What are some tips for hobbyists studying advanced mathematics and physics?

[marcioapm]

Hi!

I've always been interested in math and physics, since I was a kid, but like many of us, life takes us to different places, so I ended up pretty far away from those subjects.

My background in mathematics is a pretty good understanding of high-school level, and ever since then, I haven't been exposed to anything beyond that. Perhaps the only exception being Linear Algebra, due to my career.

Recently I have decided to pursue my interest in physics as a hobby, and so started reading a lot about GR and QM, and anything related to those. While I can grasp the general concepts, I quickly found myself lost in the maths and unable to get past that.

So, I decided to take a break from the physics studies and literature, and instead focus a bit on my maths background. My issue is that each time a pick a subject, I find it requires some previous subject that I also lack understanding of, and then that also requires something I wasn't aware of, so I kept going back, and am now at a place where I have a simple plan to progress in subjects up until GR.

Has anyone been in a similar situation and has any sort of tips, or perhaps has a road-map of the different subjects to tackle they could share?

My current method has been to read books, mostly I cherry pick chapters related to a subject in many different books, as well as following youtube lessons, and whatever else I can find. Sometimes the differences in notation are quite confusing, but nothing too bad.

One problem I have is that I don't really know how well I really understand things. When reading the books things seem obvious, and simple, but I can't help not feeling very confident about my understanding... I was wondering if someone could recommend some exercise books, preferably with explanatory solutions, on the various subjects of basic post high-school mathematics...

Thank you!

 

[Dufoe]

Suggested topics to research; Logical Fallacies, Paradoxes, Thought Experiments, Mathematical Proofs. Get your math literacy past Differential and Integral Calculus and then spend some time on Newtonian Physics. Read about the Fibonacci Sequence. Read about Descartes and his Mechanical Universe. For QM you better start with non-commutative multiplication.

Keep in mind that you need to achieve a capacity for highly abstract thought above all. Ironically this is most easily obtained through a deep understanding of deductive reasoning. Good luck!

 

[ActionPotential]

In order to really understand GTR and QM you will need to study quite a bit of mathematics and physics. To understand it at the undergraduate level you will need less of these but it will still require a solid foundation. There is a reason people go to school for so long in order to understand these subjects.

Also, the reason that you keep peeling back layers as you go is because math and physics has this beautiful way of taking a bunch of specific things that were really hard to understand at first and then abstracting and generalizing them into a more unified concept which then creates new mathematical and physical objects that are again really strange and difficult to understand (until our consciousness integrates and unifies).

Maths:
Basic Algebra and Trigonometry
Single Variate Calculus
Multivariate Calculus
Linear Algebra
Ordinary Differential Equations
Partial Differential Equations
Maybe some complex analysis and functional analysis
(if you get to this point then you will have an idea what else you will need to study to gain a better understanding - things like tensor calculus and differential geometry, etc.)

As for physics:
Classical Mechanics
Electricity and Magnetism
Modern Physics (special relativity and basics of QM)
(at this point you will know whether or not you want to study more and will know what exactly you will need to study).

 

[chiro]

Hey marcioapm and welcome to the forums.

One thing I would recommend is that you look into the Schaums Outlines series of textbooks.

http://www.mhprofessional.com/templates/schaums/

They are not a substitute for a proper learning source but they are very useful for students when it comes to a supplementary source for going through worked out problems.

Many of these outlines are available for all kinds of university science and engineering subjects including university level mathematics, physics, engineering, and other sciences.

I would recommend that you take a look at these if you want to get some worked out problems in a particular area, when you are struggling and need such a reference.

 

[marcioapm]

Thank your for the directions guys! Very much appreciated!