# Maths for quantum physics?

September 1, 2019 3:06 PM Subscribe

I’d really like to understand physics better, especially quantum mechanics, string theory all that spooky kinda stuff. But I really lack the maths brain to get in depth. What’s the best way to get my maths a bit more up to scratch?

My maths education stopped at 16, nearly thirty years ago. I got an A at GCSE so on the one hand I’m not a total dunce but on the other I’ve forgotten most of it and it was hardly advanced!

I’d really like to be able to understand books that are aimed for an audience beyond ‘complete layperson’ but as soon as an author breaks out some equations my head starts spinning. I don’t really want to be doing hours of homework exercises just to understand these things... but... maybe that’s the only way?

My maths education stopped at 16, nearly thirty years ago. I got an A at GCSE so on the one hand I’m not a total dunce but on the other I’ve forgotten most of it and it was hardly advanced!

I’d really like to be able to understand books that are aimed for an audience beyond ‘complete layperson’ but as soon as an author breaks out some equations my head starts spinning. I don’t really want to be doing hours of homework exercises just to understand these things... but... maybe that’s the only way?

A prerequisite for nearly everything is linear algebra. If you focus on only 1 math topic, start there, because whatever you care about, linear algebra will be useful for that. Quantum mechanics is almost totally linear algebra, for example (albeit on complex numbers instead of real numbers.) It is not possible to overstate how useful it is.

You probably also want a basic intuition for calculus -- like having a broad idea of how integrals and derivatives work. I would specifically advise skipping any textbook exercises that require you to compute integrals of complicated functions, it will just bore you -- just use Wolfram Alpha.

The YouTube videos of 3Blue1Brown are highly regarded for getting intuition on various topics. Khan Academy is also good.

Some amount of exercises are likely useful but I would just half ass them, just give up and look at the answers if you get bored.

posted by vogon_poet at 5:12 PM on September 1, 2019 [4 favorites]

You probably also want a basic intuition for calculus -- like having a broad idea of how integrals and derivatives work. I would specifically advise skipping any textbook exercises that require you to compute integrals of complicated functions, it will just bore you -- just use Wolfram Alpha.

The YouTube videos of 3Blue1Brown are highly regarded for getting intuition on various topics. Khan Academy is also good.

Some amount of exercises are likely useful but I would just half ass them, just give up and look at the answers if you get bored.

posted by vogon_poet at 5:12 PM on September 1, 2019 [4 favorites]

My sense is that what you want is a combination of linear algebra, some thinking about what "extra dimensions" mean in practice, and texts aimed at a more sophisticated layperson (for physics, I like Quanta and Matt Strassler's blog posts).

A lot of quantum physics is based on linear algebra

posted by yarntheory at 5:31 PM on September 1, 2019 [4 favorites]

A lot of quantum physics is based on linear algebra

*metaphors*, so even very basic linear algebra will give you some idea of the way people approach problems in practice. You should be able to find lots of resources on four and more dimensions; when I taught this stuff to students with math backgrounds similar to yours, I used a combination of Burger and Starbird's textbook*The Heart of Mathematics*and Edwin Abbott's weird Victorian adventure*Flatland*as starting points.posted by yarntheory at 5:31 PM on September 1, 2019 [4 favorites]

Probably should brush up on core algebra skills, a lot of advanced math is doing algebra on more abstract stuff. Also remember that it is hard, don't get discouraged if it takes days to grasp a single page, (not saying to scare, a new branch of math is hard for pro mathematicians) the math notation is intentionally condensed, one variable can encompass a whole lot of other detail C=AB where each is an nxn matrix breaks down to a dizzying sequence of computations, the sigma (Σ) just means add things up but, yea, whew sometimes. Some of the youtube videos are great, look for lectures at mit's open course ware. and there are some good subreddits but review the local posting rules.

posted by sammyo at 7:07 PM on September 1, 2019 [1 favorite]

posted by sammyo at 7:07 PM on September 1, 2019 [1 favorite]

I don't think you actually need to understand math better to gain some understanding of quantum physics or string theory. If you want to

Quantum is different in that a lot of it doesn't match up with our every day expectations of how things should behave. But, I still think you can get a better understanding of the important features of it with descriptions of experiments and their outcomes and analogy rather than learning linear algebra (one of my least favorite math subjects) and calculus (one of my favorites). The issue with texts for non-laypeople is that the intro text are basically manuals on how to do the math not how to understand the theory.

This advice brought to you by someone with a masters degree in physics who isn't too hot at math.

posted by runcibleshaw at 9:37 PM on September 1, 2019 [7 favorites]

*do*quantum mechanics or string theory calculations then learning the math would be helpful, but I don't think that's what you're asking. To use an analogy (very helpful when you're trying to avoid math), you don't need to know calculus to have some idea of how a ball arcs in the air when you throw it. In fact, your experience of how a ball arcs may help you understand the math, not the other way around.Quantum is different in that a lot of it doesn't match up with our every day expectations of how things should behave. But, I still think you can get a better understanding of the important features of it with descriptions of experiments and their outcomes and analogy rather than learning linear algebra (one of my least favorite math subjects) and calculus (one of my favorites). The issue with texts for non-laypeople is that the intro text are basically manuals on how to do the math not how to understand the theory.

This advice brought to you by someone with a masters degree in physics who isn't too hot at math.

posted by runcibleshaw at 9:37 PM on September 1, 2019 [7 favorites]

Just maybe The Mechanical Universe series of videos from Caltech and The Annenberg CPB Project. They're from the 1980's and intended for not-quite-yet university students. It's a full 52 course series about physics with a lot of history thrown in. They introduce and explain the math as needed using nice animations.

Nth the 3blue1brown for getting an idea of various maths. And you don't need much to understand it, just if you want to

posted by zengargoyle at 4:05 AM on September 2, 2019

Nth the 3blue1brown for getting an idea of various maths. And you don't need much to understand it, just if you want to

*do*it.posted by zengargoyle at 4:05 AM on September 2, 2019

Mathematics for Quantum Mechanics by J.D. Jackson (yes that Jackson) will get you what you need. Short 112 pages, sweet cheap paperback from Dover.

posted by heatherlogan at 6:36 AM on September 2, 2019

posted by heatherlogan at 6:36 AM on September 2, 2019

It's been a while since I read it, but I'd strongly recommend having a look at QED (quantum electrodynamics) by Richard Feynmann. It distils a range of quantum effects down to some fundamental principles whilst avoiding any maths. Honestly, I think it gives as good an understanding as is possible without spending years learning the necessary maths*.

*Be warned: this is from someone who has spent years learning the necessary maths and still has a very poor understanding of what's going on. When it comes to 'understanding quantum mechanics', be prepared to aim low!

posted by Ned G at 7:01 AM on September 2, 2019

*Be warned: this is from someone who has spent years learning the necessary maths and still has a very poor understanding of what's going on. When it comes to 'understanding quantum mechanics', be prepared to aim low!

posted by Ned G at 7:01 AM on September 2, 2019

I will say that quantum

But the mathematical building blocks themselves are actually much easier (again mostly just linear algebra) and studying quantum

To this end, I would endorse Quantum Computing for the Very Curious, even though it's not complete. It's co-written by Michael Nielsen, who also co-wrote the standard graduate reference text in the field, and is designed to take laypeople from basic linear algebra up to a genuine understanding of how quantum computing works.

posted by vogon_poet at 2:22 PM on September 2, 2019

*physics*, meaning using quantum theory to model real physical phenomena and explain the results of complicated experiments, is generally regarded as quite difficult.But the mathematical building blocks themselves are actually much easier (again mostly just linear algebra) and studying quantum

*computing*is generally regarded as an easier inroad into understanding them. (I swear this is actually true.) So this could be an angle worth looking at.To this end, I would endorse Quantum Computing for the Very Curious, even though it's not complete. It's co-written by Michael Nielsen, who also co-wrote the standard graduate reference text in the field, and is designed to take laypeople from basic linear algebra up to a genuine understanding of how quantum computing works.

posted by vogon_poet at 2:22 PM on September 2, 2019

(After getting through the very first chapter of that book, you'd understand in a precise mathematical sense what is meant by "quantum entanglement", for instance.)

posted by vogon_poet at 2:27 PM on September 2, 2019

posted by vogon_poet at 2:27 PM on September 2, 2019

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I have no fucking idea what Differential Equations means to my life. But I assume you need to know a lot of that to be relevant in a physics field that answers these things.

The best thing about the internet is that someone much much smarter will always help you out to explain things. Reddit has an "Explain it like I'm 5" thread that pretty much does this. Also if you find yourself out of your depth in pretty much any science related thread on Reddit if you post ELIA5, you will get a boiled down version.

No one there is looking to shame you. Most of the time your ELIA5 post gets people to open up and try to make things more readable and understanding. Many times it's the goddam author of the paper.

In the end, seek and you will find.

posted by sanka at 4:19 PM on September 1, 2019 [2 favorites]