What subject in undergrad math is the hardest?

[yungman]

I am not a math major. I studied cal I, II, III, ODE and almost finish PDE. I just want to gauge the difficulty of different math classes.

To me ODE was the hardest even though you need that for the PDE. ODE have so many different topics it is hard to follow all the derivation. I had to restudy the whole ODE even I was the first in the class two years ago. PDE is hard, but it has a logical progression. You go through the same thing over and over just in different coordinates. Make it easier to understand even you might miss the first go around. The only difficult part of the PDE are the Bessel's function and Legendre function.

How is complex analysis compare to ODE and PDE. that is another one I am interested in the future.

 

[Fredrik]

How is complex analysis compare to ODE and PDE. that is another one I am interested in the future.

Much easier I think. But I suppose it depends on would kind of class it is. The one I took was based on Saff & Snider, and one of the easiest math classes I've taken.

 

[Klockan3]

How hard a course is has more to do with how the course is laid up rather than what subject it is. It also depends on your own preferences and how well you know the prerequisites.

 

[Landau]

Indeed, it depends almost solely on the instructor, how the course is given, and what is expected of participants, rather than the subject iself. Any subject (even calculus) can be given at an extremely elementary or insanely advanced level.

Personally, the hardest course in my bachelor's was probably smooth manifolds, which was partly because I lacked topological prequisites.

 

[lisab]

Based solely on the posts I've seen here on PF, the class that gives a lot of math students trouble is their first class that requires proofs.

 

[MathematicalPhysicist]

Indeed, it depends almost solely on the instructor, how the course is given, and what is expected of participants, rather than the subject iself. Any subject (even calculus) can be given at an extremely elementary or insanely advanced level.

Personally, the hardest course in my bachelor's was probably smooth manifolds, which was partly because I lacked topological prequisites.

Do you refer to differentiable manifolds?

Yes I also took a similar course (analysis on manifolds), not an easy course espcially Sard's theorem, perhaps the hardes theorem I met in my studies.

 

[yungman]

Thanks for the respond. I am referring to what the college standard requirement of the class. The requirements are pretty standardized.

What class manifolds is in?

I am glad that Complex analysis is not hard.

 

[yungman]

Based solely on the posts I've seen here on PF, the class that gives a lot of math students trouble is their first class that requires proofs.

Can you give an example?

 

[thrill3rnit3]

Can you give an example?

Universities offer so-called "Introduction to Proofs" or "Introduction to Higher Mathematics" class which focuses on creating proofs.

Or probably a linear algebra class that focuses on proofs rather than calculations.

 

[derpdederp]

I am not a math major. I studied cal I, II, III, ODE and almost finish PDE. I just want to gauge the difficulty of different math classes.

To me ODE was the hardest even though you need that for the PDE. ODE have so many different topics it is hard to follow all the derivation. I had to restudy the whole ODE even I was the first in the class two years ago. PDE is hard, but it has a logical progression. You go through the same thing over and over just in different coordinates. Make it easier to understand even you might miss the first go around. The only difficult part of the PDE are the Bessel's function and Legendre function.

How is complex analysis compare to ODE and PDE. that is another one I am interested in the future.

Was your ODE class concentrated on solution methods (integrating factors, variation of parameters, etc.) or did it have more to do with the analytical properties of ODEs (existence, uniqueness, Picard-Lindelöf Theorem, etc.), or both?

Personally the first parts of real analysis have been the toughest so far (math major in third year), especially learning to work with epsilon-delta arguments. That stuff killed me freshman year in honors calc, but I think I've finally kinda gotten over that now in my analysis courses.

I'll be taking complex analysis next year, but I expect it to be a lot like real analysis, so not exactly easy. I'd be really surprised if any "analysis" course would be really easy, for the average undergrad anyway.

 

[yungman]

Was your ODE class concentrated on solution methods (integrating factors, variation of parameters, etc.) or did it have more to do with the analytical properties of ODEs (existence, uniqueness, Picard-Lindelöf Theorem, etc.), or both?

Personally the first parts of real analysis have been the toughest so far (math major in third year), especially learning to work with epsilon-delta arguments. That stuff killed me freshman year in honors calc, but I think I've finally kinda gotten over that now in my analysis courses.

I'll be taking complex analysis next year, but I expect it to be a lot like real analysis, so not exactly easy. I'd be really surprised if any "analysis" course would be really easy, for the average undergrad anyway.

The ODE class I had contrate on solving the problem. Integrating factors, variation of parameters etc, they were easy to use, but it just have so many different method and I being into learning the derivation of those formulas, found my head spinning because there were so many of them. Also the hard part I feel was the Series method. That get so tedious.

In contrast, PDE is much harder to understand, but it is not all over the place like ODE. You spend the time deriving the formulas and you learn and it get easier, everything make sense. Only the series stuff like in the Bessel equations get tedious. It is not like ODE that there are so many that I end up giving up and just remember the condition and apply the formulas. I took the class in Junior college, nothing like the ivy leaque college. But I did got the highest marks. All the students complained that they had to spend so much time compare to other classes like the multi variable calculus etc.

I guess the most difficult part for me is that ODE was just so different from the previous calculus that it really took me a while to bend my brain over. PDE is just a continuation of ODE, so no brain bending involve because it's been bended by the ODE already.

 

[aber_leider]

You go through the same thing over and over just in different coordinates...

PDE is just a continuation of ODE

Well, I can tell your PDE course was not a good one. There is a LOT more in PDE's than just separation of variables.

 

[yungman]

Well, I can tell your PDE course was not a good one. There is a LOT more in PDE's than just separation of variables.

I did not mention, it has Fourier series expansion, Fourier transform, lagendre, bessel and a little strum liouville also. Other than bessel equations, none really stand out to be that difficult. I am studying on my own by following the San Jose State Univ. Class. I actually got the chapters and topics of the course covered and the homework problems from the professor. I use 5 or 6 books to cover the topics to make sure I don't skip anything.

In fact I studied more than the school required. SJSU is not an ivy leaque college either. Their PDE class don't even require studying poisson's equations which I studied on my own. Also I've gone deeper into D'Alembert, Bessel's equations than the their book covered.

Please let me know if I miss anything. Remember this is an undergrad class. I am not a math major, I am studying these for advanced study of Electromagnetics/Electrodynamics. That is the main reason I asked about complex analysis.

 

[Landau]

Do you refer to differentiable manifolds?

Yes I also took a similar course (analysis on manifolds), not an easy course espcially Sard's theorem, perhaps the hardes theorem I met in my studies.

Yes, smooth manifolds = differentiable manifolds. We used lecture notes which were very hard to understand; the books by Lee and Lang were recommended, but they didn't really went well with the course.

I am referring to what the college standard requirement of the class. The requirements are pretty standardized.

Perhaps you're forgetting that not all people on this forum are from US.

 

[derpdederp]

Well, if your complex analysis course will be anything like an upper level math course (which it should), then I would expect it to be relatively rigorous and proof-oriented rather than computational which you might be used to in your calc and ODE (and PDE?) classes. I think that if you're not used to proving things, complex analysis might be above you. Also your lack of background in real analysis might make it hard. Of course, check with whatever dept you're taking the class from... maybe they don't teach it very rigorously...

 

[Shackleford]

Universities offer so-called "Introduction to Proofs" or "Introduction to Higher Mathematics" class which focuses on creating proofs.

Or probably a linear algebra class that focuses on proofs rather than calculations.

At my university it's called Intermediate Analysis. My vector analysis professor calls it a "Baby Analysis" course and says it's not really an analysis course. However, there is an upper-level Introduction to Real Analysis course which he says is tough. Given my experience with him, if he says that, then it's a damn-hard class.

 

[yungman]

Well, if your complex analysis course will be anything like an upper level math course (which it should), then I would expect it to be relatively rigorous and proof-oriented rather than computational which you might be used to in your calc and ODE (and PDE?) classes. I think that if you're not used to proving things, complex analysis might be above you. Also your lack of background in real analysis might make it hard. Of course, check with whatever dept you're taking the class from... maybe they don't teach it very rigorously...

I am looking at "Introduction to Analysis" also. I have two of those books, it does not look too complicated.

 

[thrill3rnit3]

At my university it's called Intermediate Analysis. My vector analysis professor calls it a "Baby Analysis" course and says it's not really an analysis course. However, there is an upper-level Introduction to Real Analysis course which he says is tough. Given my experience with him, if he says that, then it's a damn-hard class.

no, I'm talking about something else. Some schools offer a class that is just dedicated to learning and doing proofs (completely different from an Analysis class).

 

[Shackleford]

no, I'm talking about something else. Some schools offer a class that is just dedicated to learning and doing proofs (completely different from an Analysis class).

Hmm. Let me see if mine offers something similar. I don't think so, though.

This is as close as it gets from what I can tell.

MATH 1312: Introduction to Mathematical Reasoning
Cr. 3. (3-0). Prerequisite: credit for or placement out of MATH 1310 or MATH 1311, May not apply toward a degree from the College of Natural Sciences and Mathematics. Principles of logic and proof, set theory, formal and informal geometry.

MATH 3306: Problem Solving in Mathematics
Cr. 3. (3-0). Prerequisite: MATH 1312 or MATH 1313 or consent of instructor. May not apply toward a major or minor in mathematics. May not satisfy mathematics requirements in the College of Natural Sciences and Mathematics. Strategies for solving problems in mathematics: reduction to smaller problems; analogy in mathematics; conjecture and proof; the processes of abstraction, generalization, and specialization.

 

[thrill3rnit3]

MATH 1312: Introduction to Mathematical Reasoning

this one