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Advanced Calculus I (Analysis)

  1. Mar 1, 2005 #1
    Hi.

    I was wondering... this course seems pretty rigorous and tough. Was this course proven extremely difficult when you guys took it?

    I'm planning to take it during Summer quarter, but need some feedback on how hard this course will be.

    Thanks in advance.
     
  2. jcsd
  3. Mar 1, 2005 #2

    dextercioby

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    It's neither rigurous,nor tough.It's how a math course should be: rigurous...The tough part comes from the student being lazy...And hating maths...

    Daniel.

    P.S.My advice:Deal with it in a serious manner.
     
  4. Mar 1, 2005 #3

    Galileo

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    What topics are covered in advanced calc?

    (Here we just name the courses: Analysis 1, Analysis 2, Analysis 3, Analysis 4,.....,Analysis 19854 (you get the point)).
     
  5. Mar 2, 2005 #4
    Here's the course description from the university catalog:

    MATH 350 Advanced Calculus I
    Summer 2004 , Fall 2004 , Spring 2005
    Description: Prerequisite: Math 250B. Corequisite: Math 280. The real number system, limits of sequences, and limits of functions. Continuity, differentiation, and integration of functions of one variable. Infinite series.
    Units: (3)
     
  6. Mar 2, 2005 #5

    dextercioby

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    If it doesn't start with elementary notions of topology,then it's not "advanced" to me...

    They already tell you what to expect and what you should know.So that should be enough.In the end,at the exam,everything will depend on you,ONLY.

    Daniel.
     
  7. Mar 2, 2005 #6

    HallsofIvy

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    "Advanced Calculus" is not a uniform as Calculus itself is now-a-days. In some colleges, "Advanced Calculus" is "Engineering mathematics": Fourier series, partial differential equations, extended use of Green's and Stoke's theorem, etc.

    In some colleges, it is "Analysis": the theory behind calculus including basic topology and derivatives and integrals of functions from Rn to Rm. Often it is a combination of the two approaches. I would expect "Advanced Calculus" to include at least the metric topology of Rn.
     
  8. Mar 2, 2005 #7

    Galileo

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    Ok. Well when I got my first analysis lecture, I got it pretty rough. Everyone did, because the gap here between high school and university is pretty big in the exact sciences (and is getting bigger). I`m sure the same problem exists in the US.

    The rigour at which things are done is something to get used to. It's the right way to go about it. Try to understand and reproduce proofs by yourself and make lots of exercises to get the hang of it. Practice makes perfect.
     
  9. Mar 2, 2005 #8

    mathwonk

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    i found rigorous calculus difficult but quite enjoyable, because it actually explained why things were true, and even proved them. the more theoretical slant pleased me a lot, as opposed to tedious calculation without motivation.

    i.e. in a rigorous calc course terms are actually defined, so you know what you have to work with.
     
    Last edited: Mar 3, 2005
  10. Mar 2, 2005 #9

    HallsofIvy

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    My experience is that, for most math majors (mathwonk excluded, of course), find Advance Calculus (Analysis) and Abstract Algebra to be the hardest courses.
     
  11. Mar 3, 2005 #10

    mathwonk

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    when i realized he was talking about elementary but rigorous calculus i recalled more accurately that it had been quite difficult, since it was my first encounter with real math, but very invigorating and satisfying nonetheless.

    So apparently you are talking about the first course in which they use "epsilon and delta". A key factor in the difficulty of the course may be the book you use. Rudin's book is famous for its terse style, which many people find makes the subject more dificult than necessary.

    On the other hand, Spivak's calculus book goes a long way to explain clearly what is going on in this topic. Apostol is also excellent. These books were written when this course was taught to beginners, so they treat you like an intelligent beginner.

    Other more recent books have been written to help current students making their first transition to rigorous material, such as the introduction to analysis by Arthur Mattuck, or Maxwell Rosenlicht. You might look at those as well.

    The material is hard, but it is also the standard foundation on which all modern mathematics rests. It is definitely worth knowing about it.
     
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