I did this a few years ago, now doing an MS in math, after last formally studying math in high school, more than 20 years previously.
There is lots of advice in this thread, including long lists of books - at your level, I think that’s unhelpful. To get started with the foundations, I think it’s best to have one or two books at most, that you work through completely, then decide what to do next. Otherwise you can waste a lot of time time figuring out “what to do next” instead of actually doing math!
I would personally recommend “Engineering math” and “advanced engineering math” by Stroud. The first covers “foundation” topics like algebra, trigonometry etc, then covers the first year of math for a English engineering degree. The second book covers the second year.
Note that English engineering degrees are 3 years vs 4 in the US, but have no general education requirements, so the math covered in the two books is roughly equivalent to the 1st-3rd year of an engineering degree in the US. Both books are very much focused on calculations, not proofs, but will give you a fluency in handling mathematical calculation that is assumed when doing more proof-based courses later. And they are both designed for self-study, which is important.
The other book that I would get, and do in parallel once you have done the foundation part of the first stroud book, Chartrand, Mathematical proofs. This will teach you how to do proofs, using mainly (high school) algebra and basic number theory to start, but going on to cover some proof techniques in analysis, advanced algebra and others areas.
Once you have done those 3 books, you will have a solid basis for further study. I also agree with the comments about interacting with others studying the same material if possible.
Happy to chat sometime if you want to message me (contact info in profile)
There is lots of advice in this thread, including long lists of books - at your level, I think that’s unhelpful. To get started with the foundations, I think it’s best to have one or two books at most, that you work through completely, then decide what to do next. Otherwise you can waste a lot of time time figuring out “what to do next” instead of actually doing math!
I would personally recommend “Engineering math” and “advanced engineering math” by Stroud. The first covers “foundation” topics like algebra, trigonometry etc, then covers the first year of math for a English engineering degree. The second book covers the second year.
Note that English engineering degrees are 3 years vs 4 in the US, but have no general education requirements, so the math covered in the two books is roughly equivalent to the 1st-3rd year of an engineering degree in the US. Both books are very much focused on calculations, not proofs, but will give you a fluency in handling mathematical calculation that is assumed when doing more proof-based courses later. And they are both designed for self-study, which is important.
The other book that I would get, and do in parallel once you have done the foundation part of the first stroud book, Chartrand, Mathematical proofs. This will teach you how to do proofs, using mainly (high school) algebra and basic number theory to start, but going on to cover some proof techniques in analysis, advanced algebra and others areas.
Once you have done those 3 books, you will have a solid basis for further study. I also agree with the comments about interacting with others studying the same material if possible.
Happy to chat sometime if you want to message me (contact info in profile)