How hard are upper division courses compared to calculus?

[Stochastic13]

I'm taking calculus for scientists and engineers and was wondering how much harder are upper division courses like partial differential equations, ordinary differential equations, and complex analysis than calculus?

 

[ahsanxr]

I can only speak for the class I've taken out of these that is, Ordinary Differential Equations and I have to say its not much harder. Its a very calculation based class, so its sort of like Calc II, as in you're mindlessly solving differential equations and systems of DE's most of the time. At least that was how my course was. I've heard horror stories about PDE's from juniors who were taking it this semester.

 

[zif.]

I have only completed first year, but I have asked graduating math majors what they thought the hardest class they took was and almost all of them say, "Calc II, " without hesitation.

 

[Stochastic13]

You got to be kidding me, I just finished Calc II and have an A in the class, in fact I thought that it was kinda easy. Yes, I heard everybody say that it is really hard, but after taking it, I think that most just over-exaggerate, however, when asking my professors they all say that partial diff eq and complex analysis is really hard compared to calculus. I was just wondering if that is so.

 

[ahsanxr]

I have only completed first year, but I have asked graduating math majors what they thought the hardest class they took was and almost all of them say, "Calc II, " without hesitation.

Seriously? I breezed through that class with an easy A.

 

[Klockan3]

A thorough course on PDE's will make calculus II feel like a breeze. Complex analysis isn't that hard and ODE's are a joke.

I have only completed first year, but I have asked graduating math majors what they thought the hardest class they took was and almost all of them say, "Calc II, " without hesitation.

Then they didn't take any hard upper division courses, what kind of maths did they study? Most math majors don't take a course on PDE's and there is no calculus course which can be harder than a good course on PDE's.

 

[Sethric]

I have only completed first year, but I have asked graduating math majors what they thought the hardest class they took was and almost all of them say, "Calc II, " without hesitation.

I've never heard a math major say that, much less without hesitation. The most common answers I have seen to that question are Real Analysis or Abstract Algebra.

Out of the OPs list, I would say PDE is the hardest.

 

[Chaostamer]

Calculus II was, far and away, the easiest math class I've taken at the university level, with the *possible* exception of Differential Equations. I don't understand for a second why people find that class so difficult except for the fact that one actually has to put in more than thirty minutes' effort to pass a test.

The hardest class I've taken thus far was Topology. In general, though, upper-division math courses are significantly more difficult than calculus, especially once they become more rigorous and abstract.

 

[clope023]

I'm taking calculus for scientists and engineers and was wondering how much harder are upper division courses like partial differential equations, ordinary differential equations, and complex analysis than calculus?

Depends on the teacher, pde's and ode's can be a breeze compared to complex and real analysis; the opposite could also be true. I would say analysis is harder conceptually than differential equations but de requires more work. Both are much more difficult than calculus but you will need a good base in calculus to do well, they're both pretty subjects though.

 

[Jack21222]

Calc 2 was very difficult for me compared to 1 and 3 because it relied on A LOT of memorization, and I suck at memorization.

I had no trouble doing any tests for convergence, for example, but memorizing 8 of them plus Taylor expansion plus a few other things all for one exam was difficult.

The actual work was simple, but the memorization was a bear.

 

[ahsanxr]

^ That's why you need to learn how to derive, or at least see the derivation once.

Speaking of math classes, would you guys say going into an Advanced Linear Algebra course with the only math courses under my belt being Elementary LA, Calc II-III and ODE's a good idea?

 

[nlsherrill]

I'm taking calculus for scientists and engineers and was wondering how much harder are upper division courses like partial differential equations, ordinary differential equations, and complex analysis than calculus?

Any course CAN be hard if the professor/department wants it to be. So, I will comment based on my personal experience.

I just finished ODE's and Linear Algebra this semester. Linear algebra is considered an "advanced" math class by the math departments standards, and I can now see why. Definitely conceptually more abstract than ODE's(which usually means harder) and more proof based(also usually means harder). I had some pretty tough tests in calc 3 as well.

From what I have heard from some other math majors is that once you get past linear algebra/ODE's, stuff gets harder. PDE's at my school is considered difficult, and I hear a lot about real analysis. I have yet to really struggle understanding something in math classes, but I guess I haven't taken abstract algebra and analysis yet! So yes, from what I have heard the solely "math majors" courses are notably harder.

 

[Chaostamer]

^ That's why you need to learn how to derive, or at least see the derivation once.

Speaking of math classes, would you guys say going into an Advanced Linear Algebra course with the only math courses under my belt being Elementary LA, Calc II-III and ODE's a good idea?

I think that depends on a few factors.

1. Which topics does the course cover?
2. Is it a proof-based course?
3. Was your Elementary Linear Algebra class at all proof-oriented?

 

[Nicook5]

Ya my only problem with calc 2 (which I am guessing is equivalent with BC calculus) was memorizing stuff, esp those power series.

 

[ahsanxr]

I think that depends on a few factors.

1. Which topics does the course cover?
2. Is it a proof-based course?
3. Was your Elementary Linear Algebra class at all proof-oriented?

1. From the website: Introduction to algebraic systems, including groups, rings, fields, vector spaces, and their general properties, including subsystems, quotient systems, and homomorphisms. Study of basic examples such as permutation groups, polynomial rings, groups, and rings of matrices. Additional topics may include applications to linear algebra and number theory.

2. I would imagine so.

3. For the most part, no. It was just one proof every other homework or so, and none on the exams.

 

[Chaostamer]

1. From the website: Introduction to algebraic systems, including groups, rings, fields, vector spaces, and their general properties, including subsystems, quotient systems, and homomorphisms. Study of basic examples such as permutation groups, polynomial rings, groups, and rings of matrices. Additional topics may include applications to linear algebra and number theory.

2. I would imagine so.

3. For the most part, no. It was just one proof every other homework or so, and none on the exams.

Honestly, that sounds more like an abstract algebra course (which, in fairness, can motivate linear algebra). Personally, I'd recommend not taking the course until you've taken a proof course, as I imagine that class will be fairly abstract and very proof-centric. However, email the professor and see what they think. You might be fine.

 

[ahsanxr]

Honestly, that sounds more like an abstract algebra course (which, in fairness, can motivate linear algebra). Personally, I'd recommend not taking the course until you've taken a proof course, as I imagine that class will be fairly abstract and very proof-centric. However, email the professor and see what they think. You might be fine.

Ahan, but the website lists only Elementary LA as the pre-requisite for this class. I don't want to mess around in easier classes which I can avoid, as my schedule is pretty packed with Physics and Math courses and I want to be able to take the most advanced ones possible.

 

[VeeEight]

Ahan, but the website lists only Elementary LA as the pre-requisite for this class. I don't want to mess around in easier classes which I can avoid, as my schedule is pretty packed with Physics and Math courses and I want to be able to take the most advanced ones possible.

That course sounds like the book Elements of Modern Algebra by Gilbert. Maybe check it out and compare it with a standard 4th year algebra text in Dummit/Foote where you will go into more details of groups/rings/fields and then more advanced topics in algebra.

 

[ahsanxr]

That course sounds like the book Elements of Modern Algebra by Gilbert. Maybe check it out and compare it with a standard 4th year algebra text in Dummit/Foote where you will go into more details of groups/rings/fields and then more advanced topics in algebra.

That's the text another class is using called Survey of Algebra, which seems more of like an intro to modern algebra sort of class. I have that book though, thanks to a friend who took that class. So would you recommend I take that before Advanced LA?

 

[hitmeoff]

Upper-Div Math is completely different from Lower-Div math. When you talk about PDEs/ODEs, depends on the level you are taking the course. Lower div course on DE's are generally easy to not bad at all.

Once you get into Analysis, Algebra, Topology, etc...**** gets thick real quick. I breezed by Calc I-III and ELEMENTARY Lin. Alg/DE's, but upper div math has been anything but a breeze. I am consistently getting kicked in the face!

 

[Sankaku]

...how much harder are upper division courses...

Depends on the school.

Depends on the teacher.

Depends on the textbook.

Depends on the student.

 

[Ryker]

Ahan, but the website lists only Elementary LA as the pre-requisite for this class. I don't want to mess around in easier classes which I can avoid, as my schedule is pretty packed with Physics and Math courses and I want to be able to take the most advanced ones possible.

Honestly, I think you're overthinking this. If the only pre-requisite listed is what you've already done, then I don't see why you're hesitant to take the course. You can check with your advisor to make sure, but I'd say you're good to go. I mean, when they make the curriculum, they do look at other courses offered at the university and take them into account, so that it's a smooth transition.

 

[Leveret]

Such things are often self-correcting. If the course listing erroneously names only one prerequisite, then people who have fulfilled only that prerequisite will comprise a significant portion of the class. When other topics that were mistakenly left out of the prereqs are introduced, the class will struggle collectively, which the professor (if he/she is good) will pick up on and try to remedy (often by emphasizing that topic even more, to give the class a greater exposure to it, or by unemphasizing it, to eliminate the problem). Even if the professor doesn't take either of these actions, if the class's grades on the whole are significantly lower than expected, a lot of professors will curve it up a bit.