What math is required for physics?

[MightyKaykoher]

I have been aiming to venture further into my understanding of quantum mechanics( Past classical mechanics).I see many thread
s here but few with complex mathematical formuli. Is it that nobody bothers to list them or have I not looked close enough? To get a deep understanding of the universe, how far into calculus must one go? Is it just being able to solve differentiable equations?

 

[Simon Bridge]

There's no "just" about being able to solve differential equations :) You also need matrix algebra.
The actual math in QM is not all that esoteric as far as math goes.

 

[Blackthorn]

Algebra
Trigonometry
Calculus (single and multivariable)
Linear Algebra
Differential Equations

I have heard Vector Calculus helps too... though i haven't taken that personally.

 

[tony873004]

Conceptual Physics: very little math: addition, subtraction, multiplication, division, squaring and square-rooting numbers. (IMHO, Conceptual Physics is the most important. If you have a conceptual understanding of what's going on, you can go deep later in your education. If you're a formula-pusher, you won't go too far in Physics.)

Physics: Algebra (although many of the formulas you use are either derived or proven using calculus)

High School AP Physics B: Algebra (plus a good understanding of Conceptual Physics)

High School AP Physics C, Mechanics and E&M: Algebra and some Calculus (derivatives and anti-derivatives and integrals of polynomials and simple trig functions. Chain rule and U-substitution and rarely integrals involving 1/x, differential equations [separation of variables only, i.e. F=ma becomes F=m (dv/dt)]). If you don't know ANY calculus, you can still get a 4/5 on the AP C exams provided you ACE algebra stuff.

College Physics if you're NOT a Physics or Engineering major: Pretty much the same as High School regular Physics.

College Physics if you're ARE a Physics or Engineering major: Not too much difference from AP C High School Physics! It's a little tougher, and you'll be competing against a higher caliber of students. You'll also see some thermo and fluids thrown in.

College Physics if you ARE going for a Masters: Know your math. Know ALL your math. But make sure you're VERY good with Conceptual Physics. Otherwise all the math in the world will do you no good at this level.

College Physics including Quantum: "differential equations" ARE part of Calculus. If you're a Physics major, or Engineering major, or an Astronomy major (assuming your university offers it as a separate major)

To get a "deeper understanding of the universe" at ANY level, you simply need to learn more math. To understand the universe as no one before you ever has understood it, you need to make up your own math like Newton did! (he co-invented Calculus to prove Earth can be simplified as a point mass).

 

[Simon Bridge]

Conceptual Physics: very little math: addition, subtraction, multiplication, division, squaring and square-rooting numbers. (IMHO, Conceptual Physics is the most important. If you have a conceptual understanding of what's going on, you can go deep later in your education. If you're a formula-pusher, you won't go too far in Physics.)

Dunno - I agree that pushing formulas won't get anyone far but that's the same with math in general.
I've not been terribly impressed with courses called "conceptual physics" as a foundation for more advanced study. But that may not be what you mean.

Physicists do seem to think of math differently to mathematicians though - they tend to be less formal or rigorous, treating it like a language. I think that's the central point: got used to using math concepts to describe things in nature. It's why we set lots of wordy problems and use lots of pictures.

 

[Student100]

Because math has nothing to do with nature. Physics, being a natural science and all, does however.

In physics we use math to uniformly and as precisely as possible describe a physical situation , knowing math is meaningless without understanding the natural aspect of physics.

Edit: I guess the post I was replying to was deleted. Oh well.

 

[MightyKaykoher]

Dunno - I agree that pushing formulas won't get anyone far but that's the same with math in general.


I can't seem to understand this statement. Can you explain with proof/valid reasoning.

If I were to learn calculus/linear algebra and conceptual physics, what would be left to fill in my understanding of quantum physics? Just memorizing 100 formulas?

 

[Simon Bridge]

By "pushing formulas" I am talking about the approach where you memorize the "correct equation" or formula to use for each situation ... you put the numbers in the equation and get the right answers out.

Think of math as a language and "pushing formulas" as the "tourist phrasebook" version of that language.

 

[tony873004]

I've not been terribly impressed with courses called "conceptual physics" as a foundation for more advanced study. But that may not be what you mean...

That is what I mean. The course Conceptual Physics was popularized by Paul Hewitt. I took the course from him at City College of San Francisco in 1982. Now it seems that high schools are moving in the direction of offering Conceptual Physics to freshmen. I teach three levels of high school Physics: Conceptual Physics, "regular" Physics, and AP C, Mechanics. We try to use Conceptual Physics to get the freshmen, who come from many different grade schools, and even many different countries on the same page. Basic formula manipulation, how to use lab equipment such as balances (thanks for your calibration help in the other thread!), how to write lab reports, unit conversion, introduction to scientific notation, etc. Even if they have trouble with some of this material, at least they've been introduced to it, and will hopefully have an easier time with it when they see it again at a more level in regular Physics or Chemistry.

I taught Integrated Physical Science at a different high school. I actually liked it better than Conceptual Physics for the freshmen. It was a little bit of Physics, a little bit of Astronomy, and a little bit of Earth Science thrown together. But I was told that Integrated Physical Science doesn't transfer to the UC colleges, while Conceptual Physics does. It's too bad. Unless I deviate a little from the syllabus (which I always do!), students will go through our high school not knowing why summer is warmer than winter, and not knowing why the moon goes through phases.

 

[MightyKaykoher]

Simon Bridge, are you trying to say: unless you want to conduct expirements and calculate how much one H atom heats up when hit by a gamma ray, formulas prove no use?

 

[Simon Bridge]

Simon Bridge, are you trying to say: unless you want to conduct expirements and calculate how much one H atom heats up when hit by a gamma ray, formulas prove no use?

Nope.

I'm saying you won't get far just by memorizing algorithms. You need to develop an understanding of the principles that underlie the formulas and equations. I take it you are not saying that if you have the formulas you don't need to understand them?

For instance - how does it make sense to talk about a single H atom "heating up" as a result of the interaction with a gamma ray?

The answer may just be a matter of finding the right formula - but science education is supposed to train you to solve problems where there is no known correct formula or the correct one is in dispute.

I think you'll see it more clearly if you follow the introductory physics threads in PF.

Meantime have a look at:
Eric Mazur: Understanding or memorization: Are we teaching the right thing?

Also the http://www.ph.utexas.edu/~turner/classes/HowToStudyPhysics.htm guide from Texas U.

 

[Progr89]

You tend to get do better in physics when you have strong background in trigonometry,calculus and algebra ESPECIALLY linear algebra :)

 

[ZapperZ]

Simon Bridge, are you trying to say: unless you want to conduct expirements and calculate how much one H atom heats up when hit by a gamma ray, formulas prove no use?

This shows that you really have not learned any substantial amount of physics yet. You are still in the mentality of thinking that all one needs is a "formula", and then one only needs to do a plug-and-chug.

To answer your question, the minimum amount of math required to do physics is whatever is in Mary Boas's "Mathematical Methods in the Physical Sciences" text. That is as clear as an unambiguous of an answer that I can give. Whether you believe it or not, that's your problem.

Zz.

 

[wotanub]

Group Theory, Differential Geometry, Hilbert Space, and Topology are also important to modern physics. No one ever seems to mention those. You pretty much have to be a mathematician to get into theoretical physics.

 

[Simon Bridge]

Group Theory, Differential Geometry, Hilbert Space, and Topology are also important to modern physics. No one ever seems to mention those.

Probably because the question is usually being asked by someone still in High School ...

 

[Astronuc]

I have been aiming to venture further into my understanding of quantum mechanics( Past classical mechanics).I see many threads here but few with complex mathematical formuli. Is it that nobody bothers to list them or have I not looked close enough? To get a deep understanding of the universe, how far into calculus must one go? Is it just being able to solve differentiable equations?

One probably has not looked close enough.

For example - https://www.physicsforums.com/showthread.php?t=731782

And one can look through the Advanced Physics homework forum for problems in QM/QP.

This site has a good overview of the math topics one would need to master with respect to physics.
http://superstringtheory.com/math/math1.html

Gerard t'Hooft has a good webpage that discusses physics and math.
http://www.staff.science.uu.nl/~hooft101/theorist.html

Here are a couple of examples from universities (in the UK) that discuss math in conjunction with physics.
http://www.bristol.ac.uk/prospectus/undergraduate/2014/sections/PHYS/54/admissions_joint

First year
Core Maths (Calculus, Analysis, Linear Algebra, Geometry)
Core Physics (Mechanics, Special Relativity, Properties of Matter, Fields, Oscillations and Waves including Laboratory work)
Computational Mathematics

Second year
Maths (Ordinary and Partial Differential Equations, Calculus)
Core Physics (Classical Physics, Quantum Mechanics, Practical Physics)

Third year
Mathematical Methods
Core Physics (including Semiconductors and Magnetism, Electrons in Crystals, Quantum Physics)
Computational Physics
Optional units in Mathematics
Optional units in Physics

Fourth year
Final year research project in either Maths or Physics
Optional units in Mathematics
Optional units in Physics

Maths for Engineering: Notes for School Teachers
http://www3.eng.cam.ac.uk/admissions/information/maths_advice.html

Of course, one could read various physics texts and review examples of the mathematics involved in describing the physics of various phenomena.

In QM/QP, would need some proficiency in partial differential equations, vector analysis/linear algebra, complex analysis, and probably statistics.