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Complex Analysis

  1. Dec 3, 2008 #1
    I was just wondering if I was ready to take a 4th year undergrad course in Complex Analysis. The book we will be using is called Complex Function Theory and its buy Sarason. I've taken a course in multivariable calculus, number theory, discrete mathematics, differential equations and modern algebra.

    Here is the course description:

    Introductory Complex Analysis (MAA 4402) 3 credits
    Prerequisite: MAC 2313
    An introduction to complex analysis, analytic functions, Taylor
    series, Cauchy’s theorem. Calculus of residues. Recommended
    for engineering and science majors.

    The only prereq is Multivariable calculus.
  2. jcsd
  3. Dec 3, 2008 #2
    Painful Truth: You can't tell anything about a course from a course description.

    You meet the prereqs and it sounds like you're comfortable enough with the necessary calculus. But if you really want to know how it will be, go see the professor who will be teaching the class before you enroll =-)
  4. Dec 4, 2008 #3


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    :biggrin: I once taught a class called "Mathematical Methods for Economics and Business Administration" which was actually offered by the Business Administration department. The college catalog description included partial derivatives and differential equations. The only prerequisite was the remedial algebra class!:eek:

    Needless to say, the course include practically nothing mentioned in the catalog description.
  5. Dec 4, 2008 #4


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    On the other hand, I took a classical mechanics course that had no prerequisites listed... first day of class uses calculus of variations all over the place (obviously) and at the end the lecturer says "If you didn't take calculus of variations last term, you might as well drop the class, because you need it to understand what's going on"
  6. Dec 6, 2008 #5
    =/ that doesn't help at all. I've tried getting in contact with the professor but he's never around. I wrote the name of the book because I was told that the difficulty of the class is usually based on the book used. So, the book is by Sarason. Does anyone know how hard of a book it is compared to rudin?
  7. Dec 6, 2008 #6


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    I don't know Sarason.
    Which Rudin?
    Principles of Mathematical Analysis?
    Real and Complex Analysis?
    Functional Analysis?
    Function Theory in the Unit Ball of Cn?
    The Way I Remember It?

    Lets say Sarason is easier than Principles of Mathematical Analysis, what then?
    Likely the "Recommended for engineering and science majors" measns "this class is dumbed down". You do not say how much calculus you know. I you know calculus at the level of Principles of Mathematical Analysis, that should be more than enough. Multivariable calculus at a lesser level is probably enough. In some complex classes "as you recall from calculus..." is frequently said, only you know how likely it is that you do not remember, or if you can find out painlessly.
  8. Dec 6, 2008 #7
    Principles of Mathematical Analysis. The Rudin book is used to compare the levels. I've looked over Rudins book and if Sarasons is easier then that then I know I won't have too hard a time in the course.

    Well I've had 4 semesters of calculus. I still remember how to prove Greens Theorem and Stockes Theorem. I still know how to compute line integrals, triple integrals and all the other stuff from Calculus.

    The course isn't open to science and engineering majors and I know for a fact it wasn't dumbed down. I spoke with the Chair of the Math Department and he said it was one of the heavier math courses offered at my university.

    Here's the problem. I haven't been able to find the Sarason book online and I'm in the middle of taking finals so I haven't had time to go to the bookstore and get the book. The professor I'm taking the course with never rights notes and basically lectures the entire time. So if anyone has an idea of how hard Sarasons book is then it'd help me figure out if i can still do well in the course just by reading the book and doing it on my own.
  9. Dec 6, 2008 #8


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    I read a few pages (preview available on amazon.cm and books.google.com among others, read a few pages) and I wuld call it "medium" strength.
    silly books<Churchill<Lang<Sarason<Ahlfors<Copson
    (Lang being easier only so far as requiring minimum back ground)
    My heart is warmed as Sarason is old fashioned and assumes the reader knows Calculus.
    From preface
    "... The user of the notes is assumed to have a thorough grounding in basic real analysis, as one can obtain, for example, from the book of W. Rudin (Principles of Mathematical Analysis) ..."
    "...Notions like metric, open set, closed set, interior, boundary, limit point, and uniform convergence are employed without explanation. ... "
    The author added appendicies to cover some "as you recall from calculus..." for those that do not remember.
    The book is short and dense (~160 pp.) and includes only the 1 semester core material.
    The author taught at Berkeley and the book is still used there with advice of knowing the material in Principles of Mathematical Analysis chapters 1-7.
    Last edited: Dec 7, 2008
  10. Dec 7, 2008 #9
    Awesome. Thanks for all the help.
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