General Review/Preparation Prior to MS Biostats Program

[fireuponthedeep]

Hello all!

I have been researching topics to review prior to the beginning of my program, and wanted to know if these were good places to start?

-Basics of Linear Algebra

-Calc I-III, u-sub, chain rule, etc.

-Gain familiarity with R

-Dip toes into Measure Theory/Real Analysis if feeling particularly ambitious

I took Linear Algebra 4 years ago, and have been reviewing the textbook I used (Introduction to Linear Algebra, Strang 5th ed) and it's coming back quickly. However, I'm (now) realizing it's mostly applied, and it seems a proof based text would be more appropriate? Is there a specific proof based text (I've read that Matrix Analysis and Applied Linear Algebra by Meyer is a good proof based text?) I could use instead, or will that be overkill and just reviewing Strang/basics enough?

None of my calc courses were hard to understand when I took them so I'm not particularly worried about reviewing/regaining the info, but how in depth should I go? Just review some problems, or should I redo my textbooks? 

Any specific books/courses for learning R? I was planning on using 'The Art of R Programming' by Matloff. I have literally no experience with R lol.

Is trying to learn Measure Theory (Casella & Berger) and Real Analysis (Either Rudin or Understanding Analysis by Abbott) total overkill? I didn't take Real Analysis in undergrad, but planning on taking it during my program. Feels like a decent idea to at least get some basic understanding beforehand. And I just wanna hit the ground running for my program, been out of undergrad 2 years and worried about being behind the curve.

If there are any areas/topics I didn't mention and definitely need to cover, please let me know! And any other tips, advice, or good texts to use would be greatly appreciated!

[Stat Assistant Professor]

3 hours ago, fireuponthedeep said:

Hello all!

I have been researching topics to review prior to the beginning of my program, and wanted to know if these were good places to start?

-Basics of Linear Algebra

-Calc I-III, u-sub, chain rule, etc.

-Gain familiarity with R

-Dip toes into Measure Theory/Real Analysis if feeling particularly ambitious

I took Linear Algebra 4 years ago, and have been reviewing the textbook I used (Introduction to Linear Algebra, Strang 5th ed) and it's coming back quickly. However, I'm (now) realizing it's mostly applied, and it seems a proof based text would be more appropriate? Is there a specific proof based text (I've read that Matrix Analysis and Applied Linear Algebra by Meyer is a good proof based text?) I could use instead, or will that be overkill and just reviewing Strang/basics enough?

None of my calc courses were hard to understand when I took them so I'm not particularly worried about reviewing/regaining the info, but how in depth should I go? Just review some problems, or should I redo my textbooks? 

Any specific books/courses for learning R? I was planning on using 'The Art of R Programming' by Matloff. I have literally no experience with R lol.

Is trying to learn Measure Theory (Casella & Berger) and Real Analysis (Either Rudin or Understanding Analysis by Abbott) total overkill? I didn't take Real Analysis in undergrad, but planning on taking it during my program. Feels like a decent idea to at least get some basic understanding beforehand. And I just wanna hit the ground running for my program, been out of undergrad 2 years and worried about being behind the curve.

If there are any areas/topics I didn't mention and definitely need to cover, please let me know! And any other tips, advice, or good texts to use would be greatly appreciated!

Linear algebra: review "Linear Algebra Done Right" by Sheldon Axler. It's a good textbook for a second course in linear algebra (proof-intensive).

Real analysis: review "Understanding Analysis" by Stephen Abbott. Rudin is a good book, but if you haven't taken real analysis before, the Abbott book is a much "gentler" introduction to the subject. And also, reviewing analysis at the level of Abbott is probably sufficient before entering graduate school in Statistics (Masters *or* PhD). I wouldn't bother studying measure theory, unless you have already learned it before, are very interested in the subject, or plan to focus on theoretical probability in grad school rather than statistics (even in mathematical/theoretical statistics, the amount of measure theory you need to know in-depth is generally minimal and at a fairly basic level).

Learning R: It might help to get a book and work through some exercises or to do a free online course (does Coursera offer one for R?). I've found the best way to learn it is to use it regularly and to search Google when you need help on something specific. If you've never used R period, then I would try to find some exercises to gain familiarity with basics like vectorization, lists, and writing functions (vectorization helps a LOT in speeding up code). I don't have a particular book in mind for this though, unfortunately.

Calculus: You can basically skip anything with trigonometry and polar coordinates, but you do need to know how to do derivatives and integrals of other common functions (polynomials, exponentials, logarithms, etc.), including partial derivatives and double integrals. And you need to know some fairly common rules, like integration by parts, how to solve improper integrals, etc.  which will certainly  come up in homework problems from Casella & Berger. If you're comfortable with it, you probably only need to do enough practice problems to reacquaint yourself with the method of integration/differentiation  and leave it at that. If you're also reviewing analysis, then you can probably also skip anything on series from Calc II, although it would certainly be helpful to recall how to find the infinite or finite sum of a geometric series (this comes up sometimes for problems on discrete random variables).

 

 

Edited March 22, 2019 by Stat PhD Now Postdoc

[fireuponthedeep]

@Stat PhD Now Postdoc okay, sounds like I will be poring through linear algebra done right and understanding analysis for the next couple months! And I'll just review Calc with some sort of open course ware, good to know I can ignore trig and polar coordinates tho haha.

Coursera has a few R programming courses offered through JHUs Biostat department I can audit for free, but I think just jumping into would be a good idea too, that's usually how I learn best with programming. Maybe mix and match if I need more help/guidance. 

As an aside, thank you for all your help, both on this post and the others I've previously made. It's been indescribably beneficial to get an informed opinion!

[GoPackGo89]

For R I would recommend this book: https://r4ds.had.co.nz/
Visualization and manipulating data will always serve you well.

I think worrying about analysis might be overkill for a masters in biostats. If you really insist then I agree that working through Abbot would be good.

Linear algebra. Looking at the textbooks/syllabus for your regression courses will probably give you the best idea of how to brush up on linear algebra. I don't know other programs masters coursework but at my program applied linear algebra would help you more than heavy proof based books. Strang seems sufficient to me. (I'm actually going to review with Strang and pick some spots in Axler this summer before I head into my 2nd year PhD courses).

Calculus. Agree with Stat Phd Now postdoc.

In order of importance I would say:

R (programming as research assistant or in a datascience course has more of a learning curve than the calculus/algebra you're going to use IMO)
Brief derivative/integral review (You're going to get really good at turning an integral into a pdf so you don't ever have to integrate anything difficult anyway)
Lin Alg (Rank, determinants, inverse/transpose rules, multiplication)

Current students at Minnesota would have more relevant opinions than me though.

 

Edited March 22, 2019 by GoPackGo89

[Stat Assistant Professor]

For linear algebra, specifically review stuff from matrix algebra (like determinants, singular/nonsingular matrices and inverses, eigenvalues, diagonalizable matrices, trace, rank and nullity of a matrix, nullspace, column and row space, symmetric positive definite/semidefinite matrices) and vector spaces (basis/span, orthogonal decompositions, orthogonal projections, orthonormal bases). You don't need to memorize the proofs for "big" theorems, but you should be comfortable doing proofs using these concepts (e.g. proving that all the elements of the diagonal of a symmetric positive definite matrix are positive). That sort of thing.

Edited March 22, 2019 by Stat PhD Now Postdoc