Relative Difficulty of Math classes

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Discussion Overview

The discussion revolves around the perceived difficulty of various mathematics classes, with participants sharing personal experiences and opinions on which classes they find most challenging. The scope includes subjective assessments of courses such as real analysis, linear algebra, calculus, and abstract algebra, among others.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants suggest that real analysis is often viewed as the "organic chemistry" of math classes, indicating its challenging nature.
  • Others argue that combinatorics and graph theory are particularly difficult for them.
  • A participant mentions that calculus is the hardest subject, while another finds linear algebra challenging due to computation errors despite understanding the concepts.
  • Some express that algebraic topology and complex function analysis are among the hardest classes they have encountered.
  • There are differing opinions on the difficulty of calculus, with some finding it logical and clear, while others struggle with specific topics like differential equations and sequences.
  • A participant notes that the difficulty of a class can depend significantly on the teaching style and approach of the professor.
  • Several participants share that they have found advanced topics like differential geometry and topology to be particularly strange and challenging.
  • Some express frustration with the lack of practical application in certain math courses, feeling disconnected from their use in physics or engineering.

Areas of Agreement / Disagreement

Participants do not reach a consensus on which math classes are the hardest, as opinions vary widely based on personal experiences and teaching styles. Multiple competing views remain regarding the difficulty of specific subjects.

Contextual Notes

Participants express uncertainty about the applicability of certain math courses to their fields of study, and some mention that their struggles may be influenced by their lack of interest in the material.

courtrigrad
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What is the "organic chemistry" class in math? Is real analysis considered by many to be this type of class? In your opinion, what have been your easiest/most difficult math classes (in ascending order)?

Any feedback is appreciated

Thanks
 
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It totally depends on the person. For me: it's combinatorics / graph theory.
 
they are all hard. calculus is the hardest. if it isn't hard you are being cheated.
 
i thought linear algebra class was hard. I understood the concepts well, probably better than most people in the class, but I tended to make too many stupid computation mistakes. When you're given a 4x4 complex matrix on the exam and are asked to find the inverse as well as jordan canonical form, it's really easy to make a simple sign error like i*i = 1 instead of i*i=-1 and of course if you do it early enough in a long and involved thing like diagonalization it can really screw you up bad.

Most people I know would probably say calc 3 integrals, especially surface integrals, for some reason. But I don't think they're that bad, they're almost algorithmic to solve if you know a couple tricks.
 
I think algebraic topology is the hardest...so abstract.
 
Nah - at the time - complex function analysis.
 
jbusc said:
When you're given a 4x4 complex matrix on the exam and are asked to find the inverse as well as jordan canonical form, it's really easy to make a simple...

Why the heck would anyone do that by hand? That's not mathematics, that's a computational problem.
 
Rach3 said:
Why the heck would anyone do that by hand? That's not mathematics, that's a computational problem.

lol, you can tell that to my prof :)

honestly, I think I learned a lot in that class. The tests weren't...umm...yeah, but the lectures were great. It was advanced applied linear algebra and he covered everything from intro to vector spaces, some hilbert space+infinite dimensional vector spaces, Fourier series, complex linear algebra, jordan canonical form, finite-field linear algebra, boolean, gray, and error correcting codes, and elementary operators+quantum theory(spin and stern-gerlach)

couldn't really get more comprehensive than that :)
 
Depends on the teacher too. Generally the linear algebra class here is considered easy, but last spring one of the teachers got in an experimental mood. There was no textbook, he didn't teach, and you weren't supposed to use outside help. You were supposed to derive everything yourself. I didn't take this class, but I've never seen so many stressed people.
 
  • #10
At my school, the "organic chemistry" of the math department is the junior level Intro to Real Analysis. As one of my favorite math profs said, "This is the class that turns math majors into engineers," which I thought was pretty funny.

P.S. All you engineers please don't take this as an insult, I think my prof's comment was to illustrate that this course has very little pragmatic application, not that all engineers are failed math majors.
 
  • #11
At my school I have heard that Linear Algebra is also supposed to be farily easy, the classes more like Org Chem would have to be Diff Eq, or one of Real or Complex Analysis. As for somoene who mentioned earlier that Calc 3 integrals can be rather tough, that scares me as I am in Calc 3 currently, So far it has been not too bad but we are ust getting into Partial Deriviatives, we are currently working through Kepler's Laws.
 
  • #12
math is hard :(
 
  • #13
unit_circle said:
At my school, the "organic chemistry" of the math department is the junior level Intro to Real Analysis. As one of my favorite math profs said, "This is the class that turns math majors into engineers," which I thought was pretty funny.

P.S. All you engineers please don't take this as an insult, I think my prof's comment was to illustrate that this course has very little pragmatic application, not that all engineers are failed math majors.

It's ok, I could easily say thermodynamics is the class that turns engineers into math majors. :-p
 
  • #14
Abstract algebra and Advanced Calculus are the most difficult from my experience.

I'm lucky that I minored in math (linear algebra) because it's very useful for quantum chemistry.
 
  • #15
unit_circle said:
At my school, the "organic chemistry" of the math department is the junior level Intro to Real Analysis. As one of my favorite math profs said, "This is the class that turns math majors into engineers," which I thought was pretty funny.

P.S. All you engineers please don't take this as an insult, I think my prof's comment was to illustrate that this course has very little pragmatic application, not that all engineers are failed math majors.

Sometimes I feel like I'm a math major (as I look at my field and wave electromagnetics book)
 
  • #16
Intro Real Analysis, and depending on the proffesor, Complex Variables.
 
  • #17
devolopmental maths, and quantam information were the hardest for me
 
  • #18
Topology

I vote for topology too. I think calc is easy. Very concrete. Linear Algrebra is easy too. Topology takes the cake. It is STRANGE! Maybe abstract algebra. That is odd too.
 
  • #19
Yeah, I always found calculus to be a very logical and clear subject...not that abstract at all, even in multivariable calc.
 
  • #20
leright said:
Yeah, I always found calculus to be a very logical and clear subject...not that abstract at all, even in multivariable calc.

Take calculus to the manifolds and you will see some more abstract ideas...
 
  • #21
Two words: Differential Geometry. The first homework assignment basically makes you derive Linear Algebra.
 
  • #22
mathwonk said:
they are all hard. calculus is the hardest. if it isn't hard you are being cheated.

So not only am I being cheated, but I also suck at the cheated version? :cry:

I found Diff EQ's to be painful (compared to Multivariable calc and linear algebra), since I couldn't visualize it. Sequences and series were pretty bad too, though, although I think that had more to do with me being asleep during class than anything else.

In fact, most of the hard math I've taken, I haven't had an interest in, because I haven't had to use it in physics yet. It's all just been "here, learn this" without a "ok, now we're going to use it".

Until this quarter... :(
 

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