How much could I teach (myself) in 1 year?

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The discussion centers on an individual's plan to self-study math and physics in preparation for a future in astrophysics, despite lacking a formal background in these subjects. The person has a solid foundation in algebra and some calculus but acknowledges the need for extensive learning. They aim to dedicate over 10 hours a day, six days a week, to study various mathematical concepts, including calculus, linear algebra, and differential equations, before moving on to physics. Key points include the importance of understanding one's own mathematical abilities and the depth of study desired. The conversation emphasizes that the focus should not be on how much material can be covered in a year but rather on effective study methods and thorough comprehension of the subjects. It is suggested that developing strong study habits and pacing oneself will be crucial to achieving a solid understanding of math and physics, ultimately preparing for university-level coursework.
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I'm going to skip to the chase and give you the basics of my situation.

I'm very weak at physics as i didn't take any high school classes (wasn't interested at the time) and also didn't finish high school due to personal reasons.

I'm fairly good at algebra, some calculus but could use a lot more learning in the math department and willing to work my behind off to do so.

I did go back to get my NCEA Level 2 & 3 (Equivalent to GED) but at that time I wasn't sure what I wanted to pursue study-wise, so didn't focus so much on Math/Science.

My plan is to self-study as much math as possible (calculus, linear algebra, differential equations etc...) within a year. That means I may have to start from basics to really get a strong grip.

After that I will learn physics from scratch then hopefully move to more advanced levels of physics.

I have a night-shift job so have hours to study (10 + hours) throughout the day, access to books & good online sources.

After I hopefully have a good understand I wish to enter University (University Of Auckland OR Massey University).

Now, I know you can't actually give me an exact number but is it possible do you think to learn a greta amount of math + physics within a year MYSELF? I mean considering I will have 10+ hours per day 6 days a week to learn?

CheersI want to do Astrophysics.
 
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It really really depends on you. That is: how good you are in math, and how deep you want to do things.

How good you are at math is something you probably don't know right now. But if you struggle then you will struggle. In undergrad I was always very good at math. But it happened a lot of times that I struggled for days/weeks/months with a specific concept. And then it happened a lot that I could get through 50 pages of difficult math in a week. It depends on so much factors. You can't really control this.

Then there is the depth you want to do things. More depth is more understanding, but also takes more time. Will you do a lot of problems of each concept? Will you do harder/more theoretical problems for each concept? Will you focus a lot on proofs or just techniques? Stuff like that.

And what is your background. You might want to gain some depth in stuff like trigonometry and algebra first, even though you say you understand it well.

My advice to you is: you're asking the wrong question. The problem is not "how much material could I do in a year", but "how do I study the material the best way possible". Understanding something like calculus takes time. Don't start by handicapping yourself by setting a fixed time to finish this. Just start calculus/algebra/trig/whatever at your own pace and see that you study it well. It doesn't matter at all how long it takes, as long as you understand it well at the end.
 
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Honestly with the time you'll have to do this in a year, the only thing stopping you is you. Make sure to employ strong study habits so that you don't slack off and not fully take advantage of your time to get to the highest level in math you possibly can within this time.
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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