Understanding Math Tools for a Career in Physics or Engineering

[f(x)]

Hi,
Though i am really interested in physics, yet i can't figure out which math tools i need. Plz throw some light on the matter as to how these topics may be helpful. Currently, i have just begun my senior secondary courses (11th grades)
1. Complex /\/umbers
2. Determinants & Matrices
3. Topology
4. Statistics

Not that i don't understand these, but i often find them annoying. I have a real liking for calculus and trigonometry, and that's which i use the most in my physics. IS there any future use of the mentioned courses if i decide to pursue a career in physics or engineering

 

[D H]

Yes, yes, yes, and yes.

Calculus and trigonometry are not the be-all and end-all of mathematics.

• Physics and engineering would be a lot messier without complex numbers and matrices.
• Theoretical physics and topology have much in common.
• Statistics are essential for proper analysis of experiments and for monte carlo analyses. There is even an entire branch of physics called statistical physics

 

[complexPHILOSOPHY]

I hardly doubt that you understand the foundations of mathematics enough to be 'annoyed' by topology. I would posit that topology is perhaps one of the most unifying ideas of mathematics, presently and has profound implications on the field of modern and future physics

 

[Hurkyl]

I would say all four are quite important. I want to make some comments on the first 2:

(1) Complex Numbers

The complex numbers have algebraic properties that frequently makes them more convenient to use than the real numbers. And, of course, complex analysis is quite powerful. It is not uncommon for a problem involving only real numbers to be most easily solved by using complex numbers.

Furthermore, complex numbers are good for expressing physical concepts that involve a phase. (Especially things that have a phase and a magnitude)


(2) Determinants & Matrices

It's not just these, but the whole subject of linear algebra that is useful. I posit that you have little hope of understanding either quantum mechanics or general relativity without being proficient with linear algebra.

 

[Maxwell]

I have a real liking for calculus and trigonometry, and that's which i use the most in my physics.

That's what you use for your physics - in high school! At university, you'll be using all four the the concepts you listed in your initial post.

 

[jtbell]

1. Complex /\/umbers

You'll definitely need these for quantum mechanics. They're also used in optics and electronics (AC signals), indeed any kind of wave or harmonic motion.

2. Determinants & Matrices

Electrical circuit analysis (Kirchoff's Laws), anyplace else you need to solve systems of linear equations, coordinate transformations, etc.

3. Topology

OK, you probably don't need this for undergraduate-level physics.

4. Statistics

Analysis of experimental data. Also, QM is probabilistic by nature, so to understand it you need to know concepts from probability and statistics, such as expectation value and variance. Also, there's a whole field of statistical mechanics which explains classical thermodynamics in terms of the statistical properties of the atoms or molecules in a substance.

 

[Daverz]

Hi,
1. Complex /\/umbers
2. Determinants & Matrices

Physicists eat, breathe, and **** all three.

3. Topology

Helpful for theoretical physics, but I don't think a full formal course is necessary. I think the way it's usually taught, as a course in proofs, is pretty dull.

4. Statistics

Helpful for theoretical work and essential for experimental work. Probably a pretty easy course for most physics students.

 

[Hurkyl]

Helpful for theoretical physics, but I don't think a full formal course is necessary. I think the way it's usually taught, as a course in proofs, is pretty dull.

Certainly physicsts probably don't need topology in its full abstract glory -- I'm thinking more along the lines of understanding the varied topological spaces that they actually use, though. e.g. what does it really mean for one path to be a perturbation of another? What is a limit of a sequence of electromagnetic fields? Can we really raise e to the power of an operator?

 

[f(x)]

Ah..ok i got the point. Maybe learning these would be more fun now that i know these are useful.
we don't have topology as such, i just asked out of curiosity (ignore my annoyance to that )
Just one question regarding statistics-do i need go in the complete depth of the subjects? I mean Deviations, Variance and all that stuff. For probability calculations, arent Permutations and Combinations enough?

 

[chroot]

f(x),

Stop trying to figure out the bare minimum amount of education you need to become a physicst. Stop right now. That attitude will destroy any chance you'll ever have at becoming a physicist. If you think learning new things is a chore, you will fail miserably.

Instead, try to cultivate a joy of learning. Education is wonderful, and exciting, and is a privilege more precious than any other. Learn to savor every bit of it. There's no harm in learning things now that you won't explicitly use for some time. All knowledge is valuable because it will help you understand later concepts more quickly and more thoroughly.

- Warren

 

[berkeman]

I second chroot's comments (well said, BTW). Learning and applying advanced concepts is truly a joy. And you'll be surprised how much of the breadth of your overall learning that you apply later in life.

On your specific question about probability and statistics, I'd encourage you to take an in-depth course. If you end up studying communication theory (a fascinating and very real-world applicable field), you will do much better with a firm background in probability.

 

[f(x)]

Ah ok...thx for the great advice
Sorry about my attitude, will certainly try to develop more interest towards my Maths

 

[George Jones]

I think the way it's usually taught, as a course in proofs, is pretty dull.

Probably many physicists feel this way, however, I found topology (based on the first two-thirds of Topology: a first course by Munkres) to be one the most interesting courses that I took as a student.

For Hausdorff topological spaces, physical intuition is a useful tool for providing ideas for proofs.

 

[^_^physicist]

I'd support Chroot's comments; however, I think that f(x)'s question relates more as a question of what are the techniques in math that are made to work through physical problems. In which case his attempt to make sense of what is needed and what isn't is quite useful...at least when beginning to learn the topic.

Physics has that lovly habit of once you start looking at things long enough, if you have a big enough "tool-box," you can fiddle around and work towards another way of approaching a problem.