Complex Variables or Stochastic Processes?

In summary, the conversation is about a math and physics major who wants to pursue biophysics in grad school. They are undecided on which math course to take - Complex Variables or Elementary Stochastic Processes. Both courses have brief descriptions, with Complex Variables covering analytic functions, integration, power series, residues, and conformal mapping, and Elementary Stochastic Processes covering Markov chains, Poisson process, and Brownian motion. The group ultimately agrees that Stochastic Processes would be more useful for practical applications in biology, but also acknowledges the importance and fascination of Complex Variables.
  • #1

casesam

13
0
Hi, I am a math and physics major planning on going into biophysics for grad school, and i want to do computational/mathematical modelling/theoretical work in the field. I have one more math course to take and I am not sure which would be more useful. Here are their very brief course descriptions.

Complex Variables:Analytic functions, integration, power series, residues, and conformal mapping.

Elementary Stochastic Processes: Markov chains, Poisson process, and Brownian motion.

Thank You!
 
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  • #2
I vote stochastic Processes. Much of complex variables may be overly theoretical. I think basic complex analysis is very important but if you are mostly interested in applications you should just study basic complex on your own. Its not overly difficult. Stochastic Analysis has many applications to biology.
 
  • #3
deluks917 said:
I vote stochastic Processes.

Agree.
 
  • #4
deluks917 said:
I vote stochastic Processes. Much of complex variables may be overly theoretical. I think basic complex analysis is very important but if you are mostly interested in applications you should just study basic complex on your own. Its not overly difficult. Stochastic Analysis has many applications to biology.

chingkui said:
Agree.

Although I hate the thought of a mathematician not taking complex analysis, I have to concur. But I echo deluks in that you really should spend some time at some point in your career learning it. I think it's a really fascinating subject - and some of the results were pretty surprising to me.
 

1. What are complex variables?

Complex variables are numbers that have both a real and imaginary component. They are represented in the form a + bi, where a is the real part and bi is the imaginary part. Complex variables are used in various branches of mathematics and physics, such as complex analysis and quantum mechanics.

2. What are some applications of complex variables?

Complex variables have many applications in mathematics, physics, and engineering. Some common applications include solving differential equations, analyzing electrical circuits, and studying fluid flow and aerodynamics.

3. What is the difference between a stochastic process and a random process?

A stochastic process is a mathematical model that describes the evolution of a system over time, taking into account random variations. A random process, on the other hand, is a sequence of random variables that represent a system's behavior over time. In other words, a random process is a specific instance of a stochastic process.

4. How are stochastic processes used in real-world applications?

Stochastic processes are used in a wide range of real-world applications, including finance, economics, biology, engineering, and telecommunications. They are often used to model and analyze systems with random behavior, such as stock prices, weather patterns, and genetic mutations.

5. What are some common stochastic processes?

Some common types of stochastic processes include Markov processes, Poisson processes, and Gaussian processes. Markov processes describe systems with a finite number of states and random transitions between them. Poisson processes model events that occur randomly over time. Gaussian processes are used to model systems with continuous random variables and are often used in machine learning and data analysis.

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