After realizing all the math I learned in high school and college has utterly disappeared from my brain, I've been making an effort to relearn all of it. And in a rigorous, proof based way so I won't forget all of it again. Right now I'm trying to teach myself linear algebra and calculus, and surprisingly it's actually been really fun!
I didn't think I would be enjoying this as much as I am, and I think it's because of how stress free it all is when you don't have to turn homework in on time or study for exams. I'm learning at my own pace instead of the pace of a classroom. If I get the hang of something quickly, I can move to the next section. If I don't understand something I can stick to it until I do rather than being forced to move on.
I think after I finish up these two topics, I'll move on to topics I've never studied before.
I've been working through both volumes of Calculus by Tom M. Apostol which covers both calculus and linear algebra.
Taking notes on each section and then doing every exercise has been effective I think. It has just the right number of exercises for each section to be reasonable for someone self studying so you don't need to pick and choose which exercises to do as there are way too many in most math textbooks.
And, for the first volume at least, someone has taken the time to write a solutions guide here: https://www.stumblingrobot.com/index-of-solutions/solutions-to-calculus-exercises/
I haven't gotten to the linear algebra sections of the two textbooks yet, so in the meantime I've been doing a non-rigorous course on Linear Algebra offered by MIT Open Courseware as a basic refresher. Here is everything you'd need for that except the textbook but that's pretty easy to pirate on libgen:https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/
After realizing all the math I learned in high school and college has utterly disappeared from my brain, I've been making an effort to relearn all of it. And in a rigorous, proof based way so I won't forget all of it again. Right now I'm trying to teach myself linear algebra and calculus, and surprisingly it's actually been really fun!
I didn't think I would be enjoying this as much as I am, and I think it's because of how stress free it all is when you don't have to turn homework in on time or study for exams. I'm learning at my own pace instead of the pace of a classroom. If I get the hang of something quickly, I can move to the next section. If I don't understand something I can stick to it until I do rather than being forced to move on.
I think after I finish up these two topics, I'll move on to topics I've never studied before.
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I've been working through both volumes of Calculus by Tom M. Apostol which covers both calculus and linear algebra.
Taking notes on each section and then doing every exercise has been effective I think. It has just the right number of exercises for each section to be reasonable for someone self studying so you don't need to pick and choose which exercises to do as there are way too many in most math textbooks.
And, for the first volume at least, someone has taken the time to write a solutions guide here: https://www.stumblingrobot.com/index-of-solutions/solutions-to-calculus-exercises/
I haven't gotten to the linear algebra sections of the two textbooks yet, so in the meantime I've been doing a non-rigorous course on Linear Algebra offered by MIT Open Courseware as a basic refresher. Here is everything you'd need for that except the textbook but that's pretty easy to pirate on libgen:https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/
Hell yea. I dunno why but this made me feel good to read. Keep it up.