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Abstract Algebra vs Linear Algebra

  1. Aug 2, 2012 #1
    Hey guys,

    As of now, I am in a sets and logic proof based course (Intro to proof-writing). This course basically teaches logic, how to write proofs using examples of algebraic equations, sets: power sets, unions and intersections of classes, etc.

    With a C in this course, you can register for proof-based Linear Algebra 1.
    With a B, you can register for Abstract Algebra 1.

    Unfortunately, Linear Algebra is full so it's current place holder is Abstract Algebra of which I'm already registered for.

    Eventually, I'm going to take both but usually students go into Linear Algebra first. I have about 94-97% in my intro to proof course and I'm pretty sure I'll end up with an A but I have to admit that I often run into a problem 10% of the time that I either don't know if I did it right or not at all.

    I personally don't know what the differences between the two classes really are or what either expect of me but I can prepare. Since the classes start in about 20 days, I still have plently of time to look into the texts and/or make a choice. If Linear Algebra becamess available or some other course: Complex Functions or Number Theory become available, I'll consider taking the one based on my priorities.

    What are you're opinions/advice?

    UPDATE:
    Linear Algebra: Linear equations, matrices, vector spaces, linear transformations, determinants, eigenvalues and inner-product spaces

    Abstract Algebra: Sets and mappings, groups and subgroups, homomorphisms and isomorphisms, permutations, rings and domains, arithmetic properties of domains, and fields.

    How much in depth for each topic in Algebra I don't know. Is any linear algebra required for any of them? (For those who took the course/topics).
     
    Last edited: Aug 2, 2012
  2. jcsd
  3. Aug 2, 2012 #2
    Well, at my school Linear is actually a prerequisite for Abstract, just because of the so-called "mathematical maturity" that you need to study it.

    But, the fact that your school will allow you to actually take that course before Linear probably means that it wouldn't be a problem for you. You did specify that it is part 1, so I imagine that it is structured to be more of an intro (I go to a Liberal Arts university with no math grad program, so all we have is one, intensive Abstract Algebra class).

    I'd recommend asking the professor if they think it would be a good idea or if you should wait, but I do think that if your department has that policy then it means that you'd be fine.
     
  4. Aug 2, 2012 #3
    Hmm, I'm guessing the next responses will be more precise if I include the course descriptions.

    Linear Algebra: Linear equations, matrices, vector spaces, linear transformations, determinants, eigenvalues and inner-product spaces

    Abstract Algebra: Sets and mappings, groups and subgroups, homomorphisms and isomorphisms, permutations, rings and domains, arithmetic properties of domains, and fields.

    How much in depth for each topic in Algebra I don't know. Is any linear algebra required for any of them? (For those who took the course/topics).

    @Worm I'll email the professor about it tonight.
     
  5. Aug 2, 2012 #4
    Linear isn't an absolute prerequisite for Abstract, but that is the usual order in which they are encountered. LA is a standard class that every physics and math major should do so it is offered early in the standard sequence.

    As WormBanshee mentioned, the jump in mathematical maturity to a proof-based LA course is hard for many students. Also, LA provides many clear examples of structures that you encounter in Abstract Algebra. However, if the Abstract course is structured well and you are comfortable with the proofs, seeing it first and then doing LA could be an interesting way to do it. You will have much more insight behind the scenes than someone who is going straight into LA.

    Your plan to talk to a professor who is familiar with the courses is good. Sometimes just because you can do something without a prerequisite doesn't mean you should.
     
    Last edited: Aug 3, 2012
  6. Aug 5, 2012 #5
    There's a good bit of overlap, but I successfully took Abstract before Linear at my University... Talking to the prof is a good idea, and I had good access to my Abstract prof during the semester (although I did not utilize that time). I had already taken a good proof course, which was more helpful than I think Linear would have been. Good luck.
     
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