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/C...

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.

Math, big-O, and proofs are programming concepts. If you want a shallow understanding of whatever programming languages and frameworks are in vogue this year so you can be handed down constrained requirements in a code mill where you are evaluated on how many lines of code you write per day, take a coding bootcamp. But know that after a few years your skills will be out of date and you will have a hard time keeping up with the field. If you want to solve hard problems that haven't been solved before, pay attention to that math and those proofs. I'm honestly just sick of people complaining about CS degrees for not spending enough time teaching React JS or Ruby on Rails. CS degrees are for people who want to solve problems that are actually hard and new.

Seriously, do we ever hear physics majors complaining that they have to learn all this math that they're never going to use, in order to study the foundational cosmology of the universe? Why don't they just show me how to work the damn telescope!?

No; not any more than theoretical-physics degrees are for people who want to solve "hard and new" automotive-engineering or pharmacology problems. That there exist lessons from a given academic discipline that have practical application within a given profession, does not mean that you need to become an academic of that discipline (i.e. someone who can advance the state of the art in that discipline — which is what "getting a degree in X" means, if you're doing it right) in order to become a professional in said profession; or even to advance the state of the art of the profession (rather than of the associated academic discipline.)

In schools for professional (rather than academic) disciplines — e.g. medical schools, law schools, trade schools, etc. — the lessons from academia with relevant practical application to your field are taught together with the more practical material. For example, in learning to be an optometrist, you learn optics. That's physics! But it's only a certain part of physics, and it's presented through the lens (heh) of the problem domain that you care about.

Coding boot camps are shit, I'll agree. Software Engineering programs aren't. I'll take a professional Software Engineer over an academic Computer Scientist any day — especially to have on my team when working on entirely-novel problems. The professional has been taught the problem space, whereas the academic only knows the solution space. It's a lot easier to have a professional read a few books and papers to learn about the solution-space relevant to solving their problem; than it is to fix an academic's lack of appreciation of the constraints imposed by the problem being solved.

Teachers mostly don’t think their education degree made them better teachers and there’s no evidence they do[1]. It’s widely agreed that at least the third year of USAn law school is useless[2] and there are testing providers whose entire thing is teaching graduates what their law school didn’t but should have if it was professional training [3].

Professional schools are run for the benefit of the staff, so they teach what the admins and teachers want to teach. It has to have some relationship to the field but it can be completely attenuated. People learn to do their job at work, not on a university campus.

[1] It's easier to pick a good teacher than to train one: Familiar and new results on the correlates of teacher effectiveness

https://www.science-direct.com/science/article/abs/pii/S0272...

[2] https://www.businessinsider.com/third-year-of-law-school-is-...

https://forgottenattorney.wordpress.com/2013/02/01/the-usele...

[3] https://abovethelaw.com/2017/05/teaching-you-what-law-school...

It's likely pretty easy to measure that lawyers from professional law schools win more cases than self-taught lawyers. Or that doctors from medical schools have higher patient satisfaction / produce higher average QALYs in their patient cohort than self-taught doctors.

I think a more closely analogous question to the one of CS vs SWEng might be: if a group of psychiatrists (professionals) and psychologists (academics) switch places, who performs better in the other context?

The psychiatrist is an MD who can prescribe drugs. The psychologist wouldn’t have that kind of authority, so they can’t do the job of the former. A psychologist can actually do therapy, which a psychiatrist isn’t trained for. These are very different professions.

> Conclusions and Recommendations of the Interdivisional (APA Divisions 12 & 29) Task Force on Evidence-Based Therapy Relationships

http://societyforpsychotherapy.org/evidence-based-therapy-re...

> The therapy relationship makes substantial and consistent contributions to psychotherapy outcome independent of the specific type of treatment.

> The therapy relationship accounts for why clients improve (or fail to improve) at least as much as the particular treatment method.

Prof does a 'study' where they teach a class with both hands vs with one hand tied behind his back. Each class has 200 students, and he finds that the one-handed class outperforms the two handed class with p=0.045 with N=200...

And I'm like NO! This is basically an N=1 study because the teacher is common across both classes. Have you never heard of pen-effects?!?!?!

Unfortunately, fixing the problem in the study design means convincing a bunch of your friends that one-handed teaching might be better and engaging in an experimental study together... But that's obviously way too hard.

Fully, 100%, whole-heartedly agreed!

I'm leading a multi-disciplinary machine learning R&D team comprising multiple experienced Computer Scientists, Software Engineers and one Electrical Engineer who jumped from EE to SWE to ML research.

All of them are efficient in their own way, but the EE blows everyone else out of the water in sheer _effectiveness_. He may not be the strongest programmer, but his solutions have an elegant simplicity, take the right trade-offs and solve the damn problem.

The CS members are exact opposite: they care about the solution more than the problem, leading to hard-to-maintain / partial / sometimes outright wrong approaches. If they don't find the problem mentally stimulating, they redefine it to make it so, and then solve that problem instead.

Problem: display one point in an image

EE/SWE solution: calculate the xy pixel location and pass it to the renderer

CS solution: define a novel normalized coordinate space, so (0,0) and (1,0) are two specific locations in the image (not center, not corner, but two content-sensitive locations); for every image in the database, calculate a 4x4 "normalization" matrix to map pixel coordinates to normalized coordinates; now calculate a 4x4 "location" matrix with the location of the object in this normalized space; problem solved.

Note how this not only fails to solve the original problem, but it also creates multiple new ones.

Our team then had to point out that all of our user data, generated data, rendering code, user interface, user manual are standardized in pixel coordinates (_industry_ standard, with strict regulations), and that no, defining a new coordinate space, migrating terrabytes of data, and convincing the industry to switch over is not going to happen.

So yes, give me an EE/SWE problem-solver over a CS academic any day of the week!

What about tech debt? Are they writing shovelware or something? Over time, as requirements drift, how do they even know their stuff is way off of being a reasonable solution?

CS doesn’t even start to scratch the surface of reasonable solutions though. CS programs don’t teach you anything about architecture, technical debt, testing, source control, bug tracking, etc.

Bug tracking you can learn in a day. It's more about which tool your company is using than anything fundamentally difficult to understand.

Source control you can learn in three days, and I was (briefly) introduced to git in my CS degree. How source control systems work under the hood with diffs, Levenshtein distance, etc. -- that's the kind of thing CS covers. A CS major understands source control way better than someone who's just been using it for a while.

Testing is more of a habit or practice than a subject to learn about. And you absolutely learn to test your own code if you don't want to fail your assignments, because the professor sure is going to test it.

"Technical debt" is a communication term that was invented to help business people correct misconceptions about how software engineering works. If you mean they don't learn how to make maintainable software, I agree that's not a focus. Maybe it should be. But of course nobody in the industry seems very good at that either.

"Architecture" is a tremendously vague term. Are you talking about large-scale, multi-system architecture? The MVC architecture? A web tech stack? Most of those things are either just putting together things you already know, or a subject that you can learn about in a CS degree if you want.

No you can’t. You can learn how to use a specific bug tracking tool in a day. That’s not related to learning how to write/use/organize/prioritize bugs.

This is something that all of my junior engineers sucked at at Google and it took months of prodding to get them to write useful bugs and years before understanding how to prioritize bugs.

> Source control you can learn in three days, and I was (briefly) introduced to git in my CS degree. How source control systems work under the hood with diffs, Levenshtein distance, etc. -- that's the kind of thing CS covers. A CS major understands source control way better than someone who's just been using it for a while.

This is completely wrong. Knowing how a diff is generated is completely useless when learning how to use git, perforce, whatever. 99% of learning source control is about the concepts of that particular tool and how to manipulate them (e.g. branching, rebasing, squashing, merging, cherry-picking, etc).

> Testing is more of a habit or practice than a subject to learn about. And you absolutely learn to test your own code if you don't want to fail your assignments, because the professor sure is going to test it.

This is what someone who knows nothing about testing thinks testing is. Running code before you submit it is a specific type of test, and it’s a pretty bad one. Making code testable involves architecting your code in specific ways and knowing when to use fakes, mocks, functional tests, unit tests, fuzz tests, performance regression tests, etc.

To claim it’s just a habit or practice you follow just right before you submit is a joke. This is one of the hardest thing to train new grads on when they join a company. Part of it is they have notions like yours implanted by completely out of touch CS professors and grad students.

>Technical debt" is a communication term that was invented to help business people correct misconceptions about how software engineering works.

CS doesn’t teach people how software engineering works either. That’s the point.

> Most of those things are either just putting together things you already know, or a subject that you can learn about in a CS degree if you want.

No, you cannot reasonably learn about these things in a CS degree because they are completely uninteresting from a CS academic perspective so the professors don’t care about it. A professor who teaches you about the lambda calculus is just as qualified to teach you about making a maintainable and scalable service as the professor who taught you newtons calculus.

The whole point is that CS only has a small intersection with writing software at the leading tech companies and an even smaller intersection with writing software at normal businesses. It’s useful for distinguishing between new grads but it’s garbage compared to industry experience.

I say this as someone who got a phd on the CS side and then went to Google. They are just completely different universes.

By "problem domain" I mean the things that impose constraints — for a structural engineer, that'd be e.g. building materials, soil, weather, etc. The things that have tolerances.

By "solution domain" I mean the space of human ingenuity that we can apply in our designs, in order to make something possible that wouldn't be possible with a naive approach. For a structural engineer, that's things like "suspension-bridge cabling" (more general principle: tensegrity) and, I dunno, "flying buttresses."

The problem domain of building software — the parts that impose constraints — are things like what factors lead to robustness (or lack thereof) of a language runtime under production load; programming-language error-rate as a function of language-syntax UX design; evidence-driven software project scope analysis; the trade-offs involved in attempting to scale a process horizontally vs. vertically; the effects of state on ability to scale; etc.

Someone who understands these things knows how to engineer software, the same as someone who understands material tolerances knows how to engineer a structure. If they only know that, then they can't draw you a building (that'd be an architect) — but they can take that architect's blueprint, and tell you whether the building described by it will fall over, and whether there's any simple thing you can do to solve that, or whether you need to draw a different building.

But note that you learn the solution space naturally, over time, as you're exposed to the solutions people use in the field. A machinist will learn the tools of their trade as they run into them in the shop, and as other machinists demonstrate them, and as books refer to them, and as job-lots demand them. None of this requires academic rigor. It's just learning on your feet.

A SWEng might not be aware of the academic result proving some more-optimal data structure exists for something. Just like a machinist might not be aware of a not-yet-commercialized maser CNC lathe. But they don't need to be, either. Very rarely does solving novel problems require novel tools. You can build the part you want to build with the machines you already have in your shop, and maybe one new one you buy off eBay. You can write the code you want to write with your not-so-optimal data structures, and maybe one new one you find in an ecosystem library.

Every once in a while, getting things done might require you read a journal paper written by an academic. But let's be very clear: it doesn't take a degree in some field, to be able to read — and make use of! — journal papers from that field. We've got educational vloggers — people who perform on camera for a living — operationalizing stuff they saw in journal papers all the time! If they can do it, a professional in an adjacent field to the academic discipline can certainly do it.

It's surprisingly how little actual fundamental, theoretical Physics you need to know to do Physics! I'm not saying it's not important, the point of being a Physics major is not only to train you to be a researcher, but for the sake of the knowledge itself.

It's very similar to CS in that regard; almost none of formal CS is useful when doing software engineering, and when it is useful, the skills are in knowing to recognize a problem and how to research it, just like Physics!

"Computer science" is a term that no longer fits the mental model of the general population's idea. Basically nobody is thinking "Computers? Of course! You mean the lambda calculus, Turing machines, how these theories relate."

Most People are thinking about about the internet, websites, games, apps, robots, and so forth. Indeed one can build all these things without any concept of how busy a beaver really is.

Then you have a smaller subset of people who (allegedly) understood what "computer science" is from the outset, and they turn their nose up at anyone who misunderstood what this "Computer science" was. Even worse, they often feel somehow superior. How dare you be ignorant?

Practicality and value: these things can exist outside the realm of dense theory. Anyone who says otherwise is trying to feel better about the years and/or money spent on a very challenging and painful degree.

It is like the difference between a person who pours concrete foundations, and a person optimizing concrete formulas. Society needs both, but the skill sets are different.

I did take design patterns classes and such in college, but imagine taking 200,300, and 400 level design patterns classes and learning how to architect scalable systems in the cloud or on-prem.

Of course there would be programming classes too, but I think there's some room for a program that I'm imagining. Boot camps don't cover the engineering and architecture parts so it would be somewhere between a bootcamp and a CS degree where you're writing operating systems and big endean and Big O notation

You are right that these people will have a hard time later. What also needs to be understood is that paying attention to something in which you have no curiosity is hard. I never paid attention to Maths / Stats / Probability and now I am having a hard time trying to learn machine learning / AI. But now my curiosity for these technologies is dialled up all the way to 9 and in my free time, I am relearning all these concepts I missed.

And what I have discovered is that these concepts were easy. The university presentation of it was done without any motivation. It took a useful and easy subject of math and made it hard.

Amen!

I like the way you have worded this. In particular for first-year math courses, they are super useful and should be seen as "basic science literacy" and much more people should have access to this knowledge (not just people who take 3-4 years of courses in a STEM major). I've been working on products to make this happen. Links in profile.

The "basic science literacy" I can see everyone benefitting from (in particular devs): (1) math modelling skills from high school math functions, (2) vectors because EVERYTHING, (3) PHYS101 (mechanics) for the predictions-using-models skills, (4) CALC for understanding concepts of rates of change and accumulations, (5) PROB because important building blocks for modelling data, and (6) STATS so you learn how to infer model parameters from data.

It's not a coincidence the above list of 6 are part of most UGRAD degrees (either in first or second year). These are the basic tools that everyone benefits form knowing. I am really enjoying the "unbundling" that is happening of the basic science literacy teaching and the credentialism.

This totally depends on what type of engineer you want to be. It's quite possible to be very successful, have a great career and make a ton of money as a software engineer without ever tackling problems that are "hard" or "new".

What you call “shallow”, others might see as “practical”.

It’s possible that this person has chosen study path that isn’t the right one for them. That’s a tricky spot to be in especially in these times. I suggest a little more empathy, and a little less venting.

Oh… I just need to know the basics? Damn, such a great use of my time.

CS degree in a nutshell.

Usually I find proofs are what you bring in the consultant for.

I'm not going to hand on heart vouch for anything like that as a generalist.

Combinatrics, Big O and set theory absolutely. Everyone is far better off with those.

1. The definition has no bearing to what's happening in the real world, or

2. "Computer programming" ceases to exist as a productive activity and you need to invent a new name for AI-assisted programming.

Oh, and there is nothing tautological about it, at least as far as most programmers seem to work.

Pretty sure you missed a couple news articles recently...

https://news.ycombinator.com/item?id=30179549 https://news.ycombinator.com/item?id=27676266

They're not exactly reliable, but you probably could say the same for the earliest compilers (from programming languages to asm/machine code).

I'm not saying they will definitely be usable in the short term future, but that future is probably coming sooner or later, and I don't think a fragile definition (programming==="applied formal logic") is worth reiterating over and over again as if it were some fundamental truth.

If I'm reading them right, urthor's point is that the average programmer doesn't directly benefit from being skilled in developing formal proofs about code. (I rambled at some length on this topic recently. [0]) Very few software development workplaces value correctness so highly that they invest in formal methods.

That said, I think the case can be made that learning about formal methods is useful in instilling a sense of how rigorous software development can be, and perhaps to develop a healthy contempt for hand-wavy sloppiness. Perhaps it's also helpful to learn that informal requirements, formal specifications, and implementations, are three different things. I think this may be true even if we rarely use formal specifications in practice.

[0] https://news.ycombinator.com/item?id=30000146

If we could strip out of reality the bits that can be understood as a practical application of the basic branches of math there wouldn't be anything left. Nevertheless most people get a long way in life without needing to engage with that (which is lucky because there is too much to learn in one lifetime).

Looking at code as applied formal logic is not a useful view outside of some rather obscure communities. Even code as a recipe is more useful view in practice.

But that is almost the polar opposite of treating a program as applied logic. If there is one thing that is not reasonable when dealing with logic, it is "proof by multiple test cases that seem to work, I think".

And I don't clear the low bar for de Morgan’s laws, I've completely forgotten what they are. And on looking them up, that doesn't look like an important component of programming. A programmer could reasonably get away with not knowing them. Probably going to learn them by rote over a few years, but that is hardly "applied logic" in any sense that is worth talking about.

If people came for the science, everyone would ride off, discover something, and get a PhD.

I just see formal proofs as something you get a genuine scientist to do. If you're someone focused on rigorously correct proofs, you get a rigorous PhD.

I don't pretend that I'm up for that, or that I'm qualified to produce quality work in that space.

But I also don't believe any of my fellow terminal undergraduates are the right sort of people to do this work.

Let's face it, we all had a close encounter with the mathematical proofs, and ran in the other direction as fast as we could!

A lot of modern entry-level programming is the same as builder-work... take a brick, take some cement, spread the cement, put the brick in the right place, and in the corners, cut a brick to size. Yes, sure, we need a lot of those people doing random programming jobs too.

But, if you want to build something bigger than a doghouse, you also need a lot of math and calculations, before you even touch the first shovel, to calculate if the whole project is even theoretically feasable. Stuff that works in low scale, sometimes breaks horribly, with larger amounts of data, and i'm not talking facebook scale, but going from 10 to 500 users. If you want to go higher, things become even more broken for someone who just "lays bricks", and a lot more thought and math is needed to make things actually work (and scale).

I'm sorry to break it to you, but your personal belief on the virtues of ivory tower feats doesn't hold any water in the real world. At all.

The most important competency, by far, is being able to onboard. Whether it is onto projects, frameworks, programming languages, architectures... Being able to jump in and get up to speed and fix things and implement features is what matters.

No one cares at all if you know an algorithm by heart. Plenty of critical services are built upon crude O(n²) brute force implementations that are good enough, and no one bothers to waste 5mins to even switch the underlying container.

You're talking about a field where premature optimization is recognized as one of the worst and most fertile sources of problems. And who exactly is behind this problem? Precisely these short-sighted theorists, who believe big O musings has critical importance when it has close to none beyond superficial analysis of "should I use an array, a linked list, or a hash set"?

I know people with a boot camp and experience with a framework who landed jobs in FANGs, and I know PhDs in computer science that can recite inconceivable algorithms who can't get a job in the industry. How do you explain that, if waxing lirically about computer science is supposedly so critical?

Also, runtime analysis isn't that difficult of a skill to pick up.

Runtime analysis isn't that difficult of a skill to pick up if you have a decent university-level math background. You can be a productive programmer without that.

It's a really narrow mindset to put math specifically on a pedestal. A lot of hard problems with computers don't involve heavy pure math. A lot of those problems get categorized as "software engineering" and as such it is often claimed not relevant for "computer science". But given the importance of software in today's world, academic institutions seem woefully disinterested in setting up "software engineering departments", and woefully disinterested in promoting "software engineering" degrees as an alternative to the typical CS degree as a entry ticket towards a software engineering career.

You must learn this (mostly) useless skill to do enter a profession that where you're probably not going to use the skill. It's classic gatekeeping.

You might argue that research universities are not supposed to be vocational colleges, but that's a hypocritical lie too -- they basically have to be, otherwise they'd be out of an important source of funding (tuition). The existence of bootcamps are evidence that these fancy "math" people pretending to be computer scientists are basically incapable of teaching anything useful to people wanting to learn to program computers. If bootcamps are so trivial, why couldn't universities offer (for example) summer courses that do the same thing? We're not talking about CS majors here -- we're talking about non-CS non-math majors who might want to learn more about programming. Is it reasonable to force feed them CS type pure math as well ? (read the parent posts again -- Quote: 'I went to the University of Waterloo and took a "Intro to CS for non-math students" course.'

Physics majors are called physics majors, not "telescope science" majors. If there's a "telescope science" department I expect them to teach, in addition to theoretical physics, practical courses on how to operate telescopes. My not so humble opinion is that CS departments are a misnomer, but they kept the name because CS degrees are popular, the field is flush with research moneys, and they're happily eating the profits from the software engineering cake while having their math cake too.

The pure math specialists in CS departments churn out starry-eyed students who in turn perpetuate the myth that CS is (only) math, and the impression that hard problems in software engineering is not a worthy intellectual endeavor for a research university. This attitude is going to hurt us in the long term. No amount of strawman arguments about ReactJS bootcamps is going to change this fact. Those bootcamps are evidence of a total failure of academic institutions to actually do research on and teach software engineering.

------

In case it matters, I learned all those Big-O and algorithms shit in high school, and I'm not criticizing it based on ignorance of what they are and how useful they are. If anything, those concepts are too trivial to deserve so much "screen time" in the curriculum. I have friends who work in CS departments and publishes on FOCS (you know what it is, right?) etc. I'm reasonably informed about what I'm talking about, and I'm aware that many CS researchers just happen to like to research on math-ish topics (which is of course not their fault). But what I'm trying to say is that there is a fundamental, institutional problem with people snobbishly brushing off real world software engineering problems as if they are somewhat inferior. Get off the high horse already. You don't really need to learn the concepts of limits of sequences to infinity to count 3 nested for loops and know that maybe it will be slow for large inputs. Math will actually not tell you how slow it will be -- FYI sizes under 100 is usually acceptable for O(n^3). Claiming that "trust me, this math thing is so much more fundamental" is a really poor excuse for teaching (mostly) irrelevant concepts while pretending the degree is relevant to industry.

And yes, I don't have a CS degree because I already saw through this bullshit 20 years ago when I was in high school. I made sure to learn the stuff I needed to know and skipped the kool-aid. Got a degree in law (it's an undergraduate degree here), and surprise, I actually learned a few things about law -- and they didn't shove pointless math down my throat. I mean, if they wanted to, they could model precedents as an directed acyclic graph and make a couple theorems out of it, right?

Your claim about gatekeeping is later contradicted by the fact that you actually didn't have to obtain that degree at all. I didn't have to either.

I do agree that "Computer Science" is a somewhat misleading name though. It's pretty much as if we called astronomy "Telescope Science" and then wondered why people that come studying it expect to learn about building telescopes, with others arguing that you need to know a fair share of physics in order to build a good telescope anyway (which of course is true, but...).

And biology is just self-replicating organic chemistry.. and chemistry is just the physics of outer electron shells.

No it's not about react or ror.

It's about solving actual real life problems. 99% people don't do CS to do academical research, but to work on life change products(and that's more likely to come from user research and fast prototyping, than from theoretically perfect fundamental research).

Some people build millions dollars software products, solving real life problems, without having a clue what big-O, quadratic functions, or even a lot of actual theoretical programming concepts are. And I personally know a bunch of those people. Some people know almost everything there is know about CS theory and never build anything useful to anyone.

Physics have literally nothing to do with CS or SWE. I think this is just pointless elitism.

Personally, when I chose electives I chose systems electives: Operating Systems, Databases, Networks, Programming Languages, Graphics, etc. In these classes the bulk of the work consisted of programming in C.

I suppose it could be systems if you are building a compiler or vm, but that to me is different that programming languages.

You had an (mostly theoretical) Automata and Formal Languages course, which had regular/context free languages (including regexs), grammars, and pumping lemma. lex/flex/yacc/bison, recursive descent, and LL(1) LR(n), LALR were in a Compilers course. Programming Language exposure to a functional language (ML) and a logic language (Prolog) plus some other stuff was the Programming Language course.

Type Theory, lambda calculus, and so on is relegated to advanced graduate courses that are given when a faculty member feels like it.

The theory and practical realms are very tightly intertwined in programming/computer science/whatever you want to call it as long as it isn't "information technology".

On the other hand, the portion of "math" that is applicable computer science/software development/whatever is pretty distinct from much of the "math" in math departments.

-- https://en.wikipedia.org/wiki/ML_(programming_language)

The goal is to be able to efficiently solve non trivial problems.

-- https://www.cs.utexas.edu/~EWD/transcriptions/EWD10xx/EWD103...

Some comparisons are just literally true, for example Honda vs Acura is the same as Lexus vs Toyota. Their both high end car brands owned by a parent company that also puts out mass market cars. That’s a description of strategy not trying to extract meaning from caparison between dissimilar things.

Anyway, a farmer can build a shack without talking to a structural engineer, and a banker can muddle through coding an excel spreadsheet. But trying to muddle trough via trial and error isn’t enough to build the Burj Khalifa or a modern OS. Thus we want to use formal methods to minimize risks, costs, etc. That’s what gives rise to CS and engineering disciplines, not simply trying to staple math onto a field.

The course described doesn't seem to match your description of comp sci either.

Which matches my experience of a technical course in Waterloo. They need to update their pedagogy.

I agree simple math problems may not be the best exercises to program, but the point is you should be doing a lot of such specific (but diverse) exercises to get the general idea.

I think that some of the paradoxes of CS vs programming have to do with a single academic discipline trying to serve conflicting needs, such as:

1. Teaching programming to students who have never programmed before. This is handled differently by different fields. For instance math majors are expected to have a fair amount of high school math in the bag before starting college, but psychology majors have rarely taken psychology in high school.

2. Students with an actual interest in CS itself as a field of study.

3. Students who know that they want to get a college degree in something but are hoping for a career in programming.

4. Competitive students who know that CS is the "hot" major right now.

And high school guidance counselors are pretty much in the dark about it. On the other hand, every college major teaches you more stuff than you will use at your first entry level job. "Why do we need to learn this" is a constant refrain. For instance most engineers will never use their college math after college.

For me, way back in 1982, I skipped CS altogether and studied applied programming by majoring in math and physics.

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.

They’re not math degrees, and neither is CS. The emphasis isn’t math in a CS program at any reputable university; the emphasis is computer science.

When you say, "the emphasis is computer science" what exactly does the term "computer science" mean to you? I'm not trying to be a jerk here. I think the term "computer science" covers several related, but distinct, disciplines so it's helpful to know exactly what the other person is referring to.

General electives like a math major having to take a literature course is very different from a core required piece of the major being literature.

to be frank that doesn't sound like a very rigorous school for computer science... that sounds more like an information science curriculum instead of a proper computer science one. I'm talking university of california style learning or the equivalent.

Oh give me a break. CS 122 from UCI is exactly a “select * from users” kinda class. Sure, it has some sparse elements of theory sprinkled in, but pretending it’s some form of math class is outrageous.

But then UT Austin may not be a reputable university, computer science-wise.

[Certainly, they've redone the curriculum since I was there, and I don't like what they've done.]

1 of these things isn't like the others.

There are places where theoretical physics and applied math are put together, and places where CS is put with math.

Upstream comment mentions Waterloo, where CS is as far as I know still part of the math faculty (e.g. multiple departments), not engineering. In that specific sense, every CS degree they give is a math degree - but other places give B.Math also.

This isn't just pedantry, the reason is that the boundaries are pretty fuzzy, and don't really work with the sort of absolute line you are hoping to apply.

Except that those details seem to require a considerable amount of work.

The third category is mostly, if not all, implementation details. The fact that this is most of the work doesn't change that. I'd argue that most of the second category is implementation details as well.

You also compared CS to physics and chemistry which is a bad comparison. Physics and chemistry don't have an equivalent foundation to theoretical comp sci. I'd also argue that comp sci isn't a science at all. What I do on a daily basis as a programmer is closer to plumbing than it is to science.

Either that's not true, or there are an awful lot of physicists and chemists out there wondering why they took so many math courses.

But my experience was that you can get a long ways into a Computer Science degree before anyone tells you that you're studying the wrong thing for career prep. It reminds me of a student I saw who was in Electrical Engineering because he wanted to be an electrician. The university was happy to take his money, and nobody told him he was in the wrong place.

It's important for teenagers to have guidance when choosing the educational path that's right for them. I know that at 17 I was extremely ignorant about Computer Science vs Software Engineering vs Computer Engineering. They all sound the same when you're inexperienced, just know you like computers, and don't know anyone who understands the difference.

The truth is computer science is the science of computation not how to perform specific computation. General CS education follows the line of most STEM degrees, minus the degree for more advanced math like PDEs except when you're in a specialized scientific computing sub-degree. We all had to take 3 semesters of calculus, 2 semester of discrete math, and one semester of probability. ALL of these are important to various fields of CS.

Programming is rarely discussed. Most ABET programs give you one to two semesters warm up and that's the last time you see programming except for a few elective courses. Programming is a means to an end for a CS major. Once your algorithm is verified mathematically on paper you head over to the terminal to implement it and play around. Programming first then designing is like a mechanical engineer building a car and then drawing the blueprints.

The vast, vast majority of computer science even today can be done on paper (with enough paper, of course). programming is a means to an end. If you want to be a programmer get a job out of high school because it takes virtually nothing except drive to succeed. Getting a CS degree for the purpose of being a programmer is like getting a mechanical engineering degree to be a machinist. Sure, you can do machining. Just like you can do programming as a CS major. But the CS degree is so, so, so much more than programming.

Everything your daughter is learning w.r.t. math, logic, proofing, etc is CRITICAL to the generalization of ideas into algorithms that are language and implementation dependent. A mathematically verified pure algorithm can be implemented anywhere, by anyone, at any time not unlike a complicated math formula. This is why the weed out is a good thing. People who just want to be programmers leave the program and become programmers. No sense in wasting time in a CS degree if your aspirations are to become <language> expert.

Programming is secondary.

Source: Comp Sci major

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.

(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_.)

My current take is that the tech industry is so young that we are still struggling with proper definitions of titles and division of labor.

In my experience, after school I could do all the hard mathy/algo/data structure things, but I had no idea what REST even meant. So all startups instantly rejected me, while FAANG was very excited to have me. I felt like a huge imposter also, because if I were smart, how come I didn't know all the cool stuff that people at hackathons know.

When I graduated I had no clue how to correctly statistically validate a complex robotically collected set of bathymetric data or how to mathematically explain Universal Kriging. But I did know how to design and build the data collection workflow, web portal, processing software, and PDF generation. So I was ridiculously effective at my job, but any time I was near the other roboticists, I felt like an absolute fraud. They'd be writing algorithms and formulas on a whiteboard and it was all Greek to me.

You can make something, and

You can engineer something.

If what you are building is a complex distributed software system, if you are not aware of algorithms and the implications they have on the system, then you are not engineering, you are just making. And whatever it is you are making is going to fail a lot sooner that if you were aware of the algorithms and the implications.

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...

Yes, when we truly understand "competence".

A lot of "math" as talked here, is not part of what make a programmer competent FOR programming.

It only make you competent for THAT segments of math.

That is something that many has a hard time understanding: Programming is NOT math. Equally as math is NOT programming.

If you are studying FOR programming/CS, math is ASIDE. Is not the focus.

Similarly, if you are FOR math, programming is ASIDE. Is not the focus.

Basic algebra is quite useful. It's reasonable to expect most programmers to be able to do simple algebra when it comes up. There's a whole lot of reasons:

- Analysis of algorithms and work done generally involves manipulating algebraic expressions and factoring.

- Reordering numeric expressions in code means understanding the composition of operations and invertibility.

- A whole lot of work can often be avoided by being able to derive an equivalent expression.

Yes, continuous math isn't "CS math" but it's a reasonable thing to expect a programmer to be competent in.

Similar, Perform music is too. And learn about accounting. Or law.

But IS still "aside". Sometimes, here in THIS function, I need to apply to algebra. But that is not the majority of the tasks, neither, learn algebra help me much about the whole endeavor (maybe only if I'm building an algebra library).

> but it's a reasonable thing to expect a programmer to be competent in.

Any person too?, maybe. I heard identical arguments in other fields. No joking, even in a law firm.

Curiously, by people that probably are better at THAT that the actual problem they have, in their niches, where -despite not be my job- I could have better idea...

Sorry-- I completely and totally disagree with you. The core things I learned about mathematical structure in algebra classes have informed my entire programming career: pure functions, commutativity and associativity, factoring and composition. Both discrete and continuous math are necessary to be a computer scientist. Yes, you may be able to do some things without them... but you're going to be limited.

> Any person too?, maybe. I heard identical arguments in other fields. No joking, even in a law firm.

Algebra is basically required for a secondary education at this point, let alone college. Yes, it has broad applicability. Even in law: we expect many lawyers to be competent at calculations that are best addressed with algebra.

Sure, but CS is still about "Computing", not algebra or calculus!

They also offer a lot of "math for non mathies" courses, which would have been a great place to teach quadratics.

Imagine if you had been given an exercise of such a low level nature for every single topic you might touch in IT in the future. You would have had to code a function to do UTF8 decoding, JPEG rendering, TCP/IP error correction, font rasterization, ray tracing, PEG parsing, an USB driver, data diffing, model training, etc.

Also, you don't learn much about programming by creating a function to factor a quadratic equation. You seldom learn about types, side effects, algo complexity, or even about collections, iteration, branching, memory, debugging, etc.

You just learn to badly translate a very specific, narrow problem to the language you use.

Actually, I have, because I've done a fair bit of embedded development and "toss this massive lib on" is not always a reasonable solution. Inferring the structure of plant in controls is often a polynomial factoring problem and it's not something that one tosses Singular or FLINT at on small hardware. But aside from that...

Factoring a quadratic by hand is something I expect a CS major to know how to do, because they might very well be doing algebraic manipulation to develop solutions to real world problems.

And someone who knows how to factor a quadratic by hand knows a number of formulaic (suboptimal) steps to perform it-- the exact kind of things that's easiest to translate to code before you have gotten into that mindset of explicit thinking.

So--- declare and manipulate variables to do the quadratic formula. OK, what if we want to confine ourselves to integers, what can we do? Can we loop and search solutions in some meaningful way like a human would?

It's a completely reasonable space to explore as an early programming problem for someone who's familiar with it.

I'm teaching a secondary student to program right now. In his core math class he's doing a lot of trig. In turn, we're doing a whole lot of exercises like "make these dots chase the other dot using atan2 and sin/cos".

Can't argue there :)

> Factoring a quadratic by hand is something I expect a CS major to know how to do

Agreed, I'm more concern about teaching programming while asking such a task. Once you have solid foundation, you can have valuable insights by doing this exercise about float based maths, moving variables around, naming things, translating maths to code. But before that, I think it would hinder learning.

> And someone who knows how to factor a quadratic by hand knows a number of formulaic (suboptimal) steps to perform it-- the exact kind of things that's easiest to translate to code before you have gotten into that mindset of explicit thinking.

I disagree, because it takes 2 abstracts things and mix them together. It's a harsh first step. As a teacher, I get better results when I map coding to some concrete reality first. Later on, yes, you can mix.

> I'm teaching a secondary student to program right now. In his core math class he's doing a lot of trig. In turn, we're doing a whole lot of exercises like "make these dots chase the other dot using atan2 and sin/cos".

This is what I'm talking about. I have terrible results with those for anybody who doesn't really love maths. But creating small games and analysis the text of their favorite song are instant hits.

He def doesn't love math. But he just finished the swarm thing and it's awesome.

A quick search tells me that factoring quadratic equations is covered around grade 8 or 9. I'm guessing that the instructor assumed that everyone would have enough math to know how to do this or quickly refresh their memory so they could focus on the programming aspects and not the problem solving.

It is not totally unreasonable to expect students in an intro to CS course to have some basic competency in algebra (university dependent). Giving them a problem in a domain they're already familiar with (or that where familiarity can be expected) lets them, in theory, focus on the algorithm/data structure side without having to also be taught the domain. Most of the exercises in a first CS course are solved with libraries (standard in some languages, or 3rd party in others). That doesn't mean it's not useful for developing the knowledge the course is aiming for.

Do you also think we shouldn't teach arithmetic and should only teach using calculators? (You may, actually, I know people who think that way.)

Besides, most intro to CS courses also include basic algorithm analysis (that may not be true for the non-major version of the course) which means the course will require the use of at least arithmetic, probably some algebra, and some basic calculus. So why not write programs that make use of math when you're already assuming the students are competent in basic math?

At least at the universities I was familiar with, a non-major first CS/programming course was generally targeted to STEM, but not CS, majors, so again familiarity with algebra would be a reasonable assumption (at GT, these were taken by the various engineering majors and used Matlab as the language of instruction, I think they previously offered Fortran).

I feel like I'd be more on board if you said something like "compute an integral", etc. Factoring is just.... a single equation.

I've been a successful software engineer for over ten years, yet without looking it up, I don't even know what "factoring a quadratic equation" means, let alone how to do it.

Code refactoring and factoring in algebra are related in the sense that they aren't meant to change the system (that is, its meaning or behavior), but instead are meant to change its appearance. In particular, in the above, if you can factor it out you end up with the two roots (what I termed r_1 and r_2) of the equation, which are useful for various other things.

This is hard to understand because it doesn't make sense. Quadratic polynomials (or more generally, algebraic expressions) are factored. Equations are not factored.

x^2 + 2x - 3 = 0 = (x+3)(x-1)

This is not factoring?

The idea that you might not know how to do it as someone working in a STEM related field wouldn’t come to me.

I think this very much depends on what you end up specializing in. I bet a lot of the code we write every day has a dependency buried somewhere where all sorts of equations end up getting factored.

Both statements can be true, but neither negates the utility of the activity.

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.

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

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.

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.

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.

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...

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.

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.

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.

Unless I misunderstand what you're saying here, it really is intended. "Top schools are assessed on their graduation rates" so if they don't admit students that will not graduate from the major into the major in the first place, they improve their graduation rates. Therefore, it does serve the school. And it probably serves the student too, since they only spend a quarter or two getting weeded out, rather than a few years and then hit a dead end.

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.

"Linear Algebra for Engineers" is a bit late for an early filter class (Generally Calculus 102 or Physics 101/Chemistry 101 are those filter classes) and too early for a field filter class (ie. Thermodynamics, Electrodynamics, Organic Chemistry). Normally, linear algebra is a class in second term sophomore year (The sequence is generally->Calc 101->Calc 102->Intro to Vector Calc->Linear Algebra).

There are a couple of issues:

1) Never take the engineering version of math, physics, etc. if you want to learn. Engineering version of classes tend to emphasize "plug and chug" more than underlying understanding. The "math" version of linear algebra would presumably be pointing toward vector and complex analysis rather than PDEs and numerical analysis.

2) Linear algebra takes an AMAZING teacher to make relevant and interesting. Applying linear algebra is kind of like pointers to pointers in C--there is an extra layer of abstraction. Linear algebra is applied to something that is then applied to the application domain. Linear algebra is rarely the solution, itself.

3) Linear algebra really isn't a class to take without knowing why you are taking it. Motivation is significantly better if you've got something concrete you can apply it to.

Not that you put banana peels in front of the students (like problem sets with no exercises). As it to discourage them for the sake of discouraging them.

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.

It's intentional.

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.

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.

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...

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.

(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.)

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.

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.

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."

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.)

Princeton in particular prides itself on being focused on the undergraduate experience compared to other research universities. Research is (supposed) to be secondary.

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.

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.

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.

If you are learning proofs, it is going to be a bit of a slog in the way that CS50, etc. can avoid.

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.

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.

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?

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.

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.

Which, it turns out, is sufficient for the vast majority of engineers and scientists.

On the other hand, you cannot conclude from one case that math teaching is broken.

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.

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.

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.

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.

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.

Quant background coming out of high school? Good grief.

Hopefully they make that clear to all the naive students before they sign up! :-)

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 :-)

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.

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?’