I wish to take course in statistics for my graduate studies. However, only course I can take is mathematical statistics. The textbook for that course is All of statistics. I have some statistics courses, however they didn't required any mathematical background which I actually don't have.

I wish to take this course, however I don't think it is, at least for now, possible. So I decided to prepare myself for the course. I found so many textbooks recommendations which made me overwhelmed because I don't know where to start. I started with reading All of statistics, however immediately I realized I need another approach. So I've started with Introduction to mathematical reasoning and Calculus by Stewart. My issue: I don't have as much time for reading Calculus book.

My goal:

  1. Take course in mathematical statistics.
  2. Even if you think it is kind of suicidal for someone without mathematical background to take mathematical statistics, I wish to find out some suggestion books/MOOC courses that might help me to come closer to it.

Statistics books I saw many recommendation for:

  1. Probability Theory: A Concise Course (Dover Books on Mathematics) by Y.A. Rozanov
  2. Mathematical Statistics with Applications by Wackerly
  3. Introduction to Mathematical Statistics by Hogg et al.
  4. Introduction to Probability by Blitzstein
  5. The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists by Ash

I also saw recommendations put on this question: A path to truly understanding probability and statistics and The Best Books to Learn Probability.

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    $\begingroup$ Perhaps try to work backwards. You say you've started All of Statistics. Collect up some of the things assumed there that are new to you and then try to learn those, by searching or reading. That may take you back into more elementary stuff, or not. This strategy might be more efficient than trying to find the right book or books to study all of first. $\endgroup$ – Ethan Bolker Apr 21 '18 at 13:30

I have taught out of books 2 and 3 on your list, and have seen most of the others. Wackerly will possibly be the solid one with the fewest mathematical barriers. (An older edition no longer used in college classes and so cheap online would be OK; changes from edition to edition are mainly superficial.)

For all of these books, the primary mathematics you need is calculus (especially the first half of what is often taught as a yearlong course). Calculus is also generally useful in sciences other than statistics (physics, economics, etc.)

An alternate path would be to find a good pre-calculus book in statistics for study immediately. There are very many of them and you will get a uselessly vast variety of opinion as to which is likely to be most useful to you. You might get better advice here if you said more about your purpose in learning statistics ('mathematical' or otherwise). But best advice would likely come from people who know you personally and also something about mathematics and statistics.

  • $\begingroup$ Thank you for your reply! Statistics will be one of crucial thing for doing my research. I was in Social Sciences, now I am starting my PhD in Neuroscience. I was looking forward to have more courses in statistics, however mathematical statistics is only what I will get now. $\endgroup$ – Enasi Apr 23 '18 at 14:44
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    $\begingroup$ Working in modern neuroscience, I venture to say you will benefit greatly from knowing the fundamentals of calculus--quite aside from the foundation calculus provides for mathematical statistics. $\endgroup$ – BruceET Apr 23 '18 at 15:19
  • $\begingroup$ When you say fundamentals, do you think Calculus 1? Might sound a bit weird, but I am glad to be "forced" to learn calculus, statistics and similar things. Otherwise I would always find some other priority to study. $\endgroup$ – Enasi Apr 23 '18 at 19:47
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    $\begingroup$ Not trying to 'force' anything on anyone, but in my experience no one's career prospects have ever been diminished by learning basics of calculus. // Differentiation and integration are both useful. For math stat often multivariate integration. Relatively speaking, topics such as hyperbolic trig fcns are seldom encountered is statistics. // Nowadays learning a bit about such software as R and Python is also helpful. (Bootstrapping, permutation tests, analysis of huge messy datasets, often require some programming.) $\endgroup$ – BruceET Apr 24 '18 at 16:23

If you want a basic course in both probability and statistics, I recommend Schaum's Outlines in Probability and Statistics, which do an excellent job in working out examples.

In my personal opinion, the only hard part for basic probability/statistics courses you may find is in continuous probability and random variables, which uses calculus.

  • $\begingroup$ Thank you for your reply! I will check out Schaum's Outlines $\endgroup$ – Enasi Apr 23 '18 at 14:28

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