[angry_moose]

Man this would have been nice when I was in school.

For some reason linear algebra still isn't part of standard Mechanical Engineering course load (Calc 1, 2, 3, DiffEq) which made life extremely difficult in some of the later classes. I remember spending weeks brute forcing a lot of things that would have been trivial with a little bit of matrix math.

I took a superficially similar class as a 400 level elective but it assumed everyone already knew linear algebra going in, and it was a disaster.

[BeetleB]

> For some reason linear algebra still isn't part of standard Mechanical Engineering course load (Calc 1, 2, 3, DiffEq)

Wow. In my undergrad all engineering majors had to take linear algebra (calc 3 was optional for computer engineering).

[caspper69]

This would have helped me get an actual CS degree 25 years ago instead of CS-lite (networking & server admin).

It's not that I can't do calculus, I took it in high school, and then again in my first go-round in CS. It's that I hate calculus. Not the subject itself, just the grinding away at problem sets.

I did a refresher in pre-calc, calc I, calc II & discrete mathematics during COVID at the local community college (was planning to finish the few credits I need for an actual CS BS) & I started calc III twice (but dropped both times). I even got a 4.0 on my first calc III exam (and this was an in-person class, so no online shenanigans).

I just have some kind of weird aversion to 3 dimensional calculus. I have convinced myself that I'm simply not smart enough to actually do the work. I understand it, I just get clammy with it.

Truth be told, maths are my kryptonite. Despite working with numbers all day every day for 30+ years, and writing a lot of software over the years (and not just CRUD, but games of all things), I am absolutely ashamed that I just can't seem to grok math with any rigor.

I have all the Stewart textbooks on my shelf, many textbooks from libgen (ones I've seen recommended on HN from people who went to much better universities than I attended), and I even work through problems a few hours per week. I just can't seem to make that leap from a guy who's "good with numbers" (from a layperson's perspective) to a guy who's good at math.

Maybe I need to break open one of my physics textbooks and actually use the calculus in an applied context and that will break whatever mental barrier I have (I've even watched all of the 3 blue 1 brown videos, countless youtube lectures, etc).

[casey2]

A few hours per week simply isn't enough, the best success I've had studying was 6 hours a day, resting for 3 (leisure activity), "working" for 3 (class, commute, chores, related reading) and sleeping 12 hours.

In books like Stewart, staring at a theorem until you can write it's proof should trivialize most problems in the book.

If a method for solving a particular problem is too difficult for you maybe consider researching and/or inventing some new method to solve these problem. People created these methods in the first place because earlier methods were too tricky

Or just focus on work that doesn't require hundreds of hours to gain proficiency. As long as you have time every day to stop, think, and come up with an idea that solves a problem you won't become intellectually unfit.

[jamesliudotcc]

Maybe your problem is Stewart? I used that textbook and was successful, but it's not for everyone. For example, beginning calculus with limits is another bit of misguided conventional wisdom. I still don't get limits, really. Serge Lang's calculus book takes the approach to just roll with an intuitive notion of limits, saving rigor for analysis. Which seems better.

Gilbert Strang has a textbook, also more intuitive and applied. Free PDF provided by MIT. Sylvanus Thompson's book is recommended here, again, intuitive, applied.

Other comments here, 3 hours isn't enough, use Math Academy, nobody gets it on the first approach, all seem relevant. One of the textbooks recommended here says in the preface that it's for a second course in Linear Algebra. Analysis is just calculus the second (or third) go round, and it's said to be the hardest class in a math major.

I am in your boat, but about linear algebra instead of calculus. This is what I try to get myself over the hump.

[caspper69]

Thank you. I appreciate the feedback and the pointers.

[caspper69]

I honestly don't think the problem is the textbook.

I have Stewart (both the standard version and Early Transcendentals), and I also have a book from 1967 by Tom Apostol (the 2 volume set that covers single & multivariable calculus, linear algebra, a subtle introduction to differential equations and some probability as well).

My gut feeling is that I just don't know the correct way to study math in general. I have no problem doing the work. But it feels more like mechanical or algorithmic solving than it does like true understanding. There is a difference. I can't deconstruct a problem and think in the abstract to come up with a different method to solve it.

And there always seem to be some fundamental truth that I'm always missing. A part of a proof here or an axiom there that seems obvious to other people who study these subjects that I just don't "see".

It's incredibly frustrating, because deep down I know I have the aptitude for this stuff. I guess that most subjects have always been easy for me. I could ace exams without cracking the book (or just skimming).

Math is not like that. You need to read. And then re-read. And then do. And then do some more. And then go back and re-read again to see what you missed. And there's a lot of things that are between the lines, and if you're not following it, those things fall by the wayside.

I just need to learn how to learn math. I need to learn how to deconstruct notation and proofs to truly understand them. And there's no shortcut. It's grind and grind until it all becomes clear. That sort of thing is just difficult for me.

[jamesliudotcc]

I feel what you're describing very viscerally. I have tried so many times as an adult to finally get linear algebra. Worked my way through Strang to eigenvalues and eigenvectors repeatedly. Still feel like I am failing to see something.

---

I hear Apostol is hard. Like Spivak-level hard.

[BeetleB]

> It's that I hate calculus. Not the subject itself, just the grinding away at problem sets.

Most math majors I knew hated the standard calculus courses, for precisely this reason. It's taught this way because they're targeting engineers and some hard sciences (physics).

The reason is that for many of those majors (EE, physics), you will take courses where doing calculus is your daily bread and butter. You need to be as adept at it as algebra. Over 50% of HW problems in those courses will involve calculus. They really don't want students who understand circuits but can't do anything useful because they stumble on calculus.

They are the largest "customers" of the math department, so the department caters to them.

[defrost]

I swapped out from being an Engineering major (consistently in the top 5 scoring Engineering students out of a first year intake of 300) to being a math major for similar reasons - Engineering has a lot of rote learning grind exams, not so much exploration of deep fundementals.

The Math dept has numerours courses loosely covering similar material, Math 100 - first year math for math nerds, Math 110 - first math for engineering students, Math 120 - math for business majors, etc.

Math for math majors ( the 100 stream ) had 20 students in all (IIRC) most of whom now hold academic positions, Math 110 had the 300 engineering students, other streams had cross over students from business, medicine, law, et al.

Future mathematicians (and theoritical physicists, etc) are indeed the smallest group the Math Dept. catered for.

[liontwist]

There are deep concepts behind multi variable cal. But if you just want to pass the course, memorizing problem shapes through practice will get you through calc 3.

Do all the homework problems check the answer in the back of the book. You’ll make it.

[caspper69]

One day, God willing, lol.

[downrightmike]

Maybe stop torturing yourself for a bit. Sounds miserable.

[caspper69]

Such is life. We all have regrets, and being sloppy and indifferent with math in my youth is a big one for me. If I had done it then, I wouldn't have to try so hard now.

[sn9]

You should check out Math Academy.

It schedules everything for you including the review so you just have to keep showing up to do the work.

Even as little as 30 minutes per day done consistently for months will have you make tremendous progress.

And once you master multivariable calculus, fields like probability and machine learning will be unlocked for you.

[monadINtop]

If by 3d-calc you mean vector calculus then yeah I never actually understood any of it, I just moved on to differential forms and the tensor calculus and Riemannian geometry and then wondered why anyone bothered with 3d-calculus in the first place.

Most of the time I've found that the deeper I plunge into abstraction in math I get rewarded with an extremely elegant formalism. Its like upgrading your weapon in dark souls, the early game enemies get one-shotted when you go back.

[angry_moose]

Maybe some schools do but it's baffling to me its not a universal requirement. It'd be dramatically more useful than Calc3 for most engineers.

Michigan doesn't seem to require it as the College of Engineering core classes or as part of the BSME (checked because they're who this course is through):

https://me.engin.umich.edu/academics/undergrad/handbook/bach...

And my alma mater has a very similar progression.

[Sanzig]

First year linear algebra is a requirement in Canada for national accreditation of any engineering program.

[bigger_cheese]

Linear Algebra was a first year subject for me as well. I studied Engineering in Australia.

[lupire]

The Robotics concentration requires Linear (Matrix) Algebra.

And some upper level courses have a prerequisite.

But indeed it does seem a avoidable for many MechE majors.

Funny thread about UM engineering students avoiding taking UM math classes. https://www.reddit.com/r/uofm/comments/15w18gv/reminder_you_...

[tonyarkles]

I did an EE/CS dual degree and there was a really interesting difference between the linear algebra courses offered in both departments.

For the EEs we were given a crash course in GE120, which all engineering students had to take. It covered how to use determinants, Gaussian elimination and matrix inversion, and those kinds of “basic” LA tools, plus some simple numerical methods stuff like Newton’s Method. In second year we had a short lab course that focused on how to use Matlab, and a circuits analysis course that pretty much forced us to learn how to represent large sets of equations in matrix form and invert them to solve all of the variables at once. Very very practical.

And then in third year I had to take a 200-level linear algebra course from the Math department to satisfy the requirements for the CS degree. I chose the honours version of it and… holy moly. I thought it was going to be a gimme class but it turned out to be very theory-heavy, of which I had learned almost none in engineering. The first month kicked my ass pretty hard. Once we got out of the low-level theory (which was truly amazing to take in) and into the more advanced things that I’d been using for 2 years but didn’t know “why”, everything changed. Many of my peers were struggling to understand why you’d want to do some of this stuff and I was just super excited to finally understand why the “just turn the crank” math I’d been doing actually worked.

[antman]

We had the basic Linear Algebra in high school

[mp05]

Yes back in 2005 when I first went to undergrad as a mech engineering major, linear algebra was not a requirement. Our mechanics professors were highly irritated by this.

I don't think this has changed much (but absolutely should). I've watched in real time as Micron representatives reject mechanical engineers and prefer résumés from industrial engineers for design roles due to their superior grasp on linear algebra and statistics. I'm paraphrasing but "it's easier to teach an IE how to do FEA than it is to teach a mechanical engineer DOE and Weibull analysis".

[lupire]

Why can't professors set LA as a prereq for their courses?

Or use it in their courses and earn students that they need to learn it so succeed?

[mp05]

It's up to department heads and dean and they're pressured by ABET and companies that write them checks.

Education is secondary; this is job training! We need to crank out people ready to drop into Boeing's way of doing things!

[angry_moose]

Yeah, stats is the other major deficiency in the course load. I think one course is required but its basically high school level "check out these normal distributions, 68-95-99.7, here's a Z-score, see you later".

Thankfully the companies I've worked for have done a really good job with advanced stats training.

[gnubison]

What do these acronyms mean?—IE, FEA, DOE?

[angry_moose]

IE == Industrial Engineering: broad, but generally "Engineering of Systems" instead of a physical product. Laying out factories, setting up supply chains, etc. It's morphed a little bit from the original field so the name isn't super accurate.

FEA == Finite Element Analysis: advanced method of predicting the strength of a product via numerical simulation.

DOE == Design of Experiments: evaluation of how the outputs of a system change as you vary the inputs. At a high level, you build model of the system, then vary all the inputs through their entire range and to build a response surface of the output.

[mp05]

> It's morphed a little bit from the original field so the name isn't super accurate.

I'm currently doing a masters in IMSE--Industrial and Management Systems Engineering--and yeah it's changed since the 70s or whenever it had its real heyday (they come in waves).

The updated curriculum for undergrad is essentially the same as a mechanical engineering for the first two years, but as they wander off into advanced mechanics and fluids, IMSE students are doing time studies, factory design (FLOW!), and lots of stats and algorithms.

I've actually had the pleasure of getting to gripe to our school's Industrial Advisory Board which seems mostly full of Boeing people. They want to know if the curriculum serves the students well and I preach to them that, actually, if you spend 6 or 9 extra credits on proper software engineering that you've created a monster... but they don't listen. Some even get kind of offended because they think that a career in project management is a fine way to go about life (why go to engineering school?)

Sorry programming blows your mind? Perhaps that's why we need to teach it? I've done a lot of ERP integrations in my career and I'm not sure who they think is most qualified to do those sorts of things.

[WillAdams]

Currently watching:

https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-...

and that assumption seems to be there as well, so very glad of the posting of the Youtube links elsethread.

[cashsterling]

Same... I didn't have to take Linear Algebra in ChemE undergrad. DiffEq had a little bit of LA... and ChemE had few classes where bits of pieces of LA where introduced and applied.

Graduate school definitely made up for lost time... LA was very front and center in the applied math courses.