Need some advice: dive straight into physics, or do math first?

[XGWManque]

Hello,

So, I'm looking for some advice from people here who have experience studying physics outside of an academic program. Recently, I've started Griffiths E&M. Although it hasn't been long, I've been having an absolute blast: like, heart-fluttering, "helping me with suicidal depression" levels blast. However, I can also tell that my mathematical abilities are going to pose problems going forward.

Now, on a high, brittle level, I'm familiar with all the mathematics used here, so it isn't that I feel I absolutely *cannot* get through the text right now... but I can tell that the learning process isn't as efficient as it could be, with me stumbling over the math and being regularly sidetracked with re-learning (or just learning) the tools, the proofs, etc in the true understanding detail that I neglected as an idiot 18/19 year old.

I also worry that I don't truly master the physics as deeply as I could with a more sophisticated mathematical background, even if it is far from necessary: and learning things like tensor or exterior algebra would require a much more systematic, solid basis in linear algebra, one where I don't stumble to remember the basics. So, I've been considering putting off physics for a couple of years while I dive deep into undergraduate level math in full, taking time to fully master everything. If I do that, when I do eventually learn physics, I will never stumble over the math again.

However, I'm ultimately interested in physics first, with mathematics serving as a means to that end, and I'm reluctant to push my motivation too hard for a couple of reasons. For one, I'm studying outside a structured environment. But more importantly, I'm also cleaning my general mess of a life up from years of problems. As a recovering addict struggling to basically function in other areas of my life, I'm not sure I can preserve my newfound motivation and very, very fragile discipline through years of learning all the prerequisite math before doing any physics at all.

I have been checking out mathematical methods books like Boas and Arfken as possible alternatives to going through each mathematical prerequisite individually, but even if I limit it to that, I immediately feel the impulse to get the hell back to Griffiths and my-very, very embryonic-attention span struggling.

Doing both simultaneously on an ad hoc basis is an option, but I did that as an undergrad, and even if I was less of a terrible student, that's never the most productive way of mastering the material. Moreover, I work a full-time job now. Not a very intensive one, thank goodness, so I can devote time to going through a textbook, but I still don't have the free time I did when I was 19. I don't even have the money to pay for a tutor currently, albeit this might change in a couple of months.

So... yeah, your advice? Thank you for your time. As a side note, I realize my own story might be a bit unique, but I'm sure I'm not the only older person interesting in learning physics outside of school: I've already met a couple of people off this forum who are doing the same thing. I'd be happy to hear your experiences.

 

[Vanadium 50]

"helping me with suicidal depression" levels blast.

I recommend seeing a professional about that, rather than self-medicating with Griffiths.

As for your question, it seems impossible to answer. It appears that you are interested in studying physics, just for fun, and your math background is such that it requires you to often go back and brush up. Your question seems to be whether it would be better to bunch up the math learning first. Do I have that right?

I don't think there is a better answer we can give than "maybe".

 

[Mondayman]

I think it depends on how much math you already know. If you are struggling, and constantly going back to learn more math, then I would say it's probably a good idea to go back and solidify your understanding.

I'm also cleaning my general mess of a life up from years of problems. As a recovering addict struggling to basically function in other areas of my life, I'm not sure I can preserve my newfound motivation and very, very fragile discipline through years of learning all the prerequisite math before doing any physics at all.

I would recommend working to get other areas in life in order. A routine or structure that you can fall back on, even in the worst of times, so you still manage to get life's tasks and daily needs accomplished.

I have been checking out mathematical methods books like Boas and Arfken as possible alternatives to going through each mathematical prerequisite individually, but even if I limit it to that, I immediately feel the impulse to get the hell back to Griffiths and my-very, very embryonic-attention span struggling.

Boas contains everything you would need for Griffiths. If your goal is just to do physics, I would work through that. You would need vector analysis and differential equations at the least, so chapters 1-8. And a little bit of PDE's wouldn't hurt, chapter 12 I think.

I recommend seeing a professional about that, rather than self-medicating with Griffiths.

Absolutely, see a professional, but don't discount newfound motivation for learning as a means of self-medicating. Finding something you are passionate about can bring do a lot for a persons well being, and challenging your brain to learn is a healthy habit.

I was an alcoholic at age 13 and drank 12 years of my life away before reading Genius, a book about Richard Feynman. It introduced me to physics, and it had brought newfound meaning to my life. Learning physics and working on problems is fun. Suddenly there is excitement to waking up, and something to look forward to, even when you are enduring a bad day at work or going through a bad breakup.

 

[sysprog]

Please cultivate good study habits.

 

[PeroK]

So... yeah, your advice? Thank you for your time. As a side note, I realize my own story might be a bit unique, but I'm sure I'm not the only older person interesting in learning physics outside of school: I've already met a couple of people off this forum who are doing the same thing. I'd be happy to hear your experiences.

The first 50 pages of Griffiths covers essentially the maths you need for the book. You definitely need to be competent with that. If you need to go back a step to understand that mathematics, then I think you have no choice. You have to do it.

The following is a useful resource for all things calculus:

http://tutorial.math.lamar.edu/

In general I'd say keep going with the physics as much as possible, but your maths can't be too far behind.

 

[XGWManque]

I recommend seeing a professional about that, rather than self-medicating with Griffiths.

Absolutely! Sorry, I should have made this clear: I am using more tried and true methods like seeing a professional for the most part. But as another poster here commented, having a purpose to your days is nothing to sneeze at in terms of psychological effect.

As for your question, it seems impossible to answer. It appears that you are interested in studying physics, just for fun, and your math background is such that it requires you to often go back and brush up. Your question seems to be whether it would be better to bunch up the math learning first. Do I have that right?

I don't think there is a better answer we can give than "maybe".

Put another way: would getting through the mathematical exercises from the first chapter of the book be enough to have the ability to truly master the material, with me researching the mathematics in more detail on an as-needed (or if I want a deeper understanding, as-wanted) basis as I go along, or should I go through a whole text on mathematical methods here and now to gain fluency preemptively before doing any physics?

For what it is worth, I did not struggle too badly with most of the problems in Chapter 1 of Griffiths, and I am reasonably confident in my basic understanding of the tools at work. But I did find myself spending significant amounts of time and effort on researching various pieces of mathematics, whether it was out of dissatistisfaction with my level of understanding or a pressing need to relearn some long forgotten concept, and I did stumble over steps in some of the problems in a way a student who is fresh off mastering his math prerequisites would not. That is to be expected given my background. But I am wondering if those are not signs to go increase my mathematical conditioning before going forward, by going through a text dedicated to the math.

 

[XGWManque]

Please cultivate good study habits.

Well... yeah, that is another issue, considering I have had shoddy study habits all my life. I am doing my best to schedule a daily routine to my work. Not as easy as it should be with the pandemic going on, but possible. Combining exercises with Feynman processes where I try to teach the material to my imaginary friend seems to be a good combo for me, as far as ensuring understanding, and I try to visualize everything in a way I did not as a student.

Any advice here? With me having a job, having just above average habits will not cut it in the long haul.

 

[Vanadium 50]

Put another way: would getting through the mathematical exercises from the first chapter of the book be enough to have the ability to truly master the material, with me researching the mathematics in more detail on an as-needed (or if I want a deeper understanding, as-wanted) basis as I go along, or should I go through a whole text on mathematical methods here and now to gain fluency preemptively before doing any physics?

Who knows? People are different. What works for someone else may or may not work for you. All we can really suggest is try it one way and then try it the other.

 

[XGWManque]

OK, thank you for all your help. I slept on it some and decided to continue on with Griffiths for the time being, because things are going fairly well and I don't want to mess with a good thing for now. I'll see how things proceed over the next few months. If it becomes apparent down the road that I need to switch my focus toward math, I can always do so then.

Once again, thank you very much. Sincerely appreciated.

 

[jtbell]

In the US at least, students who take an E&M course based on Griffiths are generally required to have already completed an introductory calculus-based physics course (including E&M) using e.g. Halliday/Resnick/Walker, Young/Freedman, or Sears/Zemansky/whoever. Have you done that, and did any of it "stick?" If not, you might consider backing up to that level first.

 

[XGWManque]

In the US at least, students who take an E&M course based on Griffiths are generally required to have already completed an introductory calculus-based physics course (including E&M) using e.g. Halliday/Resnick/Walker, Young/Freedman, or Sears/Zemansky/whoever. Have you done that, and did any of it "stick?" If not, you might consider backing up to that level first.

I have an undergraduate degree in physics, but that was several years ago.

It depends on what you mean by stick. I remember Maxwell's Laws and what they mean. From a mathematical perspective, when I hit Chapter 3, I can probably re-learn how to do a basic separation of variables with a couple of practice examples just as straightforwardly as I've been picking vector calculus back up. But there's a gap between that kind of perfunctory recall and managing to tackle the less trivial problems that require more than just a plug-and-chug, or more generally truly understanding the material on a deep, insightful level.