Functional Analaysis or Abstract Algebra or Fields?

In summary: I'm not sure if I'm missing something or if somebody can clarify but I don't think I can do the 3rd year quantum subject without doing the second year abstract algebra subject and I don't think I can do the 3rd year quantum subject without doing the second year PDEs subject either.In summary, the third year undergraduate student is struggling to decide what courses to do for their final two subjects. They are interested in doing three different courses, but they are unsure if they should do the third year quantum subject or the third year abstract algebra subject. The third year undergraduate student is also interested in studying functional analysis, but they are unsure if they should do the third year physics subject or
  • #1
AXidenT
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Entering my third year of my bachelor of science majoring in maths/physics and having some trouble deciding what courses to do this semester. I know for sure I will be taking complex analysis and 3rd year quantum however am having trouble picking between 3 in particular for my final two courses.

I really enjoyed the second year abstract algebra subject and personally really would like to do the 3rd year abstract algebra and number theory subject (possibly my favourite area of maths in general that I've studied so far?).

I am also really interested in studying functional analysis - it seems like a very interesting area which is quite relevant to a lot of the questions I was asking/wondering about in some of my previous courses in quantum and PDEs. I've also heard from some of the lecturers at uni that the analysis subjects at our uni are quite good so would be a good idea to study them.

The third subject is the fields subject for the physics major (as far as I'm aware this is for the most part electrodynamics) which I've heard is a painful and horrible cause with a crazy marking schema that basically requires a fair bit of extra work compared to regular subjects. However if I don't do this course it's unlikely I'd meet the prerequisites (I'd have to do an extra physics subject next semester without having done the prerequisite for it) to finish my physics major meaning I'd have to drop that major and complete only an extended maths major. I could still study other physics subjects I'm interested in after but I'd feel kind of annoyed/regretful for being a subject off completing the major I feel. I've been leaning for the most part towards doing my honours in maths I think (not sure what area specifically), though occasionally I think I may be more suited for physics physics? I'm fairly sure I'll end up doing a maths honours though unless something changes (that was my original plan on entering uni vaguely anyway).

Not entirely sure what I want to do post uni or if I'll continue my studies past honours (would like to to an extent but will depend what field I want to work in/study I guess) - though if it's relevant to getting to know where I'm at I've done two research projects so far - a smallish one in experimental quantum optics and a longer one on lie algebras.

Any advice/recommendations on which subjects they think I should do would be greatly appreciated - sorry for the long post! Thank you!
 
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  • #2
It's quite hard to give you good advice as to what fits your particular degree and university. These are very sensitive to exactly what you want to do after graduating, what your department requires for your degree, etc.

Maybe you could talk to the guidance folks at your school? Or maybe you have a favourite prof who would be willing to give you some hints? There are other sources of inside info available at many schools. For example, just to get you thinking in he right way, the head of the department usually has a personal secretary. That secretary almost always knows more about the classes required for various options and goals than the department head. And more about the profs who teach those classes and how students rate them. See if you can't be friends with that secretary. At the very worst one of these folks can tell you who you should talk to.

Also, there are other students who are pondering the same question. See if there is somebody taking the same path as you. Or somebody one year ahead, who can spare you ten or twenty minutes to give you the straight story.

If you still can't decide, think about what you want for graduate school, assuming you go. Google up some schools that might be interesting and find out what those schools require for the degree you would be interested in.

While it is nice to learn as much as you can, you have a finite amount of time and ability to work. Concentrate on the things that will help you achieve your goals first. Then, if those things fit well and you still have time, then add on stuff that is just because you like studying it.
 
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Thanks for the reply!

I have spoken to a few lecturers (who at my university double as the academic advisers it seems) but typically it comes down to if I ask someone from the maths department they'll tell me to do the maths courses (with a focus on doing the functional analysis) and the physics lecturers will say to do the physics courses - as much I think because the lecturers only know the courses from their own departments - there's very few who have any direct crossover. The secretary type idea could be a good lead though thank you - might try and hunt down someone who may have a good perspective...

Haven't managed to find any students who've done what I have that are ahead of me - not entirely sure where I'd start looking - from what I've heard though it is a lot more common for people to switch from physics to maths than for someone doing maths to pick up physics. What I know from physics only students who are ahead of me is that the fields cause is extremely painful. :/

I think my dilemma comes down to whether I should study the courses I want to study now - or if I should do the courses that give me the best options or the extra major. Would not having a physics major - but having done a lot (almost enough for a major) physics courses (so quantum, stat mech, 2nd year fields, relativity, dynamics) be a poor position to be in? Would not having that extra bit of writing/qualification if I went the maths route now but still taking some physics courses hold me back if I was interested in working in physics later?

Thanks again!
 

1. What is the purpose of functional analysis?

Functional analysis is a branch of mathematics that studies the properties and behavior of functions. Its main goal is to understand the structure of spaces of functions and their relationship with other mathematical objects such as operators and spaces.

2. What are some applications of functional analysis?

Functional analysis has a wide range of applications in various fields such as physics, engineering, economics, and computer science. It is particularly useful in modeling and analyzing systems with infinite dimensions, such as quantum mechanics and signal processing.

3. What is abstract algebra?

Abstract algebra is a branch of mathematics that studies algebraic structures such as groups, rings, and fields. It focuses on the abstract properties of these structures rather than specific numbers or equations.

4. How is abstract algebra different from traditional algebra?

Traditional algebra deals with the manipulation of numbers and equations, while abstract algebra studies the underlying structures and relationships between algebraic objects. Abstract algebra also allows for the generalization of concepts and the development of new mathematical theories.

5. What are fields in abstract algebra?

Fields are algebraic structures that have two operations, addition and multiplication, and satisfy certain properties such as closure, associativity, and distributivity. Examples of fields include the real numbers, complex numbers, and rational numbers.

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