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This has been my nemesis for a long time due to having no proper Math in Highschool(low level vocational). (and almost none in uni, I went to an applied science uni)

I know simple rules and have probably seen most simplifying “Tricks” at least once. But I feel like I lack a lot of practice when it comes to rewriting the equations into a different format.

I noticed during a course in electric circuits at university that I really struggled to rewrite the equations into a a different, more simpler format. I always ended up rewriting the equation into a “rabbit hole” where there was just no end at the tunnel and I just ended up making it worse.

I also struggle really badly when people skip multiple steps, my brain isn’t trained on seeing multiple steps ahead currently, I always need to write down every step. I was alright with the physics concepts part of the course, but the exam went badly due to being either slow on simplifying the equation or getting stuck on some weird form I didn’t quite know how to simplify it next. Most other students could fluently rewrite equations and didn’t struggle on that particular bit, it felt like this wasn’t the thing we were supposed to be tested on, but it felt like the main part of the exam for me. During classes that contain Math like discrete math or electric circuits, where rewriting the equation is a common occurrence, it often ends with me not understanding what the teacher is doing 3 steps (where small steps are skipped) through the simplification of an equation. I do ask what happened when that occurs, but it still occurs very often and I haven’t been able to get rid of this issue yet. I call these skipped steps “invisible steps” myself.

It generally happens for equations where I need more than ~ 8 steps and it also ranges to applying Euler’s formula to rewrite the equation. I feel like there are a lot of gaps in my Math that I’ve been trying to fill over time, but this problem keeps preventing me from progressing in most books efficiently. I feel like I am just doing 1 step I think works and have no clue whether this will lead to a format that’s simple enough ultimately. Do people proficient at this know where they wanna head right away and form a plan for it in their head: “What steps would be needed to rewrite it in such a way?”. Or do you also just take 1 step at a time and somehow it ends up in the most simple form?

I’ve been wondering this for a long time now.

Besides that I would like to ask if you know of any particular resources that focus specifically on this “subject” or “area of math”. I only know it as “simplifying equations” or “rewriting equations”. I want to gain some form of mastery on it so it doesn’t slow me down too much when learning other fields. I can make a cheat sheet of every rule and go over it each time (which is what I do a lot of times), I want to practice it enough to get good at it.

Can you recommend any book for gaining a decent level of proficiency in this? I tried khan academy and it is great at explaining concepts but doing a lot of problems on something as the distributive property is not what I have issues with. It’s the whole collective challenge of rewriting equations that require a decent amount of steps. During electric circuits a lot of the questions were very algebra centric, it was really difficult but limited in practice problems. I have not found many similar resource that focus on algebra in the same way for electric circuit problems.

I have done research for a lot of books but I feel like I really need get my brain trained on this particular “skill”. A source that specifically focuses on this and scales up to really difficult problems would be very helpful I think. I think the best tactic is to train my brain on this for a good amount of time until I can at least see multiple steps ahead and do the “challenging” rewriting problems without having to ponder for 5 minutes on every step, maybe semi-fluently, so I can focus on the math concepts that people are trying to explain besides the simplification of the equation.

I have not had algebra in school, I had to learn it myself through resources I collected when I was prepping to go to university. This is probably part of the reason. They did give us “some” essential algebra at the start of uni, but it wasn’t anything other than what I had already learned and very basic.

I thank you kindly for any advice or info you might be able to give. Thank you for taking the time to read my post.

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