how to factor it. The experience really sucked and I gave up on university programming courses and just started learning it all practically and on my own terms. Edit: Enjoy this wonderfully styled course page: https://student.cs.uwaterloo.ca/~cs125/S08/Resources/Admin/CourseOutline.shtml https://student.cs.uwaterloo.ca/~cs125/S08/Resources/Admin/C...

artificial 5y ago
I like learning files and sockets once the syntax is a familiar and then branching out to error handling followed by more advanced topics and then circling back around to testing. Project based learning resonates best with me, hands on cements knowledge rather than pure theory.
kamaal 5y ago
The real question is in asking, what are you going to use the programming language to build? If you are going into a Math heavy domain, you are going to use a programming language to solve math problems, and hence involves learning Math. This the same problem, with whiteboard leetcode style problems in interviews. Most people fail to understand why they have to put in months to years of practice into a domain to which doesn't concern with their everyday work. On the other hand there is tremendous shortage of people with skills for real world problems and applications.
- Waterluvian 5y ago
  Yeah. I've been writing code as a job for a decade now and have never needed to factor a quadratic equation. I really just needed a course that helped me get introduced to programming (which I ended up using a LOT in the domain I went to school for: geography and remote sensing). (Every time I write something like this I immediately feel defensive about being an impostor. Someone saying, "how can you not know that? You should know that. You must not be doing _real programming_.)
  - mlyle 5y ago
    > Yeah. I've been writing code as a job for a decade now and have never needed to factor a quadratic equation. A lot of people never touch algebra again. Some of us end up touching it a lot. This is a bit of a tricky thing, in that: - A whole lot of practitioners have very limited continuous math and deep CS needs, so some of these requirements are artificial barriers to some extent for many jobs. - But is it reasonable to give them CS degrees without at least basic competence? - Plus, part of the point of a university education is to round-out students and expose them to many things...
    - Waterluvian 5y ago
      To be clear, this course was exclusively "CS for NON CS/math majors." If you were in CS, you were not allowed to take it. They also offer a lot of "math for non mathies" courses, which would have been a great place to teach quadratics.
criddell 5y ago
I think you also need to consider just what is meant by “computer science”. Is it programming? My daughter is studying comp. sci. right now and there seems to be a ridiculous amount of math and math proofs and very little programming in her program (she’s still in her first year). The spend a considerable amount of time proving stuff using big-O (and theta and omicron etc…) and surprisingly little time applying those ideas. I think what you wanted (and what should be offered to everybody) is a course designed to teach programming and programming concepts.
- weaksauce 5y ago
  computer science is not programming though it often involves doing that. it's a math degree with many different topics all related to computing and math. So yeah if they wanted to learn how to program java that's a completely different track. they generally don't teach you much programming or other practical things at a university track. you need to know it but it's ancillary to the degree.
  - l33t2328 5y ago
    A computer science degree isn’t a math degree any more than a physics or chemistry degree is a math degree. Classes like Computer Organization, Operating Systems, Networking, Databases, Software Engineering Fundamentals, the first year programming sequence, etc. could hardly be considered math courses.
    - deleted 5y ago
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    - thorajeu83 5y ago
    - weaksauce 5y ago
      > Classes like Computer Organization, Operating Systems, Networking, Databases, Software Engineering Fundamentals, the first year programming sequence, etc. could hardly be considered math courses. so a math degree has to have every single course be a math course? do they not take literature? Networking had me prove the theoretical limit of networks using calculus and other things, databases had us using relational algebra and other proofs... it certainly wasn't `select * from users;` kinda course. it's a math degree at least at my university and most reputable ones it is. are all classes 100% pure math? no of course not but the emphasis is math.
strangemonad 5y ago
Long story short, if you want to do something off the beaten path, you need to get to know some of the faculty. I also went to Waterloo but as a cs undergrad. I was also a student rep on the undergrad curriculum committee (this was all some years ago). You’ll notice that all the non Math / CS major classes are completely different offerings. Non math majors can only take those “other” cs classes and likewise math majors can’t take them and must take the classes intended for CS students. Unless things have changed, very few faculty tech these non cs major CS classes (mostly sectional lecturers). My overall impression (at the time) was that these classes weren’t that great. They mostly taught you to program (in Java) but exercises were grounded heavily in math problems but didn’t really teach math. If you really want to get a good sense of “computer science” (the discipline) rather than just learn to program, I’d try and get to know the profs that teach 135 and see if you can get a specific override exception. You could possibly do the same for 136. Going deeper down the cs course tree is a bit harder. Part of the challenge is the depth and pacing you want to offer majors doesn’t always align with the broader overview non majors are looking for. Eg you might want a single course covering algorithms and data structures rather than 3-4 courses and you might not care about the math involved to prove amortized costs. If you want to go beyond 135/136 there are a few possible paths that come to mind and involve finding cross appointed faculty and seeing if they might sponsor you for an override into their class offering. If you’re in psych, the cog Sci route would get you to know people who are cross appointed with AI folks, arts used to have cross appointed faculty with the computer graphics lab (Craig Kaplan is a friendly face in the CGL). Physics obviously has overlap with the quantum computing lab. I don’t know any of current the undergrad ce advisors but J.P. Pretti might be able to point you in the right direction
- mcguire 5y ago
  Roughly the same was true at UT Austin when I was there. They introduced CS-for-non-majors classes, but I don't know anyone who would have touched them with a 10-foot pole.
fredophile 5y ago
I can't say I'm too surprised. Waterloo is unusual in that they offer a Bachelors in Math in addition to the more standard B.Sc. and B.A degrees. Computer Science majors there graduate with a B.Math.
- alibero 5y ago
  Waterloo also offers a BCS which has fewer math requirements than the BMath: https://cs.uwaterloo.ca/current-undergraduate-students/majors#BCSvsBMathCS https://cs.uwaterloo.ca/current-undergraduate-students/major... The BMath option is only required if you want to have a double major in CS and a different area of math. Otherwise the BCS is strictly more flexible: you have 5 fewer math courses and 5 more electives (which you may use to take math courses if you really want to). From my experience most people are graduating with BCS unless they really like math.
  - fredophile 5y ago
    Interesting. At the time I was picking universities that wasn't an option they offered.
ww520 5y ago
That’s what programming is. Programming is applying computerized solutions to different problem domains. To make a successful problem, you have to learn about the targeted domain and sometimes become an expert in it. In this case the problem domain is quadratic factoring.
- colinmhayes 5y ago
  This isn't helpful for say econ majors who want to build econometric models though. The class sounds like it is specifically for non cs majors so it doesn't really make sense to get into theory that might not apply to their studies.
  - ww520 5y ago
    Right. Sometimes we are forced to go outside of our comfort zone. A software engineer might not care much about insurance actuary, bank money transfer, railroad signal rules, or econ supply/demand curves. But when the job calls for creating programs to do those areas, he better learns those fast, on the fly. That class taught an important reality of software development. You have to be willing to learn something you're not familiar to get the job done, and how well you understand the problem domain directly affects how well the program is developed. So the class was not tailored for the econ major, but at the college level, students need to learn that no one is going to hand a solution on a silver platter for your problem.
alasr 5y ago
IMHO CS, software engineering and computer programming are very different but closely related fields. Each field focus and work on different (but complementary) set of activities in order to efficiently solve a computation-based automation problems. Based on the scale and complexity level of software artifacts, you'll see an individual, a small team or very large team are working on a given challenge/problem[1]. CS is, with mathematics as its foundation, focused more on the abstract and computational aspects[2] of a computational problems/challenges. As expected, CS solutions are usually very generic and independent of any specific programming language, it presents its solution in abstract forms and along with some code (written in some programming language). From CS's point of view, the coding part of its solution is primarily[3] for demonstrating that the solution of a specified problem is computable and efficient (for some practical purpose) and can be verified independently if needed. Now, computer programming languages are just one of the tools which helps us write those codes to "communicate" our solutions to computers and fellow programmers (who, as part of the team, need to understand in order to help developing and maintaining the software program). And, there're other alternative programming languages available which practically does the same job (though some of them are more appropriate and suitable than others, due to reasons/concerns outside the scope of a particular programming language[4]). Having said all the above, I think I understand the core of the problem(s) you (and students in similar position as you) described here, in your post. I think I've faced similar challenges while trying to understand some non-CS course (for example, accounting and finance). Being new to any field of STEM/business/..., it's easy to get pulled into non-important areas of studies instead of focusing on the core ideas/concepts of the course. And I believe it's always course instructor primary responsibility making sure that core concepts/ideas are made very clear at the course and individual lectures level and, similarly, corresponding supporting concepts/activities which make up the course and its core concepts. NOTE: I've few more thoughts on the subject; however, I think, my current post is already getting too long so I stop this post, at this point. --- [1] - Btw, as you may already know, team size alone doesn't indicate that they're working on a easy or difficult problem. Sometimes it's just a consequence of some financing/time constraints or inefficient team management. [2] - For example; data model, data structure and algorithm. [3] - Other benefits are secondary and can be considered as bonus. [3] - Reasons/concerns related to either CS or software engineering.
ska 5y ago
A couple of things worth considering 1) CS::software development is a bit like physics::mechanical engineering 2) CS at waterloo definitely skews to the cs-is-part-of-applied-math thinking in many ways. Other university CS programs are very different. I'm not saying a "practical programming for non math/cs types" course isn't a good idea, just that really isn't what you signed up for.
inetsee 5y ago
"Enjoy this wonderfully styled course page" I have the Tranquility! extension on my browser, which turns that web page into something quite readable. The web page as it is is the complete opposite of something readable. https://addons.mozilla.org/en-US/firefox/addon/tranquility-1/ https://addons.mozilla.org/en-US/firefox/addon/tranquility-1...
908B64B197 5y ago
> The thing was designed and taught by CS faculty, so naturally they taught you the basics of programming using math. I would have honestly made the same assumption that students interested in programming would have no problem with high school level math. Maybe an intro course aimed toward the business school wouldn’t be as math-heavy? 6.001 was notorious for starting out with examples from calculous and required some proof reading. But it wasn’t aimed at anyone. It’s tougher to enroll in 6.001 than most other intro courses.

ianai 5y ago

True, but linear algebra being the crux of so many disciplines the linear algebra course should be especially emphasized and clear. It's not the place to throw random hurdles. It's the place to get this information into the students' brains 100% so they can leverage that knowledge correctly later. More of a foundational course in that sense. Like if you were pushing out liberal arts majors without any grammar courses. Edit- Now, the course says it's for students considering a major in STEM. I wonder if the business side of the college means to say: "Students who got into Princeton ostensibly to study some area outside of STEM but who are now thinking of going into STEM. They may take this course then add to our STEM student roster by switching majors and we don't want that for business reasons. So here's a course that will push back all but the students who have a good case to be in STEM."

ghaff 5y ago
>Like if you were pushing out liberal arts majors without any grammar courses. I would expect very few liberal arts majors (who aren't majoring in linguistics) would take a grammar course. Linear algebra is actually sort of interesting. Before computers were commonplace I'm not sure how widely taught linear algebra was. I certainly never took it but was admittedly not a CS/EE major. I do remember a robotics course I took in grad school that involved doing these ugly matrix operations by hand. (No Matlab.)

nojito 5y ago

This is true but the class the author was taking was not required for Math majors.

mlyle 5y ago

> My 2 cents: The author presumably goes to Princeton - the ivy league is in general a tough place to "start learning" things, especially STEM. Few of the staff would teach you the basics of anything, mostly because you are attending a research college, where teaching is the professors' side gig. Still, it seems there's bits of departmental strategy that are a bit kooky. Why provide practice problems (not for credit, it seems), and then never share solutions? What is the point in the student practicing without feedback about correctness? Wrong practice is just as likely as right practice.

nicoburns 5y ago
In my experience this attitude is extremely widespread amongst university departments. I think it's a simple combination of elitism and poor training in pedagogy (unlike school teachers, university lecturers typically undergo no mandatory training in teaching).
- busterarm 5y ago
  When the author described this specific math class as a required math class for Engineering majors and not math majors, I spotted it for exactly what it is: a weedout course. It's intentional.
  - speed_spread 5y ago
    Aka Institutional Gatekeeping.
bertr4nd 5y ago
Possibly the concern with sharing answers is that students could memorize the form of likely exam questions without deeply understanding the material? But that risk exists simply by sharing the questions so I’m not sure I find that argument persuasive. I’ve always been rather disappointed by the lack of solutions in math books. I mean, on the one hand, it’s a great feeling to crack a difficult problem unaided, and there’s something to be said for building the intellectual discipline one needs to attack a problem with no easy answer. But also, there are some problems that I never manage to solve because I “time out,” and it’s possible that as a result I’ve missed the opportunity to learn techniques that will be useful in the future.

lordleft 5y ago

I also went to an ivy and echo this comment. The math classes were geared towards people who had considerable expertise / interest in mathematics to begin with, which didn't help someone like me who didn't have that expertise. While I think that academic settings that cater to advanced students are worth cultivating, I don't think intro or require math sequences are the places to do that.

hnmullany 5y ago
Also went to an ivy and found the "math for non-majors" to be pretty well taught & very manageable - although I did have pretty solid high school math. I did not have the same experience with my first physics for majors course - which was taught by a guy who talked into the blackboard and spent the entire class writing on the board in a fugue. Made me switch majors.
brimble 5y ago
I'm torn because on the one hand I don't know how someone who hadn't already been programming for years, or at least been a big computer nerd and tinkerer, could have gotten through even the relatively weak CS program that I did. I gather math is similar. On the other hand, I don't think anyone expects to start learning, say, music, in college, and major in it, having had nothing but maybe a couple required and non-rigorous music classes all of k-12, and not being able to do much more than squeak out "Mary Had a Little Lamb" on a clarinet. Their first class will be them in a room of 19 others who have all been playing at least one instrument since they were 5, played in jazz band in high school and picked up tons of music theory, had extracurricular instructors and tutors for years, et c. Of course that's not going to go well. Maybe colleges should just be more up-front about that, with other majors. OTOH I don't think social science classes do this. They seem to assume no more than that you weren't asleep during your high school social science classes. They do expect you to come in writing at at least a 12th grade level, which is sometimes... optimistic. But not much else.
- ghaff 5y ago
  CS/programming (yes, I know they're not the same thing) is something of an odd beast at many top schools. I took MIT's intro MOOC a while back. And the idea that I could pass that, alongside other coursework, never having done any real programming boggles the mind. Yet, no other engineering major has that degree of informal prerequisite. And, yes, it's pretty much like the arts. (As a side note, I did take an Intro to Music class in college. Of course, I discover it's taught by a rather well-known choral director so the class is filled with people who were quite practiced in music and said choral was happy to teach to that level. I actually got something out of it but a lot was also over my head.) (As another side note, way back when I took intro to programming--or whatever it was called--for non-CS majors. This was back before PCs were widespread and I'm sure anyone here would find it ludicrously elementary for even an intro course at a good university.)

mannykannot 5y ago

I agree that one should expect challenging classes at Princeton, but it seems quite a few students struggled with this course, and I would guess the majority of those were STEM-oriented. On the other hand, you cannot conclude from one case that math teaching is broken.

tandymodel100 5y ago

spicymaki 5y ago

Here is my take: This class seems to be a filter class. A class designed to sift out students that would not cut it in a engineering/science curriculum. They are not designed for students to learn, they are designed as a barrier. That in itself is fine if it happens early enough so students can regroup and reevaluate what to do next with their lives. What I don't like about this is that there is a mismatch between what colleges are saying they want to do and what they are actually doing. They should actually state that in the name and description of the course. I wish schools would be transparent so they don't waste the money and time of the students. This won't happen of course, we will just continue the kabuki dance.

xxpor 5y ago
Yes exactly. I didn't go to an Ivy League, but it was still pretty good. The 100 level big classes were waaaaay harder than classes for the actual major. Lots of dumb problem sets that were huge just to be huge. Lots of time writing lab reports with error calculations etc. The one hack I figured out was that if you didn't include an error calculation in your lab report, they only took off 1 point. Given it took 20+ minutes to write it up in the format they wanted using the Word equation editor (this was before I knew Latex), the -1 was absolutely worth it. I never, ever, had to spend 60-70 hours a week outside of class doing work though. That's insane.
pevey 5y ago
That is often given as an excuse for this common experience, but it is not really intended. Top schools are assessed on their graduation rates. It is part of the rankings they are obsessed with. It serves no one--students or schools--for students to be weeded out in these intro courses. The truth is just that even top schools in the US (and I suspect, ESPECIALLY top schools, more so than middle-tier schools) are really, really bad at teaching STEM, even to students very interested in learning. I still have clear memories 20 years later of my awful Calc 3 (multivariate) class. In one lecture, the prof spent the entire time on one problem on the chalkboard. He never looked at his notes. At the very end, he looked at his notes and then at the solution on the board and then back at his notes...and stuttered that the solution on the board was incorrect. Somewhere along the way he made a mistake. "But you get the idea," he said. No, we didn't. Just awful. We were completely on our own. All this guy cared about was his research. We were a distraction to him.

Ar-Curunir 5y ago

My 2 cents, as somebody who did CS at UC Berkeley: it doesn't have to be that way. At Berkeley we have gentler intro courses that you can take to learn the basics of (e.g.) CS and Astronomy. These courses (CS10 and Astro C10) are award-winning. There's no reason one couldn't do, e.g., "The Beauty and Joy of Number Theory" or "The Wonders of Linear Algebra".

whimsicalism 5y ago
If you are just learning results and not proofs, I wouldn't really call that a "math" course. If you are learning proofs, it is going to be a bit of a slog in the way that CS50, etc. can avoid.
- munchbunny 5y ago
  In my experience, if there's one thing missing in math pedagogy, it's that none of the math classes teach you how to think through and write proofs. I was personally fortunate that my high school math teachers made an effort, but that's not that common. It'd be like if the first time you encountered the concept of an "essay" was when you took a history course in college. You'd have a rough time just understanding how to do the homework.
  - zozbot234 5y ago
    > it's that none of the math classes teach you how to think through and write proofs. Formal logic is usually introduced in calculus and discrete math courses. Arguably though it could stand on its own especially if it was taught using modern computer proof assistants, which make the "structuring" of even fairly complex proofs very clear.
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buescher 5y ago
Berkeley is almost an order of magnitude larger than Princeton and so can support a bigger range of courses.

dllthomas 5y ago

I spent 4 years at the local community college in place of highschool before transferring to a proper 4 year school. Wanting to make sure I was where I thought I was in math I checked with the advisors and they told me "Oh, yeah, if you did your lower-division math at Cabrillo you're probably better prepared than if you'd done it here."

uejfiweun 5y ago

So I'm wondering, what exactly are these elite programmers doing now? What companies do they tend to work for? I ask because I went to a "top" school with a small CS department, and I thought it was pretty easy - now I'm at FAANG and not having too hard of a time either. I'm wondering what kinds of opportunities I missed out on by not having a CS program with this level of rigor.

Mandelmus 5y ago
My guess would be the dividing line goes between science and engineering. The top level science work requires a lot more (mathematical) rigor than the top level engineering jobs. (I say that as more of an engineering type myself, albeit with a confidently above-average degree of mathsiness.)
whimsicalism 5y ago
> I'm wondering what kinds of opportunities I missed out on by not having a CS program with this level of rigor. People over-state the difficulty of things and generalize something being difficult for them to being very hard and difficult to everyone. The smartest people I know from school all went into academia.
- someguyiguess 5y ago
  That actually explains this whole situation perfectly. I’m making a huge assumption here, but if the people who had no trouble picking up this information, are the same people who end up becoming the professors, they probably teach in a way that does not cater to students who need the instruction and feedback of a professor.

qwrshr 5y ago

I think it depends a lot on the specific school. I'm at an Ivy League school that tries to make its classes accessible even to people without previous experience.

somethoughts 5y ago

Your comment and the OP kind of have parallels to a Malcom Gladwell discussion titled "Why You Shouldn't Go to Harvard [for STEM]" https://www.youtube.com/watch?v=7J-wCHDJYmo https://www.youtube.com/watch?v=7J-wCHDJYmo If I recall the TLDR was if you want to graduate with a STEM degree go to a strong second tier school and be the absolute best there instead.

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whakim 5y ago

Counterpoint: I went to an Ivy League school and studied both computer science and a humanities field. I didn't take an intro CS class until my sophomore year and had no prior experience. It was only because of quality/resources - as well as the tremendous effort to cater to folks with any level of background, including none - of that intro class that I continued on. I wish more intro classes in STEM were like this.

ghaff 5y ago
Anecdotally, some schools are making a genuine effort to have a legitimate Intro CS/programming course. As I noted elsewhere, pretty much uniquely among majors outside of the arts, a lot of CS majors are designed in a way that is very unfriendly to people who weren't already hacking on computers a lot.
tomtheelder 5y ago
I feel like I know which Ivy you're talking about, and if I'm right that class has been fantastically designed for that purpose. I _hate_ the idea of a barrier class. Most students are already terrified at the idea of studying STEM. Why on earth would we further discourage them?
- whakim 5y ago
  Yeah - you've probably got the right one. I think the real thing this shows is that if you teach intro classes well (and try really hard to get people from atypical backgrounds to take those intro classes in the first place), students don't drop out the moment the going gets tough because they feel unsupported and assume STEM "isn't for them." (I certainly was in that category and would never have studied computer science if I had had a different introduction to the subject.) The failure to teach many more intro classes this way is all the more acute at Ivy+ institutions because they're not lacking for resources.

raverbashing 5y ago

For real, this is not it. Yes, you can't expect to start from zero at this course. But it seems that they failed at teaching the course. "Filter course" maybe (as another commenter suggests), but my opinion is that it's a BS concept created by the universities. Sure, lots of places have "sink or swim" evaluations. But it is more a product of the universities pride than anything of real value.

kenjackson 5y ago

Unfortunately, this is common at a lot of top schools. The emphasis is less on teaching and more on weeding out. The thing that makes this so disappointing is the end product at the high end isn't much improved. But we miss out on the breadth of teaching across a wide spectrum of people. The example given of not supplying answers to study questions is a classic example. Or asking questions on tests that students have never even remotely seen before (all that's really testing is if students have some tangential information that allows them to connect the dots). Part of the problem is that we rarely (even from elementary through secondary school, much less university) hold teachers accountable for teaching. And I don't mean unreasonably accountable. I'm not trying to fire a bunch of teachers, but I do want teachers to really want kids to learn the material above all else.

black_puppydog 5y ago
> the end product at the high end isn't much improved. But we miss out on the breadth of teaching across a wide spectrum of people I think this can't be overstated. It means that these elite schools (where the elite go, and where they are recruited from) largely filter for people who are great when they enter the school, and not much else. Potential for greatness through learning doesn't matter much then, does it? Between the economic filtering for admission and courses like these that will favor students that arrive with a bunch of training you're much more likely to receive of your parents are wealthy, these schools mostly seem to aid the elite at preserving the status quo...

danielmorozoff 5y ago

Having also attended both public and ivy league schools in STEM from undergrad to PhD levels I can say from what I have seen there is a huge lack in mathematics education. This is especially true in the lower undergrad courses where profs see it as a burden to deal with in terms of teaching and the classes devolve into mechanistic / memorization exercises. very few teach students to reason with mathematics mostly prb bc 1 the profs are bad or disinterested teachers or 2 bc the profs have fundamentally other interests and are forced to each elementary classes in subjects they may mot have an affinity for or deep knowledge in- ie functional analysis or prob theory ... Once you get into the later classes math education steeply improves where fundamental questions are investigated and asked. i remember auditing a math physics class with 4 students and a prof al phd students - it was incredible and was totally outside of my area of research. all this to say i think undergrad math education is poorly designed/ incentivized and run in my experience and leads to a huge loss of talent from the practice and art of mathematics.

jimhefferon 5y ago
> Having also attended both public and ivy league schools in STEM from undergrad to PhD levels I can say from what I have seen there is a huge lack in mathematics education. I respect your experience. I want to say, though, that I teach at a small liberal arts college and everyone here puts a great deal of energy into teaching. So there is an alternative. > leads to a huge loss of talent from the practice and art of mathematics Yes, it is a terrible thing.
- danielmorozoff 5y ago
  You bring up a valid and important distinction that i have heard before surrounding liberal arts vs research unis. Having attended the latter, I have no personal experience to compare, but have heard much more positive reviews of liberal arts education from those who studied maths there. Again I believe the incentive structures at teaching universities properly match what students are there to accomplish, whereas at research unis they tend to be muddled.

omershapira 5y ago

When I was at Tel Aviv University, at the time #7 in the world in cited Mathematics works, a TA once told me they were told the method for supporting students is nicknamed "foam": Foam rises to the top. In other words, if they can't figure it out, there's no incentive in helping them, because they're not going to become PhD researchers, not going to create citeable papers, and not going to get the University a budget increase. This meant the university was comfortable with a low grade average, because school in Israel is subsidized - they're not competing for students, and the proportion of people with a BA/BSc in Israel is among the highest in the world. The only thing that mattered is more research, which means more grants, which means more staff, which indirectly means more professors to throw at teaching. In all my time at TAU, I only encountered one Maths professor who wasn't faculty, so it seems the system was working.

bradleyjg 5y ago

Few of the staff would teach you the basics of anything, mostly because you are attending a research college, where teaching is the professors' side gig. Outside of biology and a small handful of other grant driven fields, notably not including math—-the customers of the side gig are paying for everything. The least the people charging such high prices could do is put in a bit of effort.

deeviant 5y ago

> Edit: I don't mean to discourage people with this post. I was actually one of the few people who didn't have much of a CS/quanty background in my CS classes. My advisor told me to have a backup major in case I fail the tougher required classes, but I made it through. Quant background coming out of high school? Good grief.

munchbunny 5y ago
Pretty sure they meant math-heavy, not Wall Street quant.

munchbunny 5y ago

My experience, also from an ivy league college, was that the beginner classes were taught well but often lacked rigor. But if you were looking for the level of rigor that introductory courses for dedicated majors would provide, you were going to have a bad time because those were often quite unforgiving. For example, the 100 level math classes mostly did not touch proofs, just calculation. The 200 level math classes were almost exclusively proof based, but they didn't teach you how to write them. Either already knew how or you were going to have to teach yourself the mental framework on the fly. Contrast that with 100 vs. 200 level humanities courses in my college, where there really was a focus on teaching you how to argue points in writing.

Jtsummers 5y ago
That's not unique to ivy league schools. Outside of math majors, most math is taught in an "application" approach, especially at the 100 and 200 level. You're taught enough to be able to use it. You can set up your physics problems in a way that uses calculus, and you know enough calculus to compute an answer (and maybe a bit of diff eq, but likely in Physics 1-3 you haven't formally taken differential equations so your skill there is limited). You know enough linear algebra to set up systems of equations and solve problems with it. But you will rarely find 100 and 200 level courses that, beyond a cursory evaluation, cover the fundamental theorems that really define calculus and linear algebra (as a non-major) unless you end up taking a 300 or higher level course. Same with probability and statistics. The 200 prob/stat class teaches you about applications, and enough to use normal and uniform distributions (guaranteed) and maybe a couple more. You can do some limited modeling, but you won't be able to derive various properties of those distributions or other distributions unless you take a 300/400 level stats course. Which, it turns out, is sufficient for the vast majority of engineers and scientists.

dghlsakjg 5y ago

I went to a high school that did not offer competitive programming, number theory or discrete math. I probably wouldn’t have had time since I worked through most of high school Does it stand to reason that I have no business studying CS? What are students who come from a less privileged background to do, self select out of good programs?

micromacrofoot 5y ago
> What are students who come from a less privileged background to do, self select out of good programs? In my experience, more or less, yeah... self-select out and get to work as soon as possible. I worked through most of high school and all of college. Almost decided against college entirely (money fears), but I'm glad I changed my mind. There's no way I was going to an Ivy League and studying 40 hours or more a week. Years later and I still can't imagine living for a period of time where I have more than 2 weeks of work off. I've been working since I was 14. I went to a decent school, had decent-ish grades, and tried to get paid to do as much relevant work as possible. I still dream about having the ability to take a few years off to study. Must be incredible.

2muchcoffeeman 5y ago

But not providing answers? I hope the tutes were rigorous.

dan-robertson 5y ago

I didn’t go to university in the US but I aren’t to one of the most prestigious/competitive/highly ranked schools in the country (I recall thinking it was the top but could have been biased; it was perhaps number 2) which feels comparable. There were a few differences from the US: 1. Most people would only take courses from their ‘major’ which they would apply specifically for rather than taking various courses from different departments. There was choice, e.g. science students were all grouped together and could choose from ‘normal math’ and ‘extra math’ with some people (e.g. those interested in physics) encouraged to do the harder course. Another counter example was a classist I vaguely knew who took one of the hardest final-year math courses (it began with ZFC and nonsense like proving that x -> x, and quickly ramped up from there) 2. Generally people were marked on exams and (at least in mathematics) everyone took the same exams and answered questions from their courses. Homework did not count towards final marks and wasn’t even graded. Some thoughts regarding the article or courses at ‘top universities’ 1. For some students it can be good to just get a lot of practice at doing a long chain of operations without making mistakes. This is a common problem from school where most questions don’t have many steps and have lots of checkpoints, e.g. (a) prove trivial step 1. (b) hence do trivial step 2, (c) hence do trivial step 3; rather than something more like ‘solve the problem by figuring out what the 5 steps are and following through without making serious blunders’. Maybe that was part of the point of the course. I don’t think my university would have wasted a course on this point though. We did have some early courses that were partly just building mathematical maturity though. 2. Not getting any answers to exercises is bullshit. Doing the exercise is meant to teach you something, and knowing the answer (or rather the thing you were missing to solve the exercise) feels pretty necessary. Towards the purer end, it’s quite typical that an exercise is basically ‘try to prove this thing that we give you the tools to easily prove in a few chapters’ and (after a time) you are generally expected to be able to work out for yourself if your solutions are correct. But having a good solution can be very helpful. It feels like it is usually good to have students suffer on an exercise for a bit and hopefully solve it before showing them the ‘nice way’ but it is still important to learn the better way to do the thing you figured out. For example, you could blunder around doing some horrid algebra and then be shown an easier way through, or some property you ought to have spotted. [1] 3. The professor (or better, someone who knew what they were doing in small groups) should have gone through the exercises and the answers. (And they would ideally be exercises where you would learn something rather than just doing calculations). The way my courses worked is that people would get given ‘homework’ exercises, attempt them (typically alone) and then some phd student/academic would read the submitted homework and go through the answers with students in small groups of 1 or 2. There would typically be problems that were too hard but whose solutions (or incorrect proof attempts) would be instructive[2]. 4. Possibly they were expected to come to office hours for help but didn’t because they couldn’t work out how to interact with the professor or didn’t realise that that’s what they were meant to do because they were new/from the wrong class. 5. Knowing about matrices is useful and necessary for many other things but it feels like a poor introductory course. I think it’s better to focus on something that is new, mathematical (in the sense of doing proofs not calculations), and doesn’t have many dependencies. Like ‘introduction to some number theory and how to prove things’ or ‘elementary group theory up to the first isomorphism theorem’ or if they already know what integration and differentiation are, maybe ‘analysis with epsilons and deltas from sequences to Riemann integrals’. It’s also possible to have a good course with matrices (see my other comment on this thread) without having a bunch of pointless manipulation of grids of numbers. [1] two examples come to mind: 1. Consider the problem of giving someone a gift such that they get $x after deducting a flat tax rate. You can imagine giving them $x and then topping that up by $(x - tax) and then topping up again summing the geometric series to get the answer, or you can just do x/(1+tax rate). Similarly there’s the problem of the fly going back and forth at constant speed between two trains moving towards each other. 2. The question was ‘find a space X and retractions from X to the annulus and to the Möbius band’ there is an easy visual answer: take a solid torus (S1 x D2), parameterize in R3, and carefully define your functions. But there was also some even easier answer, something like take the product space of the annulus and the Möbius band and the retractions are trivial. It was useful to know how much easier things could be. (Possibly the question was about deformation retracts). [2] An example from an earlier course would be ‘construct a function R->R that takes every value on every interval’. I think I wrote some nonsense like the limit of tan(nx) as n->infty, which at least led to some discussion. The canonical answer is Conway’s base 13 function. A classmate of mine came up with a scheme based on something we’d proved earlier: any convergent but not absolutely convergent series (that is a sequence a_n such that sum_1^n a_i converges as n grows but sum_1^n a_i| does not) can have its terms reordered to make it converge to any value. Other examples could be logic/AOC puzzles about infinitely many prisoners suffering cruel punishments, hard proofs related to the topic, or ‘what is yellow and equivalent to the axiom of choice?’

WalterBright 5y ago

> 60-70 hours At Caltech, the expectation was to spend 2-3 hours studying for every hour of lecture. I found it to be pretty accurate, spending maybe 50 hours a week total. I was never bored :-)

Seattle3503 5y ago

> Few of the staff would teach you the basics of anything, mostly because you are attending a research college, where teaching is the professors' side gig Princeton in particular prides itself on being focused on the undergraduate experience compared to other research universities. Research is (supposed) to be secondary.

kwertyoowiyop 5y ago

> Few of the staff would teach you the basics of anything, mostly because you are attending a research college, where teaching is the professors' side gig. Hopefully they make that clear to all the naive students before they sign up! :-)

porknubbins 5y ago

My experience doing a huge number of MOOCs at Ivys or equivalent level CS programs is that the programming assignments are no harder than other good CS programs, but I assume the grading is more competitive. For example most OS courses make you write a memory allocator, which isn’t easy anywhere but maybe you have to optimize more at Ivies vs just making it work. That said I’ve noticed MIT expects a higher math level than anywhere else, and Stanford leans toward a kindler gentler approach, at least its MOOCs, vs the East coast competitiveness.

am3101 5y ago

I went to Princeton and actually found the "COS" department was excellent at introductory programming. A lot of people took COS 126 (the introductory class—equivalent of AP Computer Science) with no programming background and did fine. There was also a COS 109 class that was way easier that _Brian Kernighan_ (of K&R) taught that was explicitly targeted at humanities majors. https://www.cs.princeton.edu/courses/archive/fall21/cos109/ https://www.cs.princeton.edu/courses/archive/fall21/cos109/ . I think classes beyond COS 126 were _not_ like this and similar to what you describe re: meaningful hours outside of class, but if you are just exploring, 126 probably scratched your itch. I had a very similar impression of non-COS STEM classes while I was at Princeton, however... both course descriptions and other students pretty strongly discouraged me from exploring STEM classes.