Real Analysis or Complex Analysis

In summary, if you want to go into grad school to study Applied Mathematics or Physics, you should take Real Analysis first. However, it is possible to take Complex Analysis later on if you need to.
  • #1
tropian1
7
0
I'm about to start scheduling my courses for next year, and I have the option of taking either Real Analysis or Complex Analysis. I'm double majoring in Math and Physics, and I want to go to grad school to study either Applied Mathematics or Physics. I haven't taken any higher level math courses yet, (excluding calculus), so my knowledge of both these courses is pretty limited. Which one will benefit me more going into grad school?
 
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  • #2
Can't you take both courses?
I think Real and Complex analysis are both pretty much essential to any math degree.
 
  • #3
I'm actually required to take a semester of a course called "Intro to Analysis" and then I have the option of either Real Analysis or Complex for another semester. I could definitely take both, however I'm already taking a ton of courses as it is. The course description for Real Analysis says it's a continuation of Intro to Analysis, whereas Complex Analysis just has Intro to Analysis as a prerequisite.
 
  • #4
This is kind of a tough decision. On the one hand, complex analysis will be much more applicable to the career track you are looking for. On the other hand, Real Analysis will definitely be a solid preparation for complex analysis. Real isn't required for complex, but a lot of the same ideas apply, for example uniform convergence of a series. If you can, take both but take Real first. If for some reason your university only offers complex once every few years or something, you should probably go ahead and take it.
 
  • #5
Assuming I take Real Analysis, would it be out of the question to try taking grad level complex analysis later on?
 
  • #6
tropian1 said:
Assuming I take Real Analysis, would it be out of the question to try taking grad level complex analysis later on?

It's perfectly doable, but it certainly won't be very easy.
 
  • #7
tropian1 said:
Assuming I take Real Analysis, would it be out of the question to try taking grad level complex analysis later on?

Not knowing anything about you personally, I would assume this would be very difficult. I would imagine most grad complex analysis classed already assume you know a lot of stuff (like what is an analytic function, Cauchy's theorems, maximum modulus stuff, etc) and these topics are quickly introduced and these theorems quickly explained (to get to more advanced stuff).
 
  • #8
Right, it just sounds like trying the other way around would be a terrible idea. I'll try fitting both in, that seems to be my best bet. Anyways, thanks for the advice.
 

What is the difference between Real Analysis and Complex Analysis?

Real Analysis focuses on the study of real numbers and their properties, while Complex Analysis extends this study to include complex numbers. Complex Analysis also incorporates the concept of functions of a complex variable.

What are some real-life applications of Real Analysis or Complex Analysis?

Real Analysis is used in various fields such as physics, engineering, and economics to model real-world phenomena and solve problems involving continuous systems. Complex Analysis is used in fields like electrical engineering, fluid dynamics, and quantum mechanics to model and analyze complex systems.

What are the key concepts in Real Analysis or Complex Analysis?

Some key concepts in Real Analysis include limits, continuity, differentiation, and integration. In Complex Analysis, key concepts include analytic functions, Cauchy-Riemann equations, and contour integration.

What are some common techniques used in Real Analysis or Complex Analysis?

Some common techniques in Real Analysis include the use of theorems and proofs to establish mathematical truths, as well as the use of calculus and algebraic manipulation to solve problems. In Complex Analysis, techniques such as power series, Laurent series, and residue calculus are often used.

What is the historical significance of Real Analysis or Complex Analysis?

Real Analysis has its roots in ancient Greek mathematics, with significant contributions from mathematicians like Archimedes and Euclid. Complex Analysis, on the other hand, has a more recent history, with developments in the 18th and 19th centuries by mathematicians such as Euler, Cauchy, and Riemann.

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