> 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).
Wow. In my undergrad all engineering majors had to take linear algebra (calc 3 was optional for computer engineering).
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).
Do all the homework problems check the answer in the back of the book. You’ll make it.
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.
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.
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I hear Apostol is hard. Like Spivak-level hard.
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.
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.
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.
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.
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.
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.
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_...
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.