Blog, by category: learning
from the desk of travis johnson.
Five Critical Textbooks for (Applied!) Math & Physics Students (from 2011/09/04)
In the course of working through my first year at grad school, I've come up with five favorites for the basics of an undergrad understanding of the essential topics for applied math and physics. Without ado and in the order I'd take them off my shelf:
I've spent probably the most time with Boas’ Mathematical Methods in the Physical Sciences–I've worked nearly 1000 problems out of the book to get ready for the preliminary exams my first year. It was completely worthwhile.
Tunes U and Essential Mathematica (from 2009/12/13)
In a similar vein to the TED talks in the previous post, I've also been watching a lot of lectures from iTunes U lately. Mostly to get ready for preliminary exams, but also for their sheer awesomeness of the teaching and material. I've been most surprised how many people haven't heard of this yet: Nearly everyone seems surprised when they hear about it. Anyways, here's my list of favorites so far:
I'm particularly attached to the last of this list. Applications of Fourier Transforms were one of the things that motivated me to actually study applied mathematics in the first place, and continue to be a source of fascination for me. I was also throughly impressed with the biology lectures that I've heard so far; I hadn't enjoyed biology much up to that point, but it really is really a far more satisfying and interesting subject than I'd given it credit for.
Even if learning about multivariable calc isn't really your cup of tea, I still highly recommend watching what might have been the most entertaining 160 seconds of a math lecture ever caught on tape: A lovely Phone Call
In addition, my officemate also pointed to a wonderful reference on Mathematca, Essential Mathematica. It's a great reference. What'd be most excellent though, is a similar overview of SAGE, the William Stein brainchild out of the University of Washington.
Getting an AMATH Minor at the University of Washington (from 2008/10/26)
One of the secret gems at the University of Washington is the minor in applied math option. At least I think it's somewhat secret. Most of the people I tell about it haven't really heard of it. But yeah, here's the deal: You only need to get through calculus and four more classes to get this minor! And a lot of programs require calculus anyways. I've taken most of the undergrad AMATH courses, so I figured I'd write something up about which ones I recommend the most.
This will vary a little bit. Most engineering majors have to take Differential Equations and Linear Algebra. And, most opt to take MATH 307 and 308. I recommend their AMATH equivalents, 351 and 352. I would venture that the AMATH courses will be far more worthwhile in your studies after these, and in most cases they will count towards requirements. I would take AMATH352 whether or not you had already taken another linear algebra course. It covers a lot of ground you just don't usually cover in linear algebra, like defining function spaces and isomorphisms.
If you're just getting started, though, get a feel for what it's like with AMATH 410: Introduction to Computational Biology and Chemistry. The webpage says Prof. Eric Shea-Brown is teaching it next Winter ’09, and he's a great teacher and very helpful. It only requires a knowledge of calculus, but he'll show you lots of interesting stuff. And don't be put off by the relatively high course number, it's so that graduate students from other departments can get some credit for it. Hopefully this sticks around for a while.
If that went well for you, or you want to skip to the big guns, sign up for AMATH 301: Introduction to Scientific Computing. Try, if at all possible, to take this autumn quarter, with the AMATH department chair Nathan Kutz. He'll bend your mind with mathematics, but have you cracking up the whole time. Then you'll think he's trying to kill you with the homework, but he or his TA's will have helpful office hours. This class is truly what sparked my interest in mathematics in general. You'll cover a lot of ground and it will require some effort, but as Nathan says, 'You'll be a MATLAB superstar!’
Now, depending on whether you took linear algebra or differential equations(or perhaps which one you enjoyed more, if you took both and skipped out on something else), sign up for either Discrete or Continuous Mathematical Modeling- MATH381 or AMATH383. The MATH381 class counted as AMATH381 for me, so make sure it'll count if you go that route. Both are pretty interesting.
So, now you should have some idea what you're getting into. Best of luck on your studies!