Analysis vs Algebra: Math Major Career Benefits

[SMA_01]

For a Mathematics major at my school, we can choose an analysis option or algebra option? What's the difference and which is better career-wise? Thanks.

 

[hadsed]

If you don't mind me hijacking your thread just a teeny tiny bit, I'm also wondering about this but with relation to physics.

 

[Sankaku]

For a Mathematics major at my school, we can choose an analysis option or algebra option? What's the difference and which is better career-wise? Thanks.

Many schools will tend to have faculty who specialize in a specific subject and offer upper-level classes in that field. Algebra and Analysis are two of the major branches of Math(s) and your school allows you to specialize and take more of one or the other on your way to a degree. Some schools offer more specializations (Discrete, Differential Equations, Topology, etc.) but purely for career, Statistics would probably be the most marketable. However, if you are going to school just for a career, you probably wouldn't have chosen mathematics...

http://en.wikipedia.org/wiki/Abstract_algebra
http://en.wikipedia.org/wiki/Mathematical_analysis

FYI: Both of these fields are very cool and interlinked with other areas of Mathematics. I would suggest trying some upper level classes before deciding which you like more.

 

[Skrew]

I found Algebra to be boring and useless while analysis to be interesting and useful(undergraduate).

Maybe an applied abstract algebra class would be interesting but the courses I have had in it were boring. The interesting things were skipped over like representation theory, lie groups and symmetry, maybe in an attempt to simplify it but in doing so the courses lost motivation.

 

[yenchin]

Have you taken any of the algebra or analysis course? Maybe take a few and you will have a better feeling which one you like better?

 

[dalcde]

Maybe an applied abstract algebra class would be interesting

I believe that abstract algebra is too abstract to have applications.

 

[micromass]

If you're considering going into research, then both could come in handy.

For pure mathematics, abstract algebra is a must. Almost all of pure mathematics has been algebrized. Current research fields that are very important require a lot of algebraic tools, so knowing abstract algebra is no luxury!

For applied mathematics, you should take analysis. There is active research going on about wavelets, differential equations, dynamical systems,... All of these things require hard analysis. Abstract algebra is quite (but not completely) useless here.


To hadsed: in relation to physics, I would almost certainly choose analysis. It is way more important than abstract algebra. Abstract algebra has it's uses, but I think that a sound knowledge of analysis is more important than algebra...

And to the poster who thinks that abstract algebra does not have applications: you're quite far from the truth. Abstract algebra has many applications. Only one example would be group representation which is supposedly used in quantum physics. Another example is group rings which is used in telephone networks...

 

[zahero_2007]

I believe that abstract algebra is too abstract to have applications.

This is frankly wrong , Algebra , Geometry and Topology are the three most important branches in math because they are the way to describe the fundamental forces of nature and particles .

 

[axiomatic7777]

For applied mathematics, you should take analysis. There is active research going on about wavelets, differential equations, dynamical systems,... All of these things require hard analysis. Abstract algebra is quite (but not completely) useless here.

Depends a lots on what you are interested in. For high energy theory, in particular, you will need to know a fair amount of group theory, while analysis is less helpful in comparison.

 

[Skrew]

I think it is wrong to say that an abstract algebra course from a math department at the undergrad level will have any use application wise. I have flipped through books which focus on group theory in physics and chemistry and pretty much nothing in them was covered in the group theory course I have had.

I would say if you want to learn abstract algebra which will be useful for something, buy a book which focuses on it as what you will likely learn as an undergrad won't have any direct applications.

 

[flemmyd]

1. I can't imagine calling yourself a math major and being familiar with only one field. You really should be familiar with both, although you can specialize in one.

2. I've seen plenty of books that say "Group theory for Physicists" or something. I haven't seen anything professing to teach analysis to non-math people.

3. Lots of fields (like chem and physics) use Group theory/other algebra in certain areas, but that doesn't mean you need a huge foundation in algebra to understand how its used in that field.

 

[sutupidmath]

I found Algebra to be boring and useless while analysis to be interesting and useful(undergraduate).

Not to turn this into an argument, but abstract algebra, especially Group and Ring Theory, is extremely useful, especially when you are doing Algebraic Topology: that is the Fundamental Group of a space, and also the Homology Group of a space etc. serve extremely well in describing the space.