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Transition to Advanced Mathematics?

  1. Apr 23, 2009 #1
    I am a rising sophomore and am currently registered for Physics I (calc) and Calculus II. However, I am attempting a double major (phys, math), and have started late...so I would like to double up on my maths for the next 2-3 semesters.

    I am currently learning Calculus II, so when I take the course it should be a breeze. The only other course that counts towards my math major, that I have met the prerequisites for, is "Transition to Advanced Mathematics." I was wandering, what exactly is this course? The only bit of information I have about it is that it's prerequisite is Calc I.

    What gets discussed, and is it an intensive course? I'm trying to pack my schedule with as much as I can possibly take, yet don't want to go overboard.

    Thanks.
     
  2. jcsd
  3. Apr 23, 2009 #2

    jtbell

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    Staff: Mentor

    Doesn't your university have a course catalog either in print or on line where you can look up the course description? We have a course by that name here, but I have no idea how well it would match up with your course. For what it's worth, here's our description for it: "It is designed to prepare a student for advanced math courses and will cover concepts and techniques used in studying logic, proofs, set theory, relations, functions, and cardinality of sets."
     
  4. Apr 23, 2009 #3
    Since it's probably specific to your school, you'd need to look at the course description (which should be available in the "undergraduate catalog"... usually available through the registrar's office).

    Once you get a course description up, it will help people answer your question better (if it doesn't just answer this for you on its own). you might also want to talk to students at your school who have taken the course... as well as faculty at your school.

    Edit -- oops... jtbell beat me to it! I need to type faster!
     
  5. Apr 23, 2009 #4
    Oh, ha. I was in the course catalogue but didn't scroll all the way down.

    Here is the description:

    2300. Transition to Advanced Mathematics (3) P: MATH 2171. Proof methods including induction, naïve set
    theory, functions and relations, cardinality, basic number theory, completeness of the real number system.

    I'm sure many people here know of these things...does this sound like either a time-consuming or a difficult course?
     
  6. Apr 23, 2009 #5
    It sounds like something my undergraduate institution called "Intermediate Analysis." I didn't take it; since I was not a math major (rather a math minor), I skipped it and just went straight for the "advanced" courses: Complex Analysis and Real Analysis (which had the intermediate class as a recommended but not required prerequisite). I heard it was tough for some students, and a "cakewalk" for others.

    What you might be able to do... see if you can find a course website for one of the more recent classes at your institution... and check out what text is being used. Get a copy (perhaps from the library?) and look over it. Maybe you can even see some notes if those are posted. And again, I'd recommend directly talking to some students at your institution who have taken the course. That's where I always got my course advice (though I didn't always heed it and tended to overload myself!).
     
  7. Apr 24, 2009 #6
    Depends on how much you have written proofs before. Writing mathematical proofs isn't easy, and definitely takes some practice until you get comfortable with it. So you might think the course is a little challenging at the beginning. However, it's a very helpful course if you're going to take upper-division math courses. In fact, taking an upper-division math course without any experience on writing proofs would be VERY challenging and time consuming, so this would be a great course to gain some experience. And the things that are listed on the course description is something all the math majors should know. You know you took pre-calculus before you took calculus, right? This course is probably going to be your pre-math major class before you get to the serious stuff.
     
  8. Apr 24, 2009 #7
    Well, I took Intro to Logic last semester, so I know a lot of the rules. I just haven't had to apply them to math before. Not sure if replacing P's and Q's with numbers would be a huge difference, it might be. But I have no experience with mathematical proofs.
     
  9. Apr 24, 2009 #8
    Logic is basically the foundation of mathematics, so you're in a good shape. You do, however, need to apply that logic so that you can write a mathematical proof. It's a little more than just making truth tables, you know.
     
  10. Apr 24, 2009 #9
    Well, we did that, but with sentences. Truth tables were easy...but then came the "turn this into this" and it got pretty complicated. There were over 20 rules, and then the Reductio Ad Absurdum and...something else. I forget.

    I suppose that this course would be manageable, even on a already (pretty) heavy load?
     
  11. Apr 24, 2009 #10
    I'm perhaps going to say something heterodox here, but logic is to proofs as syllables are to language. Yes, you need to understand logic and be comfortable with it to do mathematics, but math is much larger than truth tables and what we think of as the rules of logic.

    Remember that proofs are a form of communication among humans, not something you program into a computer. Why not have a look at various proofs and see if you can follow them & get a feel for them?
     
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