How important is probability and mathematical statistics?

[kakarotyjn]

I'm a sophomore in math.I intend to learn mathematical and physics something like differential geometry,topology and QFT in my next years and do some research in some relative topics.I know I need to learn many courses and I feel I don't have enough time.This semester we open a course called probability and mathematical statistics.I know it's a basic course for students in math but I want to know How important is probability and mathematical statistics?

Does it play an important role in some mathematical physics fields,like superstring,gauge theory or complex geometry?Do you use it often in your research?

How deep should I learn it you think?I'm really don't interested in it and don't have time.

Thanks for your advise.

 

[chiro]

I'm a sophomore in math.I intend to learn mathematical and physics something like differential geometry,topology and QFT in my next years and do some research in some relative topics.I know I need to learn many courses and I feel I don't have enough time.This semester we open a course called probability and mathematical statistics.I know it's a basic course for students in math but I want to know How important is probability and mathematical statistics?

Does it play an important role in some mathematical physics fields,like superstring,gauge theory or complex geometry?Do you use it often in your research?

How deep should I learn it you think?I'm really don't interested in it and don't have time.

Thanks for your advise.

Aside from the obvious roles like statistician and actuary, statistics is important when considering information theory and stochastic calculus. Information theory is used in electrical/telecommunications/computer engineering and if your that way inclined it is vital to know and understand.

You will find applications in quantum mechanics and statistical mechanics, thermodynamics (particularly information theory). With regards to financial mathematics more advanced probability comes into play.

Since you have taken the basic course you are at least aware of some of the elements involved. Typically most mathematicians will specialize in a couple of areas (unless you're like Von Neumann or Newton). Being aware of the vast number of fields in mathematics will help you in general analysis because each variety of mathematics brings together its own tools, its own decompositions (ie "atoms" of analysis), and its own perspective on understanding models, representations, patterns and problem solving.

You'll find that a lot of maths outside of the "statistics/probability" flavour courses will complement those type of courses. Take for example analysis of time series. You may want to smooth out a time series graph. One way to smooth out the "chaos" in a function is to use Fourier analysis. There is tonnes of examples but I thought i'd mention one.

There are tonnes of theoretical implications of probability and statistics results that are important to a lot of fields including the central limit theorem. Information theory uses results that give indicators of entropy of data and hence theoretical compression ratios with various compression schemes (in fact huffmanns scheme was an optimal solution to a problem he was posed in MIT).

There's probably more but hopefully I've thrown a bone with some meat for you to chew on.

 

[chiro]

Also markov models are used in modelling language, financial risk, models and theories of certain music structures, and many other phenomena. Generally you should think of this as "conditional dependence". You will find that a lot of risk management and insurance is built off this mathematics and extended in any custom way necessary.

 

[twofish-quant]

Does it play an important role in some mathematical physics fields,like superstring,gauge theory or complex geometry?Do you use it often in your research?

Probability and mathematical statistics turns out to be quite important in observational cosmology. It's also pretty essential in any sort of observational physics.

 

[kakarotyjn]

Thank you for all your recommendations,I think I need to take a few classes and then make my own decision.