How important are these courses for chaos theory/dynamical systems?

In summary, the conversation discusses the speaker's interest in pursuing graduate studies in chaos theory and dynamical systems. They are considering switching to a major in mathematical physics, mathematics, or applied mathematics and are unsure which courses are crucial for their chosen field. The conversation also touches on the marketability of skills gained through studying these fields, with the speaker noting that their skills have been useful in engineering jobs and scientific research.
  • #1
Ryker
1,086
2
I'm currently a physics major with a year left, and deciding whether to switch into mathematical physics, mathematics or applied mathematics. I'm definitely switching into one of them, as I can meet the requirements for either in my last year and all of them align better with my interests. Speaking of which, at this point I think I want to pursue graduate studies related to chaos theory/dynamical systems. I did a bit of searching and this seems a field that is sometimes studied from an (applied) mathematical viewpoint and at other times from a physics viewpoint.

Not knowing how exactly I want to go about studying this, i.e. I don't know which side interests me more, since it kind of depends on the actual topic, not the approach per se, here's where my quandary comes in. Namely, which of the following courses do you find most crucial if I do indeed want to study the aforementioned fields:

A) Quantum mechanics II, Electromagnetism II [mathematics/math physics/applied maths]

B) Continuum mechanics [mathematics]

C) Intermediate PDE's (a second course in PDE's), Numerical methods [applied maths]

I've grouped this into three separate categories, because if I go with either of the courses in C), then I can't take B). In square brackets I've also listed the programs that I'd need to be in if I want to fit them into my schedule next term.

Personally, I'd like to get a taste of continuum mechanics, but then I definitely can't take either of the courses in C, and what worries me is that those would perhaps be required if I was to approach the subject from a mathematical standpoint in grad school. On the other hand, I'm not sure I could get away with not taking the courses in A if wanted to approach things from the physics side.

What would you recommend?
 
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  • #2
Maybe a old Post and forgotten by OP but I'm a physics student with same interests on chaos and non linear Dynamics , I'd like to know what happened with your career on chaos and DS
 
  • #3
Erloto said:
Maybe a old Post and forgotten by OP but I'm a physics student with same interests on chaos and non linear Dynamics , I'd like to know what happened with your career on chaos and DS

I'm not the OP, but I did considerable graduate work in chaos and dynamical systems en route to a PhD in Physics. Career? I have not really gone on to have a career or make any money in those fields. But my graduate work in those fields did provide lots of marketable skills, including: 1) Being able to numerically integrate just about any differential equation that comes my way 2) Being able to develop a sound statistical approach to reasonably model many systems that are too complex to be exactly solvable from first principles. 3) Programming skills for serious number crunching in Fortran and C. 4) A sound scientific approach to test whether qualitative hypotheses are really supported by the numerical data available for complex systems. 5) A sound scientific approach to test whether quantitative (usually statistical) hypotheses are really supported by the available numerical data for complex systems.
 
  • #4
Thanks for the quick response , are those marketable skills useful for any particular sector(kind of industry) ? Or are they exclusive in scientific research?
 
  • #5
Erloto said:
Thanks for the quick response , are those marketable skills useful for any particular sector(kind of industry) ? Or are they exclusive in scientific research?

For me, those skills have proven marketable in a variety of R&D jobs, more engineering jobs really than scientific research, as the companies that have hired me were always keen on making money by selling tech products than making fundamental scientific advancements.

The skills have also proven useful in my more fundamental scientific research, but that side of my life (while yielding plenty of publications, citations, and awards) has not earned nearly as much money, so I don't think the skills are nearly as "marketable" on the scientific research side.

I support my love and habit of science with marketable engineering work.
 

Related to How important are these courses for chaos theory/dynamical systems?

1. How does chaos theory/dynamical systems impact real-world phenomena?

Chaos theory and dynamical systems are important in understanding and predicting complex behavior in various fields, such as weather patterns, population dynamics, and stock market fluctuations. By studying chaos theory, we can better understand the underlying patterns and processes that govern these phenomena and make more accurate predictions.

2. What are some practical applications of chaos theory/dynamical systems?

Chaos theory and dynamical systems have practical applications in various fields, including physics, engineering, biology, economics, and social sciences. For example, chaos theory is used in weather forecasting models and in designing more efficient aircraft engines. In biology, it can help us understand the complex behaviors of biological systems, such as the synchronization of firefly flashes or the spread of diseases.

3. How important are these courses for understanding nonlinear systems?

Chaos theory and dynamical systems are essential for understanding nonlinear systems, which are systems that cannot be easily described by linear equations. Many real-world phenomena, including weather patterns, population dynamics, and biological systems, exhibit nonlinear behavior. These courses provide the necessary tools and concepts for analyzing and predicting the behavior of nonlinear systems.

4. What are the key concepts in chaos theory/dynamical systems?

Some key concepts in chaos theory and dynamical systems include sensitive dependence on initial conditions, bifurcations, attractors, and fractals. These concepts help us understand how small changes in initial conditions can lead to drastically different outcomes, how systems can undergo sudden and dramatic changes, and how complex systems can exhibit self-organizing and repeating patterns.

5. What skills can I gain from studying chaos theory/dynamical systems?

Studying chaos theory and dynamical systems can help develop skills in mathematical modeling, critical thinking, and problem-solving. These courses also require a strong understanding of calculus and differential equations, so they can help improve your mathematical skills. Additionally, studying chaos theory can also enhance your ability to analyze and interpret complex data sets, which is valuable in many scientific and research fields.

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