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Help a math major choose his classes

  1. Jul 15, 2008 #1
    For my undergraduate mathematics program the required classes are Calculus 1,2,3, Linear Algebra, Differential Equations, Introduction to Advanced Mathematics, Advanced Calculus, Algebraic Structures, and Mathematical Statistics I. Then I am told to choose 3 classes from each of the lists below. I am planning to go to graduate school for math and i was wondering which 3 classes from each list would benefit me in the future. I have underlined the ones that seem important in my opinion but i would like to know others peoples opinions. Which ones are not useful at all. Which ones are the most important.. and so on.

    List 1
    Introduction to Combinatorics
    Complex Variables
    College Geometry
    Number Theory
    Topics in Advanced Calculus
    Topics in Algebraic Structures

    List 2
    Advanced Differential Equations
    Graph Theory
    Mathematical Modeling
    Mathematical Statistics II
    Numerical Analysis
    Mathematical Logic
    Axiomatic Set Theory
  2. jcsd
  3. Jul 15, 2008 #2
    Well, it 100% depends on your major. Are you majoring in Pure Mathematics or in Applied Mathematics?
  4. Jul 15, 2008 #3
    That's not a bad list there, well rounded and all. But, yea like roam said, it depends on where you're heading.
  5. Jul 15, 2008 #4
    Take as many as possible!

    If you're going to study pure math in grad school, Number Theory, Topology, Complex, and Topics in Alg Structures (which I assume is Advanced Abstract Algebra) are MUST HAVES.

    If your going the applied route, your course selection will depend heavily on what you want to specialize in during grad school (stats vs. analysis etc...) . However, definitely take as much Real Analysis as you can.

    Hope this helps.
  6. Jul 15, 2008 #5
    If you're going into grad school in math, I would take complex, topology, and topics in advanced calculus (probably will cover undergrad analysis, no?). You will need to take these in grad school, and they will be tested on the GRE.

    As far as the other ones go, it's up to your personal taste. You can be a very successful researcher in mathematics and never study logic, combinatorics, graph theory, statistics, etc. at all.

    Numerical analysis, advanced differential equations, mathematical modeling, and statistics will be useful only if you plan to go into applied math or industry.

    As an aside, it seems pretty bizarre to have two undergrad classes in logic and none in, say, differential geometry. Does your department have a lot of logicians or something?
  7. Jul 15, 2008 #6
    Well my school doesnt offer the choice between pure or applied mathematics, so im simply majoring in mathematics. I dont really know which i would want to go into (pure or applied) because they both seem to have their pros and cons.
  8. Jul 15, 2008 #7
    so what your saying is if after taking the classes if i prefer advanced differential equations, numerical analysis, and mathematical statistics i should go for applied and if i prefer advanced calculus, abstract algebra, and complex analysis i should go for pure?
  9. Jul 15, 2008 #8
    I know you said you underlined the ones that seem the most important for grad school (although as everyone has noted, the importance is relative depending on whether you want to go into pure or applied mathematics)

    Here's an exercise: Read the course descriptions for each class, then come back and tell us which ones sound the most interesting to you - if there was nothing else that went into the decision, which classes of the sets do you think you would most enjoy?
  10. Jul 15, 2008 #9


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    How far along are you now in your program? If you're in the early stages (beginning of freshman or sophomore year), you probably haven't been exposed to enough math yet to have a good sense of which way you'd like to end up going.
  11. Jul 15, 2008 #10
    well i sort of did a backwards route and decided first which classes i thought were unnecessary (which im not sure about). i figured no math major takes college geometry unless their majoring in math education. i didnt think the logic classes (mathematical logic and axiomatic set theory) sound neccesary nor fun (but i may be wrong). graph theory doesnt seem useful for graduate classes. mathematical modeling seems fun but also seems as its not very necessary.

    this leaves me with the 3 underlined classes in list 2 which all seem more useful than the rest of the ones in list 2. and 6 classes in list 1 (all excluding college geometry) of which i have to pick 3. i just want to know which 3 are the most important and if you cant choose only 3.. choose more (meaning i would have to take extra classes). and do u agree with my underlined in list 2.

    i am entering my junior year
  12. Jul 15, 2008 #11
    Junior year, strikes me as odd that you do not have a taste of applied/pure maths.
    I would encourage you to take another look at the math modeling course, as a fall back at the very least. I imagine you will get exposure to several different problems and some coding exposure.
  13. Jul 15, 2008 #12
    well i have taken calc 1,2,3, linear algebra, and diff eq.

    my junior year will be:
    fall- intro to adv math
    math stats 1
    *course from math list*
    spring- adv calc
    algebraic structures
    *course from math list*

    senior year
    fall- *course from math list*
    *course from math list*
    spring- *course from math list*
    *course from math list*

    and i was hoping you guys would help me choose those 6 from the list (3 from each)

    i will be getting a taste of pure math in the fall. unless linear algebra counts as pure and diff eq counts as applied. then i would definitely have to say i enjoyed diff eq alot more than linear algebra
    Last edited: Jul 15, 2008
  14. Jul 15, 2008 #13
    Are you kidding me? Graph theory rocks!

    Although you'll get your fair dose of it in "Introduction to Combinatorics."

    Also, I think Topology should be in every math majors education.
  15. Jul 15, 2008 #14
    I agree that you should absolutely take topology, and I also think you should take algebraic structures. Intro to combinatorics? Without the course description I can't tell for sure what you cover, but from personal preference, I say you skip it (but take graph theory from set 2). I'd recommend complex variables as the third, mostly because it's fun.

    Filling out set 2, I think advanced diff.eq.,... and I guess numerical analysis, even though it's mind numbingly boring.

    Granted, this is simply what I would do if taking undergrad classes over again... And assuming I was a math major.
  16. Jul 15, 2008 #15
    I would say avoid doing things like complex variables, topics in analysis, and topology or say combinatorics, number theory, topics in algebraic structures. If you are preparing for graduate school, I would recommend topics in algebraic structures and topics in analysis. Then I would say you should consider the other one from list 1 as an elective, but I would probably not choose combinatorics or college geometry. I think topology would be the most useful.

    From list 2, well gosh, I took graph theory and that counted as a science elective not a math elective --- the rest of them I never even looked at. I always considered myself as someone going to grad school for pure math. If it were me, I would take math logic, axiomatic set theory, and graph theory...but its not and you may have an interest in applied math. I think if you are not sure, you should definitely take mathematical modeling. Then I would say graph theory and differential equations.

    This is advice if you are not sure on what area of math you want to study. It would definitely change if you said 'I want to do pure math' or 'I want to do applied'.
  17. Jul 15, 2008 #16


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    In my opinion, the one thing that really matters if you're planning on going to grad school (applied or pure) is that you take topology.

    For the rest, go with your personal taste, but imho, Complex Variables is the second most useful.
  18. Jul 15, 2008 #17
    which classes do you guys think arent necessary?
  19. Jul 16, 2008 #18


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    All of those can be necessary depending on what part of math you are interested. Since you have no real preference we can't tell you what isn't necessary. Later you may figure out that you like something for which a class we said was not necessary actually is.
  20. Jul 16, 2008 #19
    It really depends what you want to go into. That's why a lot of people have been advocating taking classes that will server you no matter what you go into. No matter what, if you go to grad school in math, you will need to be a wizard at algebra and analysis (if only to pass quals). Same can be said to a lesser degree about complex, since some schools require a qual in it, and also because it pops up in almost every area of math. Undergrad topology might be nice, if only to make metric space analysis easier.

    After that, it completely depends on the field you want to go into. If you want to go into something related to algebra, topology, etc. you will find almost every other class on the list useless. If you want to go into something applied, you would probably benefit from advanced differential equations, numerical analysis, and math modeling.

    But once you have the courses you think will prepare you for grad school, just take the courses that sound fun/interesting. If you think graph theory sounds cool, take it. If you think Mathematical Statistics II sounds interesting, don't go to grad school in math (kidding).
  21. Jul 16, 2008 #20
    Complex Variables
    Number Theory
    Topics in Advanced Calculus

    Advanced Differential Equations
    Graph Theory
    Mathmatical Logic

    I would choose these as they will provide the most solid mathematical foundations.
    Number Theory and Graph Theory- If you want to discover anything, a must.
    Complex Variables and Mathematical Logic- Great for when writing your dissertation
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