Update (6/21/20): The learning curve for Maxwell's Equations is incredibly difficult.
| 6/21/20 | Electrostatics, Electric Fields, Gauss' Law I, Gauss' Law II | Gauss' Law for Electric Fields (C1), Gauss' Law for Magnetic Fields (C2) |
|---|---|---|
| 6/22/20 | Magnetism I, Magnetism II, Ampere's Law | Faraday's Law (C3) |
| 6/23/20 | Lenz's and Faraday's Law | The Ampere-Maxwell Law |
| 6/24/20 | Maxwell's Equations I | From Maxwell to Wave Equation |
| 6/25/20 | Maxwell's Equations II | From Maxwell to Wave Equation |
Update (6/22/20): Almost done with the first equation! I'm thinking of an Airflow-like simulation as an anlagoue for Maxwell's Machine. Very fine progress.
Update (6/23/20): I did it! Yes! I thought it was nearly impossible, because there's a whole host of Mathematical Prerequisites first and foremost that one must master and on top of that, Physical Intuition. But I tell you here that the end result is absolutely worth it. I now understand both the Integral and Differential forms of Gauss' Law for Electromagnetism. Later we're doing the 15 problems in the book and finishing Prof. Shankar's Lectures. At the end, I can hopefully create a visual demonstration akin to a Airflow Wind Tunnel.
Update (6/24/20): Not really much to report today. I did come up with some proposals for the Maxwell Machine to visualize Gauss' Law for Electric Fields. An actual Wind Tunnel is too much of a hassle, but a much more simplified and pragmatic model should do the job just as well.
Update (6/25/20): Yeah, 0. Did nothing
Update (6/26/20): Formalized my Mission, Timeline, and Prerequsities. I've also added a great problems section below. In terms of actual content, I'm really struggling to understand the derivation of Divergence in a Spherical Coordinate System, so I'm starting back from square one to try to understand it better (for me, that means going back to starting from Partial Derivatives, which I'm working through right now)
Update (6/27/20): OK, here's the plan:
- Derivatives of Multivariable Functions
- Partial Derivatives
- Multivariable Chain Rule
- Gradient
- Divergence
- Curl
- Laplacian
- Jacobian
- Integrating Multivariable Functions
- Line Integrals
- Surface Integrals
- Double Integrals
- Triple Integrals
- Flux
- Theorems
- Green's Theorem
- Stoke's Theorem
- Divergence Theorem
- Maxwell!
Update (6/28/20): Alright! Finished notes for Partial Derivatives! Onto Gradient! I'll probably post here every time I finish a unit. By the way, it's 5:40 AM, and I've got quite some time on my hands. Anyway, onewards and upwards!
Update #2 (6/28/20): OK, so apparently did *not* finish as much as I expected, but nonetheless, today is a very important day. Why? Well, simply put, it is the first official day of Special Relativity Lectures.
Update #3 (6/28/20): Just finished the first problem set for the first lecture on Partial Derivatives! Very excited! OK, right now I'm gonna try to conjure up a good visualization of the Partial Derivative.
Update (6/29/20): Here's the goal today: finish Unit 1 of the Maxwell Journey (Derivatives of Multivariable Functions) and come up with Key, Motivating Problems for each idea/concept. OK! Here goes! Oh, and I added the Motivating Problem for Partial Derivatives (Look under Great Problems)
Update #2 (6/29/20): Here's how the goal is progressing so far: I just finished taking notes on Directional Derivatives and Gradients. Coming up next ... Multivariable Chain Rule, More Partial Derivatives (!) on Vector-Valued Functions, this time, and then Divergence, Curl, and Laplacian. OK! Wow! Lot to cover. Not much time.
Update (6/30/20): I had lost all hope, but today has been a day of solid, solid progress. I spent 4 hours just on Khan Academy learning the prerequisites. I'll attach a few photos of proof after I finish the next few sections. OK. Good, good.
Update (7/1/20): Well, well, well. I did it. Unit 1 is done. Grad, Div, Curl, Lap(lacian), Jac(obian) -- they're all done! Not to mention Multivariable Chain Rule, Partial Derivatives, Directional Derivatives, and tidbits like that. It all adds up to just about 15 hours of watching Khan Academy, and more if you factor in the offline stuff. Anyway, I'm gonna attach my notes and everything now! Oh, and here's the progress meter:
Update (7/2/20): OK, so today I'm just solving problems from all the concepts I learned over the last couple of days, just to reinforce everything. OK! Here goes! I'll post any updates once I make significant progress
Update (7/8/20): So haven't done any SR in quite some time (6 days, to be precise), and now I'm back! Here's what's going to happen: I'll finish all the Problems in Div, Grad, Curl, Lap, and Jac quickly (i.e., before car). In car, I'll watch all the Khan Stuff. Lastly, at home, I'll work through a bunch of problems. OK, let's go.
Update (7/9/20): In an effort to understand Maxwell's Equations, I have spent the last 5 hours harvest two rare-earth neodynium magnets from obselete and abandoned Apple Earbuds. It cost me my sanity, I'm afraid. There are iron fillings all over my nails and the majority of my time was wasted extracting the magnet from its metal heatsink. I can only hope it was worth it. Some experiments I'm hoping to try: (1) NM through a copper tube vs aluminum ball (2) Spinning Homopolar Magnet -- I'll need some copper wire for that one (3) Spinning Nail (I tried this so many times! I burned my index finger on the last try)
Update (7/10/20): Not much updates
Update (7/11/20): Updated all the files and added all my explanations and solutions
Update (7/12/20): Learned about line integrals! (Note to self: Red Iron Curtain between East and West Berlin = Path Integral)
Update (7/13/20): OK, so now I will make a concentrated effort to do Line integrals in vector fields, double, triple, and surface integrals.
Update #2 (7/13/20): OK, so I just learned a couple of things about double integrals. There's really four ways to think about them: you can slice in the x and find the area of that 2D function and then sum up along the y and then vice-versa (just switching the x's and y's). The second major approach is through squares (i.e., dx*dy) and then sum up those infinitesimally small columns either along the x (method 1) or the y (method 2). OK! Upwards and onwards!
Update (7/14/20): Here's the plan for today: I'm gonna give lectures on every single topic *except* Surface Integrals. And then outside, I'll learn about the Multivariable Calculus Topics. OK! Here goes! For every idea or concept, what I'll do is come up with a motivating problem, a convincing and useful physical analogue and finally a solution. (Yeah, it's not as easy as it sounds). Also! I've been thinking about a Newton's Cradle, but for Electromagnetism. Can you believe it? Newton's Cradle is a physical analogue for the 3 Laws of Motion (essentially motivated by Gravity); Now take 5 magnets, all of identical size and set them all repelling! It might be like a Newton's Cradle, but with no contact! Can you believe it? There's GPE and EM involved! The only problem is finding 5 magnets of identical size ... I mean sure, I could order 150 Neodynium Magnets for about 10 Bucks, but that's not really fun, is it? On the other hand, I already have 2 Neodynium magnets (one of whose bases I completely seperated) -- so just 2 more obselete headphones, and I'd be good to go. Although I don't know if they'd be of sufficient size. Mix in some LEDs, compasses, and that's what I call a science experiment!
Update (7/15/20): Needless to say, none of that actually happened. OK. So I just got to finish Surface Integrals. And then I'm done. Callin' it quits!
Update #2 (7/15/20): OK. So I didn't get through ANY of the Surface Integral videos. According to some back-of-the envelope calculations, it's gonna take about 3 hours for the whole thing, which is -- needless to say -- a huge investment. OK. Here comes the first hour. In this first hour, I will watch the first four videos. And then I'll summarize what I learned to my little brother. I will try to use the simplest language possible. OK! Here it goes! Let's go! 'Alright, good luck.' ~ Soborno Isaac Bari
Update (7/16/20): Yep, nothing today ... bummers. BUT I DID LEARN TENSORS! WOW! And they're connected to GENERAL RELATIVITY! THEY'RE the bridge between SR & GR.
Update (7/17/20): OK. I will make it my mission TODAY to complete ALL of surface integrals. No more postponment. NO more fooling around. We are finishing Surface Integrals. TODAY! It will obviously take more than 3 hours because I have to A) watch the videos and then B) actually comprehend them. But, IT SHALL BE DONE! Here we go!
Update (7/18/20): Yeah, no, nothing happened.
Update (7/19/20): OK! OK! OK! WOW! I just learned SURFACE INTEGRALS. You heard that right -- Surface Integrals, arguably the hardest idea in Multivariable Calculus, and really the coolest idea I've learned thus far. This has so many applications that my mind is just blowing up right now. Jacobian Matrices, Black Holes, Linear Transformatoins, *Curvilinear* Transformations, if those even exist! So far, I've done two problems on parametrizing and then finding the surface integral: A Donut and a Ball! Also! I learned tensors! In fact, I'm writing a paper on it right now (or close to right now ... in a few hours, perhaps -- it's already 10 AM!)
Update (7/20/20): Alright! Today's the big day that I learn the Green's, Stoke's, and Divergence theorems. Here goes!
Update (7/21/20): OK, so I learned Green's Theorem yesterday and it was absolutely amazing! (Note to self: Use the idea of *Mass* and *Work* to connect Line Integrals to Green's Theorem; Also, the Fundamental Theorem of Calculus is hidden in G.T.) OK, so here's what's gonna happen: I'll do 2D Divergence theorem lecture in a few minutes; then in the evening, I'll do Stoke's (stoked for that one), and finally in the wee midnight hours, I'm doing 3D Divergence theorem. Alright! Let's get on it!
Update #2 (7/21/20): I think I might just be going crazy. So much. But! Greens & 2D Div Theorem are very interconnected (think slicing & dicing a pizza) and I finally learned the difference between flux and divergence (which was one of my top ten questions). It's essentially a matter of a globalized operation over an entire region vs a localized operation on a point. The bridge between these two ideas -- the big and the small -- is the 2D divergence theorem. Same thing with Green's Theorem (so many different notations!) -- it connects the big (curl over entire region) to small (circulation over infinitesimally small region). I also learned a big lesson: don't, I repeat *don't* mix up dr and dN. dr is a small differential in the position vector along the path of the particle's motion, whereas dN is the normal vector. Also! Another *big* misconception I held was the difference between dt and dr/dt; one is an infinitesimally small scalar (just a small number!), and the other is an actual function -- an actual derivative. This seemingly small difference can cause huge confusions over notation and whatnot. OK, so right now it's 2 AM in the morning on 7/22/20, which is why I'm technically assigning this under 7/21/20. My plan is to just understand Stoke's theorem, and then be done with the lecture! Wow. Lots to do, lots to do.
Update #3 (7/21/20): I'm really sleepy;
Update (7/22/20): I regret to say I got nothing really done today (*CORRECTION*: I got a lot done!, but still no lecture ... ), but I learned a lot about Stoke's Theorem. I just couldn't do a lecture because I'm too tired (I'm actually writing this at 4:02 AM); I have a lot of gaps and holes in my understanding and I hope to take tommorow to fill in those gaps and flaws. Anyway, Stoke's is just Green in 3D (i.e., if the region in xy plane could actually float in R^3); I still need to review Line Integrals, Surface Integrals, Double Integrals, etc. just so that I don't have any shaky business in my foundation. So here's my plan for tommorow: After LA, A, and H and ACC, it'll probably be ~ 4 PM. 4PM-8PM, I'll review everything, and then finally give the lectures! Aw jeez
Update (7/23/20): Yep uploaded a 34 minute lecture on solving Line Integrals over a Scalar Field. But, -- here it comes -- I'm learning VfX! For Maxwell, of course -- using Blender.
Update (7/24/20): OK, here's the plan: From 4-5 PM, a lecture on Line Integrals over a Vector Field. Then, Stoke's Theorem, and then finally a 2 hour lecture on it, so from 7-9PM, about.
Update #2 (7/24/20): As you can tell, I've been brushing up the website. For future reference, here are the Notes for Parametrizations and Parametrizations of Vector Fields; I decided to delete the row for them because they have no problems/solutions and I'm too deep into the complex math to go back to that.
Update (7/25/20): Just blown over today. Had literally no time.
Update (7/26/20): OK! OK! This is the formal announcement that I am embarking on Maxwell's First Equation: Gauss' Law of Electric Fields! Hope to have a few experiments ready by the end of today. Anyway, I finishing Dan FLeisch first chapter of A Student’s Guide to Maxwell’s Equations in the car. OK!
Update (7/27/20): Nothing, really
Update (7/28/20): Yeah, nope
Update (7/29/20): Working on Tensors ...very hard
Update (7/30/20): Tensors again!
Update (7/31/20): Almost there ...
Update (8/1/20): Just made 9 videos on Special Relativity, or more specifically on Gauss' Law of Electric Fields.
Update (8/2/20): Nope, blank day
Update (8/3/20): OK! Finished Maxwell's third law! Wow! Rapid fire!
Update (8/4/20): Nope, nothing ...
Update (8/5/20): Not much ...
Update (8/6/20): I spent so long trying to understand the derivation of the del operator and divergence in spherical and cylindrical coordinates. I finally get it, but I have to do it a few times
Update (8/7/20): Wow! OK! I just got Maxwell's 4th equation, the Maxwell Ampere's Law. I understand it pretty well. If only there were some experiments to visualize it ...
Update (8/8/20): OK, here's what I'm aiming for today:
- Derive the Wave Equation!
- Derive Lorentz Transformations
- Prepare ~10 experiments to visualize and understand each of Maxwell's 4 Equations
- Brainstorm and Formalize 30 possible theses
- Develop criteria to narrow down best possible theses
- Narrow down to 10 best research theses on the basis of aforementioned criteria
Update (8/9/20): Boom! Of the 6 items above, I finished 5 of them! Go productivity!
Update (8/10/20): Alright! Today marks the commencement of my research! What a day! What a privilege!
Update (8/11/20): Yeah, nope
Update (8/12/20): I formulated two abstracts, a mission plan, and everything I need to jumpstart my research. Let's go!
Update (8/13/20): I finally constructed a homopolar motor. It took 2 months, wafting through hundreds of papers, but I finally did it! I'm gonna do a 60-second Science video on it.
Update (8/14/20): Turned out it wasn't 60 seconds at all. In fact, it was almost 8 minutes -- and it took a lot longer to prepare it. But in the process, I learned (or rather, reviewed?) a lot, lot, about Electrostatics and Magnetostatics.
Update (8/15/20): OK, so here's what's gonna happen. It's 2:40 AM Midnight here in New York on the 15th of August. So, I'm gonna review all the key ideeas of Vector Calculus, which I've taken the liberty of dividing into three stages: (1) Integrals, (2) Operations, and (3) Theorems -- Integrals of course being Line, Surface, Volume, Double, and Triple Integrals, all of which give me a *major* headache when it comes to Electrodynamics. Then of course, comes (2) Operations, including the famous ones Grad, Div, Curl, and Lap (I never used Jac yet ... hmm) and of course finally (3) Theorems includes all the famous ones like Stokes and Greens and Divegence theorems. OK! I'm not quite sure if there's a collective resource out there containing a succint review of all these ideas, but now is the time to start! This is, of course, all in preparation for my thesis on Maxwell & Einstein. OK! From hereon, I'll supply regular updates every time I learn something or get stuck. OK! YES! YES! Let's GO! (I do realize that incessant capitalization is a symptom of enthusiasm about Vector Calculus)
Update (8/16/20): Hm, not much?
Update (8/17/20): Uploaded three videos on the Line Integral. That idea is now cemented in my brain! Really, there's three ways to break down any major type of integral: (1) Geometric (2) Scalar Field -- Physical (3) Vector Field -- Physical
Update (8/18/20): Yep, I actually did nothing (Mt. Morris Point Vacation!) By the way, note to self: Make a video on Flux using Hairdryers? Curl on the Whirlpool? That might be a really good idea.
Update (8/19/20): Right here. Right now. I make a commitment: 6 pages of full Vector Calculus review in less than 2 hours. That means at exactly 4:00 PM today, *right now*, my vector calculus theory shall be complete! Let us commence!
Update (8/20/20): OK, so today is the day I actually made the *most* progress on the paper and it's running at 10 pages! By the way, this is the paper on *Vector Calculus*, not my actual research paper
Update (8/21/20): Gotta admit I got basically nothing done today
Update (8/22/20): No progress ... but, I did uplaod something like 7 videos tonight! (That's gotta be a record, right?)
Update (8/23/20): It's not going too well ... or well at all, actually. My research is at a stall.
Update (8/24/20): Freaking finally! I got it! I grasped Surface Integrals! These things are like the crux of Maxwell, and now that I know them like the bones of my hand, I can break down Stoke's and Divergence. This is just fantastic! Also, I updated the site just a bit with my new Mission, Prospectus, and Timeline. Wow, just realized how much easier it is to type with paddings on,... huh. Alright, so here's the plan! I'll solve problems for everything -- really one key takeaway I'll share right now when it comes to doing mathematics is *you cannot get away from doing problems*. Really, the only way to learn an idea is to solve problems, *not* to learn theory (at least for me). That being said, here's my plan:
Update (8/25/20): Uploaded a bunch of videos on Maxwell today (although some are not on Maxwell). Two are on Divergence, one is on Wave Interference and how light behaves much like a wave, and one is a problem sponsored by Brilliant.org. Also, I was drenched in the rain while recording the Divergence video, which turned out to be a great application of all the mathematical concepts I've learned over the past few months.
Update (8/26/20): What a great, chaotic day! I made three videos for our Sponsor, Brilliant.org, which was absolutely fantastic (also got to try out the new mic, which turned out to be no less than a hassle -- would be better if it was wireless, but no). Anyway, all three of my problems were on Area.
Update (8/27/20): Not very productive today in all honesty. But! I did make the great sponsorship message for Brilliant.org, which was good.
Update (8/28/20): Made two videos -- one for Brilliant and one for Regents Physics. Regents Physics was SI Units, which was on Mass, and Brilliant was on the permutations of non-degenerate triangles from an array of dots. Interesting. The answer was 720, if you're wondering.
Update (8/29/20): No progress on my research, although I occasionally read a few papers here and there. I think this meets the record for most number of videos published to the channel in a day (9!) -- although I myself uploaded only two, both of them Sponsored videos on Geometry for Brilliant.org;
Update (8/30/20): Nothing really done today. I did find out Monopoles *may* exist near Black Holes.
Update (8/31/20): OK, so I've been brainstorming the different components of my research paper. Thus far, I've got 3: Section I: Maxwell’s Equations, Section II: The Bridge, and Section III: Einstein. Each of the 3 sections aims to answer some pivotal questions, including: (1) How can one visualize Gaussian Surfaces?, Why is Magnetic Flux always zero?, What makes Amperian Loops analogous to Gaussian Surfaces?, Why does Special Relativity suggest there be a displacement current in Ampere’s law?, Does Maxwell's displacement current produce a magnetic field?, Why does Faraday's Law have a negative sign?, (2) How do we convert from the Integral form of Maxwell's Equations to their Differential form?, How can the Wave Equation be derived from the differential forms of Maxwell's Equations?, How can the Lorentz Transformations be derived from Maxwell's Equations?, How can we use the Electromagnetic Tensor to describe EM waves in Space-Time?, and finally (3) Can the effects of Relativity be derived from a simple electromagnetics scenario? Can we use special relativity to generalize coulomb's law to apply to a charge a) moving at a constant velocity and b) accelerating?
Update (9/1/20): OK! So! Today is the first official day of reserach. I've read an extensive amount of literature. All that's left to do today is -- well, a few things, as a matter of fact. First and foremost, my goal is to do a few practice problems just to refresh my mind on Stokes and Divergence Theorem. I'm fine with Green, because that's only on the plane and much easier. After that, I'm going to start brainstorming the actual questions my paper will tackle. -- I've also developed the Galilean Transformation program in Python (in Google Collab); it took a few hours, but thankfully, I had the PlotLy library to work with (matplotlib is a pain). I also tried programming an actual 3D wave, but that's way out of my scope -- you need FDTD (finite differential time definite equations) for that.
Update #2 (9/1/20): I began the day excited, but it's been very dissapointing. I've been brainstorming, writing, rewriting, and pondering my research questions for hours, *HOURS*, by now and still I haven't got anything good. OK. Well, hopefully tommorow I'll get some new ideas.
Update (9/2/20): Wow! Talk about starting the day strong! I've already got some ideas going. My paper will probably be divided into four parts, all of which are concerned with the bridge between Maxwell's Equations and Special Relativity. I'll update if anything new happens.
Update (9/3/20): OK, so I'm just pondering and twiddling with the ideas a little bit; I think I'm developing a good paper so far; I've been revisiting my Google Slides on Maxwell's Equations recently for inspiration and ideas. Google Scholar is also pretty helpful, so props to them. I also tried to create the program for the moving sheet of charge, but that didn't work out to well.
Update (9/4/20): OK! OK! I got it! Not only do I have a relatively well-established research idea composed of the best questions from my prospectus, but I'm making some fine progress.
Update (9/5/20): I again tried to construct the moving infinite sheet of Charge in Python, but failed to do so. I'm trying to think of plausible alternatives, but there seems to be few, if any.
Update (9/6/20): It took me 10 tries! 10 tries! But I finally got it! I generated the constant electric field for an infinite sheet of charge! In Glowscript, no less! (optimized for Javascript and Coffeescript; Under VPython). OK, OK, this is good. I'm still getting the hang of it, but this is great.
Update (9/7/20): Spent the whole day trying to animate the actual movement of the electric field and the sheet of charge. The documentation for Glowscript is so poor! Not even sure if this is possible ... Nevertheless, I've done a couple of things -- animated the construction of the electric field and set the color of the vectors based on their magnitude. I've also put the test charge q and generated its electric field which turns out to be omega/2*epsilon_naught. But I didn't just plug that in (which by the way, can be derived from Gauss' Law); the program actually constructs *all* the electric field vectors and sums them up! Not bad, I say. Not bad ...
Update (9/8/20): Didn't get to do much research, but nonetheless a busy day -- I made 2 videos on a combinations and permutations problem for our great sponsor Brilliant
Update (9/9/20): OK -- so here's the thing. I've got the equation for the velocity boost, length contraction, etc. that's all good and fine. But the problem is when it comes to actually visualizing the particle -- the test charge -- and its movement, I see literally no change. After much frustration, I finally realized it takes a magnitude of 10e11 for their to even be a noticeable shift in the horizontal movement. What a value ... for the velocity! That breaks the speed of light! It's superluminal! Anyway, I found out some kinks and scale factors in my code, removed them, and no I'm finally subluminal (i.e., just under c, so I guess that's still relativistic speeds). Well, that's good.
Update (9/10/20): OK, so did a few things today. #1 -- I tested the camera movement and whether I could change the camera's view on click, so that a user can experience the movement of the test charge as both a stationary and moving observer. So far not much success. #2 -- I tried creating the XYZ axes (rudimentary, but *extremely* helpful, especially for me, so that I can figure out the direction of my vectors and do my right hand rules, etc.) multiple ways. That's basically it. It doesn't sound like a lot, but it took quite some time.
Update (9/11/20): Wow. That's it. I got the moving magnetic field and charges. That's it. That is it. It took the whole day, but I got it. Wow. Wow, wow, wow.
Update (9/12/20): Not much research, but much videos -- which is still good. Sometimes I get a new idea after making videos -- today I made two videos, both for our great sponsor Brilliant.org
Update (9/13/20): I made the Biot-Savart Law program in one day! More or less ~150 lines, but the interactivity is what makes it great. I think it's the best program I've made in my life to date by far, although it probably shares that privilege with my aforementioned code of the moving magnetic field and the charge.
Update (9/14/20): It's done! It's done! The paper is done! Now all that's left to do is just go ahead and reread, revise, and chop it down. Right now, it stands at 25 pages, although my goal is to get it down at *least* to 20. Ideally, 10 would be great, but that would sacrifice too much of the substance of my paper, I'm sure. But of course, I'm not cutting anything down without revising and rereading many, many times. Today, I'm going to read my paper not once, not twice, but thrice. I'm going to make sure everything is cohesive, relevant, and contributes something *new* to the field. I'm still not sure how I'm going to space out my readings of the paper. I'll probably figure it out. Near the end, I'll print out copies of the paper just to highlight, edit, and revise. Hm, ok. Right now, it's 10:40 AM in the morning in New York. I've been up since 6 working on the paper, and finally it's done for good (although I obviously have to revise/edit it). Now I'm just thinking how I'm gonna go about actually reading my paper.
Update (9/15/20): I will read and profreed my thesis twice today. I'm keep track here:
- Read #1 of 2, 10:10 AM: Just started reading my thesis. A few things -- (1) I should always keep the main point fresh for the reader (2) Don't go too far advocating for computational programming, or that will distract from the main star of the show, which is Maxwell's Equations. Now for a few more particular comments -- (1) Add an intro, i.e., a brief overview of the main steps prior to each section, including both the computational programming and mathematical derivations section(2) Add a conclusion! (3) Possibly expand Literature Review, (4) Add references (remember E.M. Purcell, J.D. Jackson, and Griffiths and Healds; possibly also D.A. Fleisch and J.A. Callahan). It's 12:10; I finally finished reading, editing, and revising my thesis. I've added a lot of things, edited the code for brevity and clarity and added auto-wrapping to the minted code, which I didn't know existed (which is why I had to manually add in code wrappings previously). I also modified the whole tone of the paper, and everything's been revised from top to bottom. The paper looks great. Just one more reading to go. Just finished putting lot of things in the paper. It's 2:27 AM
- Read #2 of 2, 2:30 AM: This time, I'm looking more for typos, small changes, etc. OK! Just finished reading the paper again. What an exhausting day. It's now 4:43 AM. Seems like it consistently takes me two hours to read it every time. Nonetheless, here's a few improvements I've made: (1) Fixed lot of typos, (2) Lots of little code snippets cut off here and there fixed, (3) Other minor changes. That's essentially the gist of all I changed. Everything looks pretty good to go. Looks ready for production. Anyway, I'll most likely do my final read at night. Oh! One more thing, which is I have to fix the order of the citations. I'll fix that immediately. Nevermind, that's really minor. Not really in my best interest to fix that anyway (due to my limited time).
