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Math 3X03
Complex Analysis I
Published by Mowicz
06072009

Published by 

Elite Member
Join Date: May 2008
Posts: 1,538


Author review 
Overall Rating   7 
Professor Rating   8 
Interest   8 
Easiness   7 
Average 75%




Math 3X03
I've decided to put up a few reviews for any wandering Math majors (or enthusiasts!) entering third year. I remember I had no clue which Math courses were interesting, since the names suddenly shift to stuff you've never heard of and your course options suddenly become more broad.
Math Stream: Analysis (Pure Math)
Taken with: Dr. Speissegger
First off, it is worth noting that this course, as well as Math 3A03, are manditory for any Math degree...regardless of your course interests. So get used to this course, you've got to take it. So this review is not aimed to convince you to take or avoid this course...instead it is intended to show you what to expect.
Course Description:
This course, as did 3A03, revolves around the concept of mathematical proof, and drastically increases one's mathematical maturity. This course is a little more relaxed than 3A03 was, but be prepared for a course full of rigorous proofs.
Unlike 3A03, there will be some calculatory aspects to this course. This is a crash course in Complex number systems, as opposed to Real number systems.
First, you will receive a crash course in complex numbers. How to view the Complex Plane, and how it is isomorphic to R^2: every complex number a + ib, corresponds to exactly one ordered pair, (a,b).
Next you will learn what it means for a function to be holomorphic...also known as 'complex differentiable.' The basic property is that the function must satisfy something called the Cauchy Riemann equations (very easy to check), which intuitively means that the limit that defines the derivative (in the Real sense) makes sense under rotations. After all, a limit only exists if no matter how you approach it, you get the same result. Then you will learn about analytic, and entire functions...those which have convergent tailor series expansions in some region. Then you will learn a beautiful relationship exists between analytic and holomorphic functions...they are one and the same! Every analytic function is holomorphic, and vice versa.
Finally, you will continue to learn many beautiful results in Complex Analysis, such as integration of any function over a simple closed curve in any analytic region is zero! Regardless of path.
One thing of note you will prove in this course is the Fundamental Theorem of Algebra. That is, every complex polynomial of degree n, has exactly n roots, which need not be distinct.
Professor: Dr. Speissegger is a very skilled professor who has a knack for proofs and class involvement. Often times he invites students to give a suggestion for how to solve a problem, and then follow through with it, knowing well in advance that it may not work. This helps to build a student's problem solving skills. He may not be the most sympathetic professor however.
Good luck!
Melanieee
says thanks to Mowicz for this post.




01082010 at 09:56 PM

#2

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Real name: Mah
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Hey Mowicz, I was looking at some upper year courses in math (2A03, 2C03, 3D03 and 3H03, namely).
Did you take any / all of those?



01092010 at 01:00 AM

#3

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Real name: Mike
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Having read this review over again, I realize I worded some things very badly...but hopefully no other math majors will come here and nitpick lol. For future reference, I know that I've said some things quite poorly, like claiming that a region is analytic. S:
Anyway, here's what I know about those courses (**Note: These responses are specifically intended for Mahratta and may not apply in a general setting**):
Math 2A03  I took (and just TA'd last term) 2A03...it's more or less an introduction to differential/integral calculus of multiple variables (that's the big change from first year calculus), and an introduction to vector calculus, which is creating mathematical objects called vector fields and doing calculus on those. It's a beautiful subject, very visual with lots of pictures to be drawn. By the end of this course, you can set up integrals to solve questions like "What's the volume that lies between the unit sphere and the unit cylinder?"
Math 2C03  A standard course in what are known as Ordinary Differential Equations (Or ODEs...there are other types). I'm sure you're familiar with say, polynomial equations like x^2 + 5x + 3 = 0...ODEs are equations involving derivatives.
For instance, y' + y = 0 is a differential equation. y here stands for a function...how do we solve it? Well, y' = y...what function do you know which simply 'turns negative' upon taking a derivative? e^(x) + C will work.
Solving differential equations is, in general, very difficult. So this course, as an introduction, will basically teach you some tricks used to solve some standard ODEs (kind of like how you learn types of integration in Math 1A03/1AA3).
Math 3D03  Actually, this course is an antirequisite for Math 3X03 (which is reviewed above). This course teaches a first course in complex variables, is far more computation based than 3X03 (uglier computations however), but focuses less on the theory. It's really a toss up here, you can either do more tedious work (3D03), or more difficult work (3X03)...I'd recommend 3X03 over 3D03, but that's just my personal choice (I hate tedious computations).
Math 3H03  Number theory is highly theoretical...it's a bit heavy for the purposes of a minor, but it depends on your specific tastes and what you'd like to do with your degree. Send me a PM if you have questions, but in general I'd advise against it. If 3CY3 (Cryptography) is offered, that's like Number Theory applied to coding and code breaking, which is kind of a fun course.
If not, I'd recommend 3U03 (Combinatorics) or 3V03 (Graph Theory) as two 'fun' 3rd year maths that help build exposure to various areas of the subject.
Melanieee
says thanks to Mowicz for this post.



01092010 at 11:37 AM

#4

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Ah, thanks for the feedback!
Regarding number theory  I thought it would be a bit heavy, but it seems really, really interesting (that's probably because I don't know very much about it ) from the description...



03302018 at 11:00 PM

#5

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thanks I realy need books about this



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