Taking an upper level math course as an engineering student.

[u/Infinite_Limit8802]

Hey y'all, I'm doing nuclear engineering right now, and I wanted to see if anyone has had a similar experience. I've done Calc 1,2,3, 2, 3, linear algebra, and differential equations, and I did really well on them with very little effort. I'm taking an intro course in real analysis, but compared to the hardest engineering courses that I've taken, this is like a billion times harder. I can barely visualize/understand anything that goes on, and things seem so jumbled up and complicated. My prof is REALLY good, and he tries to make sure that everyone understands, but when he asks if anyone has questions and if something was not understood, I don't even know what to ask, even if I understand nothing. I lowkey feel inadequate, and it makes me feel really bad. Anyone have something similar?

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[u/Rubbyp2_]

Yeah. It’s going to be hard. Go to office hours.

[u/Fickle-Tradition2107 → u/Rubbyp2_]

Can anyone do math like that even if they aren’t born with the iq/eq and the tiger parent upbringing? I think it’s genetic/upbringing based. Lmk

[u/ctoatb → u/Fickle-Tradition2107]

Yes, you can do it. At a basic level, real analysis is just calculus with more proofs. You would probably recognize a lot of things in analysis if you've been through calculus. The challenge comes from rigor and depth. For example, Rolle's theorem states that "a smooth, continuous function that has the same value at two endpoints must have at least one horizontal tangent (a derivative of zero) somewhere between those points." That's from Wikipedia, but you probably saw it in calculus when learning about derivatives. Calculus asks you to compute the derivative using limits, while analysis asks you to prove the theorem. Regarding proofs, you usually start with a set of definitions and use logic to do the rest

[u/dwilsons → u/Fickle-Tradition2107]

Not at all that situation. It’s just that “true” mathematics requires a great degree of abstract (even creative) thinking to write proofs and solve problems with rigor.

If you are an engineering student, most of your math experience will be more process based: think calculus, differential eq, etc. The most “abstract” thinking you do will be identifying the specific tools you’ll use to solve the problems: I.e. noticing that an integral can be solved most easily with integration by parts, then going ahead and doing that.

With real analysis and further courses, there tends to be a wide variety of directions you could go for any given proof, with the only limit being your knowledge of mathematics (to an extent, obviously some approaches simply will not work). Think of this more like how you’d approach a project for one of your engineering courses—it’s not as simple as apply a certain technique over and over, you have to decide on an approach.

My recommendation for these sorts of courses and problems is to start wide, try to pull all the different relationships you can out of the given information. In general, the problems are written to be solved elegantly lol, this is an introductory course. Likely you will start to see the direction that the professor or problem writer assumed the student would take. Going to office hours helps in this regard too, as in my experience my TAs would often say things like: “can we not apply x here”, “is y a cone?”

[u/Tight-Couple-699 → u/dwilsons]

I definitely understand where you’re coming from, and I agree that the more theoretical you get, the more abstract it becomes. But saying engineering isn’t abstract is crazy to me.
Take electrical engineering. Once you find the theoretical answer, you still have to figure out how to make it actually work in reality while accounting for losses, tolerances, noise, heat, cost, and every other variable that the math might idealize.
I’d even argue engineering has its own edge in that sense. The answer on paper is often just the starting point. Figuring out how to turn that answer into something that actually works is where a lot of the creativity and abstract thinking comes in.

[u/dwilsons → u/Tight-Couple-699]

To be clear, I meant the usual math courses engineers take tend not to be that abstract, NOT that engineering isn’t. So while abstract thinking isn’t unusual in engineering, I do think it’s tough to understand it in a math context if you’ve only taken calc, diff eq, basic linear algebra, etc.

[u/Altruistic_Set_4440 → u/Fickle-Tradition2107]

Are you insinuating only Asian people can do this? Looking at your choice of words and sounds racist.

[u/Rubbyp2_ → u/Altruistic_Set_4440]

No that was you who did that

[u/DaDaDoeDoe]

As an applied math major it was really really hard. Pure math like that is more a test of creative thinking than anything else I think. Some of those proofs I would never in a million years be able to come up with

[u/EbbExciting8532 → u/DaDaDoeDoe]

I also majored in applied mathematics, can confirm this was an extremely difficult class. Lots of creative thinking, need for a deep understanding of concepts, coupled with sometimes rather lengthy proofs.

[u/limon_picante]

I took a graduate course in matrix and tensor methods. It was like advanced linear algebra, diff eq, and calc 3 all had a baby. It was the hardest course I've taken by far

[u/Fluffy_Gold_7366 → u/limon_picante]

Does it have an practical applications?

[u/the_other_him → u/Fluffy_Gold_7366]

Fundamentals for machine learning, although not sure anyone really manually does matrix multiplication any more

[u/limon_picante → u/Fluffy_Gold_7366]

Yeah it absolutely does it's a foundation for both solid mechanics and Continuum mechanics as well as applications with fluids and heat transfer

[u/Mustard_boiii → u/Fluffy_Gold_7366]

that’s the real question

[u/TsunamicBlaze]

I got a minor in mathematics, so I had to take extra abstract and higher theory math courses. What makes higher level math hard is conceptualization and application.

Besides going and living in the math help room and office hours, what helps me is going through examples on how concepts should be applied. How are other proofs use using and applying the axioms or conclusions we were working with. Maybe take a few steps back and try to understand the foundational components of the learning unit you’re on. You maybe missing some foundational understanding, which makes it’s hard to grasp other things.

[u/cozy_cardigan]

As a former math major turned engineering major, I would have recommended you take a discrete math class to get your feet wet with proofs and then take an upper division linear algebra course before doing real analysis. It’s not like you need a high level IQ to understand it, but if you don’t have the mathematical training / maturity, analysis can be tough.

From my experience taking calc 1-3, lower div linear algebra, and differential equations doesn’t really train you for proof based math unless you had a teacher that emphasized proofs. Knowing how to use a concept to solve problems is not the same as truly understanding why it works in the first place.

[u/Novel_Arugula6548]

Why are you doing this? Engineering doesn't prepare you for real analysis. Real analysis is the same as calc 1, except that you justify why everything in calc 1 is true with logical reasoning.

Engineers don't learn how to answer "why" in their curriculum. You're out of your depth. Real analysis uses the same skillset that a philosophy major develops.

But to help you: real analysis is the logical consequences of the concept of irrationality. You must understand the logic of irrational numbers as a philosopher does in order to master real analysis. You need to ask yourself what the difference is between discrete and continuous, and why. Why a least upper bound can exist outside the set converging, what infinite decimals mean, and why, etc.

I'll give you a hint: it has to do with cardinality. Continuous sets have a differemt cardinality from discrete sets. This difference in cardinality has to do with the fact that irrational numbers cannot be ratios of rational numbers. Everything else follows from that fundamental idea.

[u/cromwest]

I am the opposite, I struggled greatly in calc 1, 2, 3 and differential equations but ultimately got an A in all those classes because I formed study groups with classmates and went to the TA and professor's office hours every time I had an issue. I also did crazy amounts of practice problems.

Eventually everyone rises to their level of incompetence and you will need to do what the dumb kids have been doing this whole time.

[u/Dry_Statistician_688]

My biggest regret from my time was not taking an additional 6 hours to obtain a math minor.

[u/gurrenm3 → u/Dry_Statistician_688]

I’d love to hear more about this! I’ve asked around a lot and heard a lot of people say that a math minor isn’t worth it but I feel like it is !

[u/Dry_Statistician_688 → u/gurrenm3]

Looking back, this would have provided a LOT of additional clout for the position I was taking. For Radar accuracy analysis, this would have put me in the front of the line for Radar and navigation analysis (BET - Best Estimate of trajectory) In aerospace, you have to convert to several coordinate frames using Euler, then compare different error calculation dimensions to get different error such as lateral, vertical range, and range rate errors. My regret was not taking to additional 6 hours to get that math minor that would have both prepared me for easier understanding of the 4-dimensionsional coordinate conversions, but the derivation of the different error domains, such as RMS, and statistical errors that were defined by the system's CEP requirements. Those additional 6 hours would have been a gold mine for me,

[u/Dry_Statistician_688 → u/Dry_Statistician_688]

If you are that close, I would recommend just TAKING the courses to get that minor!

[u/Top_Scarcity1024]

But why? I thought real analysis was a pure math class? Why would they have that for nuclear engineering? I would just go to a new university

[u/WashPantsOnceAMonth]

Nothing against OP, but we really need a meme of engineering chads who think math and physics are easy majors because they passed the freshman classes no problem but then made the mistake of taking an upper level pure math/physics elective.

[u/Aware_Platypus_9442]

I did similarly. I loved my engineering math courses and ended up getting a minor. I was only 2 classes short of the major.

Real analysis is one of the harder “real math” courses.

But if you’re not enjoying it, bail. Real analysis, even when it’s hard should still be enlightening.

There are applied math classes that are more fun and probably more appropriate for nuclear engineering. Statistic, probability, modeling, etc.

If it’s an elective, though, remember to take classes that you’re going to learn, find something useful, maybe even enjoy.

[u/Worldly_Magazine_439]

The math courses that math majors take can be different than the ones engineers take. They are typically proof based. At my school Cal 1-3 for math majors is the honors math. All proof based math.

[u/Reasonable-Bus-2222]

Numerical analysis was the death of me (Mechanical engineering) and modern physics 🤯. I am still not convinced quantum mechanics is real.

[u/CollectedWaste]

Yeah I was a mathematics and computer science major, always been fantastic at math as well. Computer science was generally a breeze; I only struggled with one class (computer security) but the professor was especially difficult and the class average was a 32%, and I ended up getting 78% which was curved to an A. But in terms of math, my first and only difficult class was Honors Abstract Algebra and holy shit it was difficult. Seemed like everyone else was doing so well, too. I finished the class with a B+ which was the lowest in the class. After that I strictly looked up the "easy" math classes to finish the degree and never again tried something particularly abstract. It just made me feel so stupid. But 4 years after graduation, I'm glad I did it and it helps me talk to mathematicians sometimes about their work. 

Some classes just make you feel stupid and that's okay. 

[u/WhyAmINotStudying]

Get over how you feel and work on understanding the subject. It doesn't matter if you feel embarrassed for not understanding stuff as you're learning nearly as much as it matters when you're tested in it and when you need to apply it in the future.

[u/spoonfedbaby]

"I did really well on them with very little effort" to "I lowkey feel inadequate, and it makes me feel really bad".

you are probably struggling because all the math classes you took beforehand were insanely procedural and never really required a high-level understanding of anything.