> Well, I am about to enter into medical school and I am very interested in the mathematical aspects of medicine.
I'm not sure what the mathematical aspects of medicine are. As I'm sure you're aware practicing medicine (being a doctor) and medical research (being a scientist) are two different things. There are certainly people with MDs who do clinical research, but it usually tends to be more along the lines of drug studies or experiments with treatments/surgeries.
> By the time I got my degree I would like to be prepared to do research in the field of mathematical/theoretical biology.
Well, I think you will have your hands full with learning medicine. I mean most people who do research in theoretical biology usually get Ph.Ds in mathematics, physics, or neuroscience. Theoretical biology is really a sub-field of mathematics. Actually, believe it or not, very few people in the field even have much biology training at all.
I know some people who did dual MD/PhDs but those PhDs were almost always in biology/psychology where you can double-dip on the coursework. I had a friend in medical school who wanted to do one in CS, but he was turned down because they felt it didn't align with the goals of the MD program.
Probably the easiest entrance into theoretical biology would be from the epidemiology area. They use a lot of so-called compartmental models which are approachable with relatively little mathematical knowledge, basically an undergrad course in differential equations.
I would say the minimum course work you need to be able to approach an elementary book like this one would be:
beyond that it all depends on where your interests lie because there are a shit ton of approaches from physics/mathematics in biology.
If you're looking to bone up before you start with calculus, I wouldn't waste too much time. A lot of the crap they teach in algebra is irrelevant and boring.
Depending on just how bad your algebra is, you can start on the calculus and then simply dip back to the algebra books if you get confused on a step with working out a calculation. Algebra, in the sense it's used in high school, is really just a handful of calculation rules so it doesn't pay to waste too much time on it proper. You'll pick it up as you work through the calculus problems.