I Know My Calculus

Despite a rather strange schedule today, I pushed through some laziness and finished my studying for the day, so I’ll count it a success! It really was a success, as I actually followed the math today quite easily. Vector calculus > linear algebra. I did the first half of the vector calculus chapter, so I covered just basic integration and differentiation for vectors. It was definitely a relief to understand what was going on in all the examples. Even so, it took a couple tries to get through the sections, but that is because I went to the beach during my “lunch” today and that made me very sleepy for my afternoon studying! It was a lovely day, though, and I want to take advantage of my current schedule to do things like ride my bike to the beach on a Tuesday afternoon. I am, after all, paying for the privilege!

Prior to the beach, I read another chapter in Bob. This one was on light-matter interactions and, once again, was a retread of material I’ve already reviewed. Seeing things multiple times, especially from different authors/perspectives, is definitely helping me feel more comfortable just in the general arena of physics, which is good. That is one of the things I have lost the most in the intervening years. Topics ranged from Compton scattering to the Pauli exclusion principle and a lot in between. A good high-level view of quantum physics, especially as it relates to astrophysics—primarily in the area of spectroscopy.

Feeling energized going into tomorrow, ready to keep crushing and building my physics skills and confidence.

Bonus: Here is the (awful, awful) song that today’s title comes from!

I Don’t Want to Be a Stupid Girl

Happy Monday! I didn’t sleep well last night, so I was a bit surprised that I woke up relatively early and ready to go. I guess I’m just too excited about studying!

Today I had the short chapter in Mathematical Methods that I didn’t get to last week. It dealt with normal modes. Due to the length and the subject matter (oscillations, we meet again!), I thought it would be easy. I was wrong. This was mostly more advanced-level matrix manipulation. I don’t find this intuitive at all, so when the text claims that this is an “easier” way of doing the math, I have to scoff. I know that it is, really, but to me it just doesn’t quite click. Still, I did get through the chapter. I really hope that I can get better with matrices. I’ve always had a knack for math and enjoyed it, so it doesn’t sit right to be struggling here!

The afternoon was devoted to diving into some physics Python programming. I made it about halfway through the chapter I was working on, and got to write up several neat little programs to do things like calculate a planetary orbit, the probabilities of reflection and transmission of a particle wave function, and so on. I wrote a lot of code, and I was pretty pleased with it. For the examples, I didn’t even need to follow along with the author’s coding, I just took the prompt and did it. Of course, this chapter is intended for people who have no programming experience, so it should be easy for me with at least the basics under my belt.

Midnight, You Come and Pick Me Up, No Headlights

I didn’t post the past couple days because it’s been a little bit of a mess for my, studying-wise, but I’ve decided I’ve just got to own up to it and move on! So Thursday I had planned to work on Python (starting on the Computational Physics text as discussed in my previous post). That didn’t go quite as smoothly as I hoped! Before, I was using basically a faux-dev environment via the Codecademy course. Now, I need to get something set up to actually run Python on my own machine. This isn’t actually very difficult, but somehow I managed to have to do three different installations and several computer reboots and various mucking around that managed to frustrate me and waste a lot of time without actually even getting to the stuff I wanted to do. But at least I now have a working version of Python 2.7.13 and a vague sense of how to run modules through it. Success! Sort of.

Thursday afternoon I was supposed to finish up my chapter on matrices. However, I scheduled a call with a professor from my department that I had been procrastinating, and that basically took my entire afternoon. Not that it was a long call—it was not even 20 minutes—but because talking to people is a Big Weakness of mine. I know it sounds kind of silly, but I’ve always dreaded it. I remember crying as a little girl if my dad made me tell my order directly to the McDonald’s cashier. I handle it a little better now, but I’m still much much more likely to try to handle any business over email or text. Talking on the phone makes me nervous, and video calls can be downright terrifying. So once I knew I was committed to making a video call, it really wiped out my ability to concentrate for the rest of the day.

Of course, once I took the call, it was totally fine. These things never turn out to be as horrible as I worry they will, and yet I still worry every time. I also got to discuss some potential projects that sounded quite interesting, and he sent me some items to take a look at (including a Python program—I am so glad that I’ve been working on my coding already!!), so things are starting to feel almost Real in a scary but cool sort of way.

So anyway, I tackled the matrix stuff on Friday. And hoo boy was it a whopper. I’m pretty sure the last couple sections I was barely hanging on to understanding and definitely wasn’t able to complete the examples on my own. I’m sure singular value decompositions are child’s play to some, but my brain felt all stretched out trying to follow along. This was a little discouraging, but I am trying not to be too hard on myself. I can always revisit the material later!

I also read another chapter in Bob, this one on special relativity. This is now the third time that I’ve reviewed relativity, so it’s starting to feel pretty comfortable. Which is great! Even so, there managed to be some stuff in here that I hadn’t encountered in Tipler and Mosca. It’s a big topic, after all, and a crazy one no matter how familiar I am with it.

I intended to also do the next chapter in Mathematical Methods, this one on normal modes, but I ran out of energy/motivation/whatever. So I intended to do it yesterday. But I didn’t. Sooo I guess I’ll have to write it into my schedule for next week.

Today’s fun “new” fact: The relativistic headlight effect causes light emitted from a moving source to be concentrated into a cone to a stationary observer. This effect can be observed in synchrotron radiation from relativistic electrons

Photo by Georg-Johann / CC BY-SA 3.0

Too Hot (Hot Damn)

This morning I bid farewell to my boyfriend, as he is off on the Navy’s bidding for a few weeks. I also dealt with a malfunctioning air conditioner (a lizard fried himself on a capacitor, poor guy) in 90F+, extremely humid weather, a morass of bug bites on all my limbs, and the cavalcade of documents that go along with a mortgage. I also had to talk on the phone multiple times, which for me is super unfun. All in all, it was A Day, and I could be forgiven for letting my first day back at studying slide.

But! I did not! I guess I’m just stubborn enough. Or scared enough. Or I actually enjoy doing this enough. Well, a little bit of all of it, I suppose. In any case, once the internal temperature settled back down into the 70s, I was able to focus on learning more about matrices. In today’s sections, I got to the key part about determinants. No wonder I was having trouble remembering how to do this—they are, like many matrix-related things, supremely annoying to calculate. I am not sure if it the spatial element of it (if I am not careful I will get my rows and columns mixed up halfway through) or something else, but I have to go slow and frequently use my finger to point at the numbers I am trying to work with within a matrix. However, they are useful little beasties, and doing these sorts of calculations by hand is only for the theory of it and so a little painstaking is fine.

I read through another chapter in Bob today as well, this one on light and the electromagnetic spectrum. After having gone through this at least a little rigorously in my physics text, it was nice to get the astrophysics perspective here. A lot of focus on blackbodies, magnitude, and luminosity, which are key to our observations of the universe. Surface temperatures in the thousands of Kelvin! Distances in parsecs! I also re-learned some interesting info about color indices and getting a little bit into the practical side of things, with at least some attention given to correcting for instruments, atmospheric effects, etc.

One thing popped up that illustrates the downsides of using my old college textbooks for studying. For the most part, it’s quite adequate, as the things I am reviewing have been settled science for many decades, but sometimes the time gap rears its head. In this case, the text referenced an upcoming NASA mission called SIM PlanetQuest. It sounded quite interesting, and I was intrigued about a mission I had never heard of. So I pulled out my phone, googled it…aaaand it was canceled in 2010. Well damn. Better luck next time!

Back to the Grind!

But in this case, it’s not so bad, since the grind is just studying math and physics at my leisure. ☺ I’ve got it good right now and I know it!

I went up to Chicago this past week to attend my cousin’s wedding and do some house hunting. I was pretty worried about this, as I found out my current lender doesn’t finance co-ops, which wiped out like half my favorites list, and a lot of the units I liked had already gone off the market. But after a lot of visits, I ended up putting in an offer on the very first one we saw! And it was accepted today, so if I’m lucky it’ll go all the way to close and I can spend tons and tons of money having some place to live. Yay! It’s definitely nice to not have to keep stressing about the house hunt—although of course, it ain’t over til it’s over. While we were there, I stopped by the campus and showed my boyfriend around a little, but I felt too shy/nervous to go inside. Yep, introvert!

I gave myself a free day when we got back, but yesterday I put some things down on my study schedule and got back to it! I ran out of time before we left to finish my vector chapter, so I worked through the last sections of that. Then I broke open Bob, aka the Big Orange Book, aka An Introduction to Modern Astrophysics, 2nd Edition by Bradley Carroll and Dale Ostlie. I already ready chapter one a couple months back, so I hit up chapter two, which delved into heliocentric theories, Kepler’s laws (which we already know I love!), and the theory of gravity. Very interesting stuff, including a detailed derivation of Kepler’s laws from Newton’s laws and a basic breakdown of conic sections and orbits. This reminded me that I have been dallying in my reading of the Celestial Mechanics book I’ve been working on!

After that, it was back to Mathematical Methods to start on the chapter dealing with matrices. This is important stuff and I am definitely very rusty on it. It’s a long chapter, so I’ve broken it down over 3 different sessions. This first one mostly dealt with laying the groundwork (and making my brain hurt by trying to nail the concept of M-dimensional vector space) and some basic matrix math: addition (easy), subtraction (easy), and multiplication (painstaking).

In all, it felt good to get back to it! September is getting closer every day, and I am trying my best to get all the pieces to fall in place. I still don’t really have any clue what to expect/what I will be doing come fall. That’s making me a bit of a nervous wreck, but at least I am taking some proactive steps to help assuage my anxiety. That being said, it’s a holiday weekend, and my boyfriend is about to leave for some Navy crap for the rest of the summer, so I’ll be taking a few days off to chill with him! But Wednesday it will be ON again!

Square Cut or Pear Shaped, These Rocks Won’t Lose Their Shape

The end is drawing near for Tipler and Mosca! Today I read two chapters: Solids and Relativity. There was an optional relativity chapter in the first volume, so that was mostly a repeat but always a good one refresher to get! More fun brain benders like the twin paradox and non-synchronous simultaneity. And a bit of general relativity too, which wasn’t in the first relativity section.

As far as the material about solids, that was interesting but also a bit difficult to follow because most of the math is hand-waved (too advanced for this text), so it becomes a bit abstract. There are a lot of interesting practical effects that are very important to the world today condensed into this chapter, such as semiconductors, transistors, etc. I had to laugh because one section talks about current technology and lists laptops and appliance processors as cutting edge. No mention of smartphones because, back when I got this book, smartphones didn’t exist yet! Yes, that’s right kids, the very first iPhone was released when I was in college. I got a BlackBerry Curve my senior year and thought I was fancy.

Over on the math side of things, I started the chapter on vector algebra. This was pretty easy, since I haven’t forgotten how to do vectors and they’ve been all over my physics textbook. Of course, Mathematical Methods manages to make topics that I already understand sound confusing, but I figured out what they were trying to say eventually. I can’t say I really understand the order that this book is going in, but that’s okay. I think it’s intended to be more of a reference than a book to work through, so I’m not using it in the most optimal way.

Today’s fun “new” fact: Superconductivity (a truly bizarre situation in which a material has zero resistivity and can sustain a current indefinitely without an emf source) is due to electrons forming Cooper pairs. Because the pairs act as a unit, they become bosons (integer spin) and are no longer bound by the Pauli exclusion principle. Although, as with most things in quantum physics, I believe this is more of a way of explaining it rather than a precise description what is actually happening.

(And as a bonus fun fact, Cooper pairs are named after physicist Leon Cooper, who is also the namesake of fictional physicist Sheldon Cooper on the TV show The Big Bang Theory.)

I Ain’t Trying to Do What Everybody Else Doing

Another day another dollar! Except not, because I have no dollars coming to me at all right now. Which is fine. This is fine. (Actually, it is fine, because I planned for it, but it is a little…unnerving?)

Today I got some more modern physics refreshed into my brain. I read two chapters, Atoms and Molecules. As advertised, I got to learn about both atoms and molecules! It was a very interesting perspective on things that are familiar from high school science classes. Ionic bonds! Covalent bonds! Except now with added quantum physics! Which I think is pretty damn cool. Suddenly the why of rather arbitrary things, like having 6 electrons in each p-orbital, makes sense. Or at least, makes as much sense as quantum physics ever does. =) Reading about the spectra for molecules made me think about taking spectra of exoplanet atmospheres and I got all excited all over again about what I get to do.

And then I got scared.

Forgive me for waxing a little personal/philosophical here, but reading about all these amazing physicists like Schrödinger and Dirac and Pauli is intimidating. These people were brilliant and able to come up with these new ideas that changed the way we understand the universe. I certainly can’t hope to do that. Don’t get me wrong, I’m a pretty smart cookie. And I’m really good at learning physics. But am I good at doing it? I honestly don’t know. And this is part of the reason why it took me so long to pursue this path. Anyway, it’s scary, but I just have to button up and carry on. I’ll do my best and not get ahead of myself.

In other news, I finished up my Python course today! That was pretty exciting. Do I feel like a coding genius? No, not even close. But I have a better understanding of the language now, and I feel more confident about my ability to tackle it and make it work for me. Overall, I think the Codecademy course was very helpful, and I recommend it to anyone trying to get the basics of Python down. Plus free is always a good price! But it’s definitely only a stepping stone and not a full education in a language.

I think I earned myself some ice cream!

Today’s fun “new” fact: The letters used to identify the l quantum number (s, p, d, f for l=0,1,2,3) were not just arbitrarily chosen to frustrate young chemistry students. According to a footnote in my textbook, they are “remnants of spectroscopists descriptions of various spectral lines as sharp, principal, diffuse, and fundamental.”

A Whole New World

Today I got to start on the part of the physics textbook that deals with the somewhat-misleadingly-named modern physics (dating back about a hundred years now!). Excitingly enough this is also the last section of the textbook. The end is drawing near for Tipler and Mosca! So today I read two chapters, Wave-Particle Duality and Quantum Physics and Applications of the Schrödinger Equation, and these were an introduction to quantum physics. They’re actually a pretty well-written introduction, explaining Schrödinger’s equation and wave-particle duality and probability densities in a matter-of-fact way that makes it sound like, okay that makes sense, and not like that is Totally Fucking Weird, which probably should be the default reaction to quantum physics. It covered some of the stuff that had previously been mentioned in the light chapters, and it was a good recap plus adding Schrödinger and some of the quantum things that arise that are classically forbidden like tunneling and partial reflection.

Math-wise, I worked on integrals today. It was actually a pretty easy chapter—I did the whole thing in one go—on multiple integrals. Basically integrating over areas and volumes. The trickiest part here is defining the limits of your integrals, and there was a fun section on change of variables which didn’t make a whole lot of sense because it was said to just use the determinant of the matrix, and if you don’t know what that is we’ll cover that in two chapters. I don’t really remember anything about matrices so that was not quite so helpful for me, but other than that I do feel like I have a good handle on the material in this chapter. I was pretty comfortable working through the problems, although I got a little bogged down in some of the actual calculations. But that’s just me being out of practice and doing stupid things like dropping random x’s when I was doing multi-line integrals.

Really, it was a good day. I feel happy with where I’m at, and I am looking forward to the rest of this week. It’s a little bit of a short week because I’m going to Chicago on Friday, both to go to my cousin’s wedding and to look at houses for when I move to Chicago in just a couple months now! I’m looking forward to that, and I’m a little nervous and hoping that all the places I see don’t suck and that I can find something I can afford. I’m also excited to show my boyfriend Hyde Park so he can get a feel for where I’m going to be living—and for me to get a better feel it because I’ve only been there once!

Today’s fun “new” fact: While I remembered the Pauli exclusion principle, I forgot that it can be seen in the construction of anti-symmetric wave functions, where if both quantum numbers are the same, the wave function will go to zero and so therefore, while it is still a valid solution mathematically, it is rejected as a wave function because it cannot be normalized. It’s a simple way of thinking about a complicated assertion.

Mysterious as the Dark Side of the Moon

Good morning and happy Monday! I had another nightmare about grad school last night. That was fun. My brain needs to just get over being anxious! I’m a grown-ass woman, I shouldn’t be this nervous about making a huge, upending life change. Oh wait. That’s totally normal.

Before I dive into my books this sunny Monday, I wanted to finish my Friday/Saturday update so I don’t fall so far behind again. Because I basically forgot to do a section on Thursday, I planned to do three on Friday. That didn’t quite work out, but I only pushed one and I got it done Saturday. So I did meet my goals last week! Just a teeny bit off-schedule.

Friday morning I finished off the chapter on partial differentiation. This got into some pretty interesting stuff, including deriving some of Maxwell’s thermodynamic equations, the Boltzmann distribution, and a series of problems where I got to solve systems of equations with some fun middle school algebra tricks. It took a bit of doing, but I enjoyed the problems.

In the afternoon, I turned back to trusty Tipler and Mosca. I had set a rather lofty 3-chapter goal that included the entire Part V on Light with the chapters Properties of Light, Optical Images, and Interference and Diffraction. This pretty much covered the entire (non-quantum) spectrum from wave-particle duality to color to rainbows to interference rings and ray diagrams. There was even a neat section about a rough physical model of how the eye works. Plus lasers, measuring the speed of light, and more! Light is a pretty cool topic, and one quite relevant for astrophysics, so this was a good refresher. They even included a few examples from astro, which is always nice to see.

After my lengthy physics read, I didn’t get to my Python course, so I tackled that on Saturday, finishing a lesson on classes. I wanted to do two lessons, but I also have a life and a boyfriend so that didn’t happen. Only one lesson to go before the final project! That’s on the schedule for this week, and I’ll do the final when I get back. I’m pleased with what I’ve learned so far and think it will help me out a lot going forward.

Today’s fun “new” fact: Mirages are due to the differing densities, and therefore differing indices of refraction, of air of different temperatures. Hotter air closer to the ground (near asphalt, for example) creates a boundary with the cooler air above. Some of the incoming light is reflected.

(Binary Solo) 0000001 00000011 000000111 0000111

It was only as I went to write a blog post for today (welcome to the present!) that I realized I hadn’t actually finished my studying according to my plan. Yes, for the first time I have failed to meet my study goals. But given that it is 9:30 PM already, and I am rather tired, I think it is prudent to not try to learn the latter half of the chapter on partial differentiation right now. After all, the goal is to study, not just to put a check in the box. It will just mean a rather busier day tomorrow, or perhaps having to push something into the weekend. Not the end of the world!

What I did get done today (besides an assortment of personal errands and such) was another couple lessons in my Python course. I’m up past 80% complete now! I have another session scheduled tomorrow, and I plan to finish everything except the final project then. Today I learned about bitwise operators, which meant the joy of trying to think in binary. Not impossible, but never as easy as good old base 10!

So today was a little light on the studying, but I’m still satisfied with what I accomplished and looking forward to crushing tomorrow!