Topics to review before grad school?

[Standard Deviant]

Hi all,

 

I'll be starting a Master's program in Biostatistics come this fall. I've been out of school for a few years, so I want to be sure I'm prepared for whatever academic challenges I might encounter. Thus, I want to take some time off work and review my math.

 

I'm especially interested in perspectives from current Master's/PhD students or instructors, but anyone is welcome to contribute. What topics are most important to review/relearn? Also, any recommendations on textbooks or strategies for tackling such an endeavor?

 

I'm willing to dedicate roughly 40 hours/week and spend a bit of money if needed - should I hire a tutor?

 

A huge thanks to anyone who can enlighten me!

 

[cyberwulf]

Calculus, calculus, and calculus. Oh, and did I mention calculus? In all seriousness, you need to have differential and integral calculus down cold so that you can focus on learning the statistical concepts. It also wouldn't hurt to review some basic linear algebra (mostly vectors and matrices). Fortunately, there are tons of online and offline resources for reviewing this material.

[Standard Deviant]

Thank you for the insight! That's what I was thinking, too. I think I remember quite a bit of my differential/integral calc, but what about multivariate and related topics? Also, would you be able to recommend any resources in particular? Thanks again!

[wine in coffee cups]

You don't need 40 hours per week (perhaps not even 40 hours total) and you don't need to spend any money thanks to all the internet resources out there. I had not taken calculus in about 10 years when I started my program and did not review anything before starting, which made for a rough adjustment back to school. Here's a pretty exhaustive list of the high school/early college math I used in master's-level theory and methods coursework:

• Common differentiation rules (power, product, quotient, chain)
• Partial derivatives
• Univariate integration techniques: primarily integration by parts, u-substitution (I don't think I've ever needed trig substitution, actually just stay away from trig functions altogether). 90% of the integrals you evaluate will look like the definite integrals on my fave wikipedia page, if you can figure out how to do some of these then you're probably set.
• Infinite series representations, Taylor approximations
• L'Hopital's rule, general comfort evaluating limits, understanding of continuity and piecewise-defined functions
• From multivariate calculus: Jacobians and change of variables, inverse function theorem, iterated integrals and multiple integrals. You do not need to review line integrals, Green's theorem, all that physics-y vector field stuff.
• Linear algebra: vectors and matrices in general, multiplication, lengths/norms of vectors, orthonormal bases and rotations, matrix representation of linear transformations, projections, geometric interpretations of determinants, what positive definiteness is and how to test for it, eigenvalues and eigenvectors, inverting 2x2 matrices by hand, general awareness of special matrix decompositions (Cholesky, spectral, singular value)
• Logarithm and exponentiation properties in general, representation of exp(x) as lim n-> infty (1+x/n)^n
• Software: Mathematica is useful for checking your work, or just get good at using Wolfram Alpha if your school won't have a Mathematica student license. Knowing enough R to do simple simulations to check answers non-analytically is good too (e.g. how to generate a bunch of realizations from an exponential distribution and transform them, plot them against whatever distribution you're claiming they have)

[Standard Deviant]

Wow, thanks for such a comprehensive list! It looks to be just what I needed. I'm glad to hear that review won't be as intense as I was planning. Still, better to be overprepared than underprepared. I think I still remember most of these concepts, which is comforting. And physics was always my area of weakness, so I'll take a moment to breathe a sigh of relief. That wiki page may become my favorite too; very helpful.

 

Unfortunately, I lack familiarity in R (have experience in other languages). I'll see if I can find some resources to pick up on a bit in my time off.

 

Great list - I'll probably print and frame it somewhere

[statisticsfall2014]

What would be some recommended calculus/linear algebra texts/online resources?

[Stat Assistant Professor]

I like MIT OpenCourseWare a lot. I have been studying for the first year qualifying exam, and the notes on that site have been very helpful.

[statisticsfall2014]

WOW! I never even knew that existed. Thanks!

[Standard Deviant]

That site looks very useful, thank you. Also glad the more experienced folks here were able to help others through this thread as well! Maybe even future apps can benefit.