Fundamentals of Applied Probability Theory

Somebody recommended this book (by Alvin Drake) to me yesterday. Since I’ve been having trouble getting through the Ross textbook A First Course in Probability, I thought I’d take a look at it and found it available online.

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Python lectures!

I’m a huge fan of Python, but the main lectures at Stanford only teach Java and C++.  I just discovered that MIT introductory programming courses now use Python, so I finally have a resource to point people to instead of telling them to go download one of the many free books available.  If you have no programming background at all, you may want to go over the ‘pre-introductory’ material first (here or here).  Be sure to check out How to Think Like a Computer Scientist.


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Another course recommendation

I just started learning R about a month ago for use in my research.  I had planned to take STATS 202 Data Mining this semester to help with this process, but did not have the time.  There is a version of this course online, which I think was part of Google’s ‘Summer of Code’.  For those of you who are not familiar with R, it is an open source (free)  data mining/statistical program that is one of the most widely used in academia.  The learning curve is a bit steep  because it’s also a (slightly quirky) programming language, but this is also one of the biggest advantages.  Anyway, don’t take my word for it, give it a try!

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Online course recommendations

I’ve spent the last several months taking classes and going over old material for the prereqs of the Biomedical Informatics program at Stanford. Being a product of a six-year MD program (graduated in 2000), I found that what little I had of the prereqs (other than biology-related stuff) I’d forgotten long ago. The quality of material available online varies widely, and I hope this information is helpful to anyone following the same path.

Linear Algebra
This was my first time taking Linear Algebra, and I really enjoyed it. Made me wish I had taken it in college.. The only real contender for this is of course Dr. Gilbert Strang’s outstanding lectures available on OpenCourseWare at MIT. These courses follow his excellent textbook. However, I think the assignments on OCW refer to the 3rd edition. An up-to-date list of assignments (and answers) can be found on the current Linear Algebra website. Thank you Dr. Strang! One unforeseen consequence of going through all of these lectures is that I was absolutely spoiled. Well.. you can’t have it both ways.
If you need to take this for credit, University of Phoenix or Empire State College are good options. I say that these are good options in the sense that they are ways to get credit for Linear Algebra, not that they are anywhere close to the caliber of the MIT lectures. I actually didn’t think ESC’s course was challenging at all, mostly teaching students how to do matrix calculations that one uses MATLAB or Maple for.

Statistics (Pre-calculus)
Most people probably do not need a refresher on this, but if you do, UC Berkeley provides a good set of lectures. The companion text to this is Statistics, 4th Edition, by Freedman, Pisani, and Purves.

Univariate and Multivariate Calculus
If you need help on these, welcome to the club. There are good lectures on OCW (single and multivariable). Thankfully I remembered enough that I could view these selectively. The text used by the first course is very good, the second one not so much. There’s one by Dr. Strang that takes a slightly different approach, in his signature conversational style. This text (and his LA text above) also has the best description of complex numbers that I have seen.

For this the Stanford lectures are hands down the best. Having audited a course in Python at the University of Pittsburgh, I thought I was pretty well versed in programming techniques. This showed me how little I actually knew, and even helped me understand Python better.

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