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In the last two years I've been trying to brush up my mathematics from the basics. My bachelors was in medicine and surgery, so I had a huge gap (almost 10 years) of no mathematics. A lot of the work I do involves simulations, and I superficially understand the mathematics behind it. But I really, really want to understand the nitty gritty details—to think mathematically about physical problems and how they can be modeled. More than a desire, it's become a need for me. I dream of the day I can do advanced mathematics such as dynamical systems to understand neural systems in a more formal manner, rather than the clunky paragraphs I read in med school.

I originally started with MIT's online calculus resource, however, it proved very difficult and then I started on Morris Kline's Calculus: an intuitive and physical approach. It was going well, however, I felt that I kept stumbling on basics. It was then that I discovered this side, and saw Micromass' post on learning calculus, and decided to do the relevant chapters from Lang's basic mathematics.

After doing that I went back to Kline (April this year) and restarted the book. The earlier chapters were a little easier than the first try, however, now I find it difficult to gage when I am moving too slowly or am getting stuck on problems that I need more background material on. At this point, I am unsure if I should just push through, or try to get some kind of tutor to mentor me through this? One of the problems with my current book is that I do not know which parts I should be really remembering, since there are no tests/exams.

For example, am I supposed to know by heart how I derive an eclipse and hyperbola? Other issues include constantly getting stuck with algebraic manipulation and just finding it difficult in general to solve questions. Alternatives also exist: I could do Calculus made easy to get an overview, and do something like Strang's Calculus book since the online resources include tests and exams.

I believe I have the work ethic and have committed a minimum of 15 hours a week to this. I would love to hear any advice regarding this.