Scheduling: Abstract algebra, numerical analysis, Probability, or?

[Tuya]

I need to choose one more math class to reach a full-time status for next fall.
So far I am already taking Classical Mech I from Physics Dept, Analysis I and PDE from Math Dept.
I hear Analysis is already time-consuming hard class and I guess PDE isn't easy either, so I am considering to take relatively easy class as my fourth one.

Taking abstract would be great, because it is a requirement for my major (math&physics major). How hard is abstract? Is it same difficulty as Analysis or easier (or harder)? I would like to make a sensible schedule and get good grades in my classes.
I think numerical analysis is really easy, but it does not seem interesting to me. Or should I altogether forget about adding another math class and take something different like drawing, just so I can be a full time student?

What should I do?

 

[hsetennis]

The difference between Algebra and Analysis is much like the difference between steak and ice cream. Both are delicious and require a high level of formal proof. Some prefer the sweet, cold taste of ice cream and some prefer the savory, satisfying taste of steak. Some like both. You cannot have a complete meal nor a complete understanding of mathematics with just one.

 

[Dembadon]

I had a rough time in abstract algebra; it was difficult for me to develop a feel for what was going on. I cannot speak to analysis yet. Keep in mind the professor plays a big role in how difficult a course is. Ask fellow students about each professor's expectations and teaching style.

 

[verty]

I think Analysis I will not be as difficult as you expect, for the reason that it is well known, well trodden stuff. Same with Abstract Algebra, very well-trodden ideas and probably similar not in content but in approach. Each is a body of knowledge that you are aiming to learn via the same method so it should be similar.

 

[MarneMath]

It's hard to say, I personally found modern algebra much more difficult, because I had no real interest in the topic, but it is important that you as a math major should study it at one point. I just tend not to recommend both to be taken together, unless you already have a strong ability to write proofs.

PDE can be a mixed bag. Some PDE courses focus on technique, which while tedious, tend to be a much more manageable in terms of difficulty. My PDE class had a good deal of technique but also had some basic prove uniquness and boundary stuff. Nothing to difficult, plus the topics were interesting.

Numerical Analysis may be the least interesting course, but depending on the university it can be extremely difficult. Some courses on Numerical analysis just teach the theory and techniques, but focus little on programming. Other courses focus heavily on programming and help students build a portfolio. If your university focuses on the programming and theory, then I would highly recommend this course, because more than likely, after your graduation, the ability to program and show what you can do will be more important than many concepts you will have learned.

Lastly, I'm not entirely opposed to taking a free elective either. Taking all science and math can be hard on a person. If you can take general electives, it sometimes can provided a break from the rigidness of science and math and give your mind time to explore other interesting ideas.