What knowledge of mathematics is needed to study mathematical statistics?

Question

Mathematics

Good afternoon!

There is a need to study mathematical statistics. The current level of knowledge of mathematics is the elementary mathematics of the school curriculum. I would like to know what is needed from higher mathematics for math. statistics? It is clear that, ideally, a full university course of matan, linal, etc. would be needed. cover by. But wouldn't it be redundant within the existing goal? The same mat. analysis according to Fichtenholtz, for example - 3 considerable volumes. I am sure that for further study of statistics, part of the topic from there will not be needed. But what exactly will be needed - I can’t figure it out due to incompetence. Can someone suggest not just sections of mathematics, but some selection of topics from there?

Answer 1

Usually, statistics is preceded by a study of probability theory. To understand it, you need to have an idea of ​​what a limit is and what an integral is. Well, the basics of combinatorics. Then, in mathematical statistics, it will be useful to understand what the optimum is, how to search for it analytically and numerically. As the complexity increases, you will need linear algebra, an understanding of vector calculus, and, well, multidimensional optimization. (By the way, the book by Wentzel E.S. is considered a textbook "for all times" and "for everyone" - here it is self-sufficient, by the way.)
There are several useful resources. They mostly talk about Machine Learning, but in fact they can also be interpreted as "Statistical Sciences"
https://habr.com/en/post/432670/
https://www.datasciencecentral.com/profiles/blogs/ ...
https://www.analyticsvidhya.com/blog/2019/10/mathe...
In this very good book, there are no complex mathematical foundations for you at all.
loveread.ec/view_global.php?id=76269
In general, a Fichtenholtz-type course and a Theorver and Mathematics course are parallel branches of mathematics that intersect each other. But their mutual influence - if you do not climb into the deep jungle, as is done in the mathematical departments of decent universities - is quite relaxed. Another thing is that taking a course in classical higher mathematics is very useful, since it is there that a general mathematical culture and the ability to think mathematically are developed.
But if there is no such goal, and the matstat is needed only for evaluation, then you can not bother with this. Look, economists and even doctors study statistics without any Fikhtengolians and nothing, they live for themselves.

Answer 2