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How much math do you need to become a theoretical physicist?

  • Thread starter xbomber88
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  • #1
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Main Question or Discussion Point

I kind of doubt that I have the intelligence to become a theorist but let's just pretend for a minute that I do. How much math would I need to learn? So far I've completed multivariable calculus and linear algebra and the only other math course that I'm required to do for my physics major is differential equations. But from what I understand to be a theorist you need to go beyond that and know some very advanced math. What courses specifically would I need to take? And does a theoretical physicist really need to understand those more advanced topics as well as a mathematician does or do they just need a more basic superficial understanding? One problem for me is that I really hate mathematical rigor and I'm not very interested in or very good at writing proofs. It all seems really tedious to me. Are those things essential to being a theoretical physicist? And do the people who became theorists usually have to take tons of math courses or can you learn the necessary math in your physics courses? Clearly I don't know much about it. I'm only in my first year of undergrad physics. But I'm trying to plan ahead so I have as many options available to me as possible in my future because right now I think it would be more interesting to be a theoretical physicist than an experimental physicist but I'm not sure if I actually have the ability to do it.
 

Answers and Replies

  • #2
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Hi,

I'm not sure I understand as I'm not from the US, but how is it possible that linear algebra, differential equations and multi variable calculus are the only maths courses you need to take at university?

What about probability and statisitics for instance, I think you will probably have to do these at some point in your degree.
 
  • #3
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Here's all the math you should know if you want to be a theoretical physicist:
Algebra
Geometry
Trigonometry
Calculus (single variable)
Calculus (multivariable)
Analytic Geometry
Linear Algebra
Ordinary Differential Equations
Partial Differential Equations
Methods of approximation
Probability and statistics
Real analysis
Complex analysis
Group theory
Differential geometry
Lie groups
Differential forms
Homology
Cohomology
Homotopy
Fiber bundles
Characteristic classes
Index theorems
Supersymmetry and supergravity
K-theory
Noncommutative geometry

For more info:
http://www.superstringtheory.com/math/index.html
 
  • #4
374
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What kind of theoretical physicist do you want to be?

I don't think that anyone who studies physics can get away without being well versed in everything up to and including group theory in the list posted by EnSvensk. Beyond that, though, the rest of that stuff is useful if you want to do high energy or nuclear theory, string theory, gravitation, etc. There's plenty of other theoretical physics out there, though.
 
  • #5
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Hi,

I'm not sure I understand as I'm not from the US, but how is it possible that linear algebra, differential equations and multi variable calculus are the only maths courses you need to take at university?

What about probability and statisitics for instance, I think you will probably have to do these at some point in your degree.
Many things are introduced within physics courses. I remember partial differential equations were touched upon in E&M, and elements of group theory and probability were taught in quantum mechanics.
 
  • #6
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Many things are introduced within physics courses. I remember partial differential equations were touched upon in E&M, and elements of group theory and probability were taught in quantum mechanics.
I'm actually quite surprised by this, at my university in the UK the course tends to be very mathematical, partial diff eqs for example we go into depth by the 2nd year. But maybe that's just the school I go to.

Either way, to answer the original poster. I would imagine that for one to become a theoretical physicist one needs to be very comfortable in all the branches of maths used in their area of physics.

It is highly unlikely you will need to have a strong grasp (or even a weak one..) of the long list provided by EnSvensk while still an undergrad.
 

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