I'm hoping to start a masters in mathematics in the fall, and am hoping to find a good book on mathematical statistics to study so that I'll be able to take graduate level mathematical statistics once I start my degree. For context, my undergrad was in music, and I'm in the midst of taking prerequisites to qualify for the masters program. I'm taking finals for Linear Algebra and Calc III, and after that I will be taking Differential Equations, Methods of Proof, Real Variables, and Abstract Algebra. Are there any books you recommend for self-study in mathematical statistics? (preferably not too expensive if possible -- trying to save for school) Thank you!
Given you seem to have zero exposure to this material, I would just look for a reasonable undergrad text.
I would avoid classes "for business" or the like (although really they are way better than nothing!)
I would also be a little careful about asking for "mathematical statistics". Some people may interpret that as asking for a hyper theoretical course.
[Edit: I just checked your post on MSE and, as expected, one user has already commented in minutes, suggesting a very hard core already grad level stats book (Shao, Springer publ.) that emphasizes "measure-theoretic probability theory". This is insane for a person with zero previous prob/stats experience and who is a music major looking for a reasonable math masters. But it's par for the course on SE to see these kind of recommend a too-hard book and ignore progression in the learning process. And ignore the student's particulars.]
You do want a standard middle of the road class that a math dept would teach. It's fine if there is some calculus involved. But you don't want something super theory heavy. Not with what I read between the lines in your math background (not extensive) and ambitions (masters). Plus it's really beneficial to just get some insights in prob/stats, not just a blizzard of formulas.
A good general, low-cost, easy-to-self-study option is the Schaum's Outline:
It's calculus based, but very gentle. Not encyclopedic, but covers the key areas. And an omnibus can be daunting. Better to make a first pass that is more prioritized. And it is cheap. And easy to read, has answer key, etc. (good option for self studiers.)