Undergraduate in Biomedical Engineering wants to pursue a Graduate Math degree. I have a bachelor's degree in biomedical engineering, but I am looking to go to graduate school for mathematics; I know that the switch would not be easy (obviously an undergrad in math would've been best). I am looking for advice on what courses I should take to both prepare me for graduate school and to show graduate schools that I am "prepared" (if such a thing exists). 
I've started reading Spivak's Calculus, but because I don't have an undergraduate degree in math I believe I need to take courses to prove I am ready (again, if I can). I am looking for any general advice for this pursuit and would appreciate if anyone has any advice on how to further strengthen my preparation and application. 
-Thank you 
P.S. I have looked through a few (not all) other posts to see if my question was answered, so I guess I should say I am looking for a more "structured" answer in terms of courses and what graduate schools are looking for. I'm not at all sure that makes any sense.
 A: I will attempt to answer your question, the first thing you need to realize is that Graduate math degrees take many different forms. Are you looking to do applied math? Pure math? Do you want to pursue a masters degree? PhD? These types of questions will largely determine you kind of coursework a program will expect you to have under your belt before you arrive.
I am not qualified to assess what applied math programs want, but I can try to give you an idea of the basic prerequisites for starting either a masters or PhD program in pure math. The bare minimum expected would be a full a year of both Algebra and Analysis, I have never used Spivak's book but my understanding is that it is not quite at the level of an undergraduate analysis course. You have not mentioned studying any algebra and depending on what kind of math you want to do you may not need to know much but certainly graduate schools are looking for at least some knowledge of groups, rings, and fields. In my opinion having background in these areas qualifies you to start graduate work (although a broader background would be better).
The reality is that without formal coursework in advanced mathematics it is almost impossible to get accepted into a PhD program (some masters programs may be more forgiving but you would also be expected to pay for your education). My advice to amounts to this if you can try to find a post-bac program that will allow you to take some serious math courses. Taking these classes serves two purposes first it lets you determine if you really enjoy math and are willing to commit a significant portion of your life to pursuing a graduate degree, second it will show graduate schools that you are serious about moving into mathematics.
