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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!

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    $\begingroup$ You might have more luck asking over on stats.stackexchange.com or possibly math.stackexchange.com. If you do so, please link the questions to each other (or delete the question here). $\endgroup$
    – J W
    Jan 11 at 16:20
  • $\begingroup$ Will try those next. Thank you! :) $\endgroup$ Jan 11 at 17:40

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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:

https://www.amazon.com/Schaums-Outline-Probability-Statistics-4th/dp/007179557X/ref=cm_cr_arp_d_product_top?ie=UTF8

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.)

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  • $\begingroup$ Thank you so much, I will check that out! It will definitely help. Thanks for thinking about the context of where I’m at and where I’m hoping to go as well — that’s very helpful. Just to clarify I have also taken an introduction to stats course so I’ve had a little experience in stats, but yes, not much. $\endgroup$ Jan 11 at 18:20
  • $\begingroup$ grad level stats book that is "method-theoretic" in emphasis -- Did you mean "measure-theoretic"? That makes sense to me, but "method-theoretic" doesn't, although admittedly I know very little statistics. $\endgroup$ Jan 11 at 19:37
  • $\begingroup$ Fixed (spaces...) $\endgroup$
    – guest
    Jan 11 at 19:59
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    $\begingroup$ Might try engaging with Sue VanHattum (poster, this forum). She has a masters and teaches at a juco. It sounds like you're getting decent local advice also. Good luck. Wish you the best--think the kids will like you as a teach. $\endgroup$
    – guest
    Jan 13 at 13:41
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    $\begingroup$ I skipped this question because statistics is not my focus. But it sounds like you've gotten good advice. $\endgroup$
    – Sue VanHattum
    Jan 15 at 20:00

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