8 / 1 / 2018 //

So I keep seeing posts on studyblr about how to take notes, some of them “official” methods like the Cornwell method or whatever it’s called, others more based on personal experience/ideas, but basically all of those don’t work well with math and physics.

So I made examples of how I take notes in physics and math, which based on what I’ve seen from professors and other students is pretty standard. (Blue text is commentary on the notes)

In math always start by defining the variables, because you will forget and you need to know all the assumptions you’ve made (like “did I define the function f as continuous, differentiable, bijective or just continuous and bijective?”). Drawings are good since they help visualise the abstract stuff (and look pretty), but not necessary. Always write down definitions, theorems, and lemmas, and ESPECIALLY their proofs. Exercises (both proof exercises and application exercises should be written down too, with varying detail based on how easy it is for you.

In math, and a bit less so in physics, you should always try to use mathematical symbols to shorten text. For the theorem I wrote what I would actually write in white, and below in blue I wrote the full, no symbol version of that. It’s pretty obvious which will be written down faster in class.

And never forget to write that sweet little quod erat demonstratum square at the end of a proof.

In physics the only thing you ALWAYS have to write down is a work through of an exercise or proof (this, of course, includes defining the variables, unless you’re the same variables as last time and can refer back to those). Since physics is about THE REAL WORLD you should strive to draw diagrams constantly, since sometimes you won’t be able to find a solution until you draw the diagram and examine the system (some proofs, especially those in optics, rely heavily on diagrams to explain what the fuck is even going on).

Unlike in math, in physics everything has a unit, which you should ALWAYS mark SOMEWHERE, because you might figure an exercise out solely based on your knowledge of units.

Here it is folks:

My definitive ranking of my least favorite bodies of water! These are ranked from least to most scary (1/10 is okay, 10/10 gives me nightmares). I’m sorry this post is long, I have a lot of thoughts and feelings about this.

The Great Blue Hole, Belize

I’ve been here! I have snorkeled over this thing! It is terrifying! The water around the hole is so shallow you can’t even swim over the coral without bumping it, and then there’s a little slope down, and then it just fucking drops off into the abyss! When you’re over the hole the water temperature drops like 10 degrees and it’s midnight blue even when you’re right by the surface. Anyway. The Great Blue Hole is a massive underwater cave, and its roughly 410 feet deep. Overall, it’s a relatively safe area to swim. It’s a popular tourist attraction and recreational divers can even go down and explore some of the caves. People do die at the Blue Hole, but it is generally from a lack of diving experience rather than anything sinister going on down in the depths. My rating for this one is 1/10 because I’ve been here and although it’s kinda freaky it’s really not that bad.

Lake Baikal, Russia

When I want to give myself a scare I look at the depth diagram of this lake. It’s so deep because it’s not a regular lake, it’s a Rift Valley, A massive crack in the earth’s crust where the continental plates are pulling apart. It’s over 5,000 feet deep and contains one-fifth of all freshwater on Earth. Luckily, its not any more deadly than a normal lake. It just happens to be very, very, freakishly deep. My rating for this lake is a 2/10 because I really hate looking at the depth charts but just looking at the lake itself isn’t that scary.

Jacob’s Well, Texas

This “well” is actually the opening to an underwater cave system. It’s roughly 120 feet deep, surrounded by very shallow water. This area is safe to swim in, but diving into the well can be deadly. The cave system below has false exits and narrow passages, resulting in multiple divers getting trapped and dying. My rating is a 3/10, because although I hate seeing that drop into the abyss it’s a pretty safe place to swim as long as you don’t go down into the cave (which I sure as shit won’t).

The Devil’s Kettle, Minnesota

This is an area in the Brule River where half the river just disappears. It literally falls into a hole and is never seen again. Scientists have dropped in dye, ping pong balls, and other things to try and figure out where it goes, and the things they drop in never resurface. Rating is 4/10 because Sometimes I worry I’m going to fall into it.

Flathead Lake, Montana

Everyone has probably seen this picture accompanied by a description about how this lake is actually hundreds of feet deep but just looks shallow because the water is so clear. If that were the case, this would definitely rank higher, but that claim is mostly bull. Look at the shadow of the raft. If it were hundreds of feet deep, the shadow would look like a tiny speck. Flathead lake does get very deep, but the spot the picture was taken in is fairly shallow. You can’t see the bottom in the deep parts. However, having freakishly clear water means you can see exactly where the sandy bottom drops off into blackness, so this still ranks a 5/10.

The Lower Congo River, multiple countries

Most of the Congo is a pretty normal, if large, River. In the lower section of it, however, lurks a disturbing surprise: massive underwater canyons that plunge down to 720 feet. The fish that live down there resemble cave fish, having no color, no eyes, and special sensory organs to find their way in the dark. These canyons are so sheer that they create massive rapids, wild currents and vortexes that can very easily kill you if you fall in. A solid 6/10, would not go there.

Little Crater Lake, Oregon

On first glance this lake doesn’t look too scary. It ranks this high because I really don’t like the sheer drop off and how clear it is (because it shows you exactly how deep it goes). This lake is about 100 feet across and 45 feet deep, and I strongly feel that this is too deep for such a small lake. Also, the water is freezing, and if you fall into the lake your muscles will seize up and you’ll sink and drown. I don’t like that either. 7/10.

Grand Turk 7,000 ft drop off

No. 8/10. I hate it.

Gulf of Corryvreckan, Scotland

Due to a quirk in the sea floor, there is a permanent whirlpool here. This isn’t one of those things that looks scary but actually won’t hurt you, either. It absolutely will suck you down if you get too close. Scientists threw a mannequin with a depth gauge into it and when it was recovered the gauge showed it went down to over 600 feet. If you fall into this whirlpool you will die. 9/10 because this seems like something that should only be in movies.

The Bolton Strid, England

This looks like an adorable little creek in the English countryside but it’s not. Its really not. Statistically speaking, this is the most deadly body of water in the world. It has a 100% mortality rate. There is no recorded case of anyone falling into this river and coming out alive. This is because, a little ways upstream, this isn’t a cute little creek. It’s the River Wharfe, a river approximately 30 feet wide. This river is forced through a tiny crack in the earth, essentially turning it on its side. Now, instead of being 30 feet wide and 6 feet deep, it’s 6 feet wide and 30 feet deep (estimated, because no one actually knows how deep the Strid is). The currents are deadly fast. The banks are extremely undercut and the river has created caves, tunnels and holes for things (like bodies) to get trapped in. The innocent appearance of the Strid makes this place a death trap, because people assume it’s only knee-deep and step in to never be seen again. I hate this river. I have nightmares about it. I will never go to England just because I don’t want to be in the same country as this people-swallowing stream. 10/10, I live in constant fear of this place.

Honorable mention: The Quarry, Pennsylvania

I don’t know if that’s it’s actual name. This lake gets an honorable mention not because it’s particularly deep or dangerous, but it’s where I almost drowned during a scuba diving accident.

Edit: I’ve looked up the name of the quarry, it’s called Crusty’s Quarry and is privately owned and only used for training purposes, not recreational diving.

Achievements of 2021 (both academic and non-academic)

I'm still very much on break (basically just eating, sleeping, reading and swimming, it's delightful), but I want to sum up this year. It's been a fucking rollercoaster of a year and I still can't believe like half of the things that happened, both good and bad. Nevertheless, I want to focus on the positive ones to kickstart the new year in the most uplifting manner I'm able to pull off. Which is not very optimistic nor uplifting, but I can be at least not full of doom, haha.

I want to do this chronologically, just because I tend to forget the good stuff that happened more than two months ago.

Let's wrap this up!

Academic Achievements of 2021

presented at my first international conference (February)

prepped two PhD dissertation projects (April) and successfully defended them during the PhD programs interview (June)

wrote my diploma thesis while cooperating with the best mentor ever (January till June)

got accepted to two PhD programs and currently doing both of them! (June)

co-written three papers over the summer - two already published, one under a promising peer review (June-September)

defended my thesis and passed my state exams with straight As, meaning I got my master's degree! (September)

wrote a book chapter that got accepted (November)

Non-Academic Achievements of 2021

quit the job I hated (January)

got rid off so much stuff I didn't need (mostly July, August)

read 130 books, yaaay

stopped saying yes to meetings with acquaintances just because I felt like I should see them (big one!)

found a functioning skincare routine (September)

started swimming again (and loving it) (September)

A lot of this year has been mostly about surviving, to be honest. I was battling a lot of anxiety and depression, I was extremely stressed at times and couldn't sleep. Swimming and taking proper days off helps, close friends help. I'm gonna do a post with some goals for 2022, so I won't spoil here that, haha.

It was a good year after all.

Take care!

M.

Astronomers are the funniest people on earth actually

very specific types of physicists

emeritus: a well-meaning retired professor who still frequents the department. occasionally seen jogging up and down the halls of the lab. it’s how he gets his daily exercise. his field of research is obsolete and he spends most of his days making art based on physics equations. asks all of the female undergrads if they plan to teach high school physics.

star child: no one will measure up to this alumnus. they started research in high school, graduated from undergrad a year early with a few papers already under their belt, and finished their phd (at a very prestigious university) in two years. they visit occasionally to present their research and talk to the undergrad physics students. very down to earth and kind. undergrads, grad students, and professors alike are in awe.

father figure: this prof’s lectures are full of dad jokes, metaphors comparing the behaviors of particles with sugared-up three-year-olds, and digressions about something that’s more fun to talk about than the subject matter. says “i’m not angry, just disappointed” when the class does poorly on an exam. when you go to his office hours there is almost always a child or two underneath his desk or drawing on his whiteboard (the bottom third of which is always covered in stick figures and scribbles). intensely watched the construction from his office window as a new laboratory was being built.

academic rival: you were friends over the summer when you were both doing research but they became distant. small talk always turns into bickering about the importance of your respective research when you run into each other getting coffee in the common room. begrudgingly you admit to yourself, they’re really good at what they do. thank god you don’t belong to the same research group.

harsh but kind: brilliant researcher with high expectations of their students. will offer and make you tea as they grade your problem sets (with commentary) in front of you. after your semester in their class, you buy a bag of loose-leaf jasmine green tea because they got you hooked on it.

the politician: buddies with some higher-ups in university admin and the heads of other colleges. your peers derail class by bringing up current events. has a fixation on swords and genealogy. a bit of an anglophile. you took apart a transistor radio with them once. will make formal complaints to the math department on your behalf.

melancholy teaching professor: very cynical from a career in academia but here to have fun. one of the friendliest faces in the department. organizes the students and faculty to do outreach and lugs physics demos all around the tri-county area. talks to the undergrads like they are people. always kind of sad, it makes you wish you could fix all of the ills of academia for them.

math help bc i can’t watch ya’ll suffer anymore

I’m in my fourth year of engineering school and I didn’t get here without lots of outside help bc assigned math textbooks are lame and confusing and professors/teachers are more worried about feeling superior to bunch of groggy teenagers than actually teaching.

I have personally used all of these websites without receiving any security warnings from Bitdefender TrafficLight or AdGuard AdBlocker. They are all either completely free or have a free version that isn’t shit.

Wolfram Demonstrations (animated graphics)

Khan Academy (arithmetic through differential equations)

She Loves Math (arithmetic through differential equations)

math24 (calculus & differential equations)

Paul’s Online Math Notes (algebra through differential equations)

MIT OpenCourseWare (calculus through graduate-level mathmatics)

OpenStax Math (precalculus, trigonometry, & calculus)

Wolfram Alpha Examples

Desmos (online calculators)

GeoGebra (online calculators)

SparkNotes Math Study Guides (pre-algebra through calculus)

eMathHelp (calculators, but more specific)

Software for your TI calculator

ticalc (programs for your TI calculator)

Wikibooks Math Department (all the math)

Andy’s Cheat Sheets (calculus)

Cheatography (find free cheat sheets)

Open Access Math Textbooks

Engineer4Free (Calc, DiffyQ, & Linear Algebra tutorials)

Flammable Maths on YouTube (general high school/college level problems and derivations)

3Blue1Brown on Youtube (very, very good for understanding spacial concepts in calculus and beyond)

Vihart on Youtube (explaining math with doodles)

Bonus: Stay hydrated, take vitamin c, study next to a window during the day if possible, and remember not to let people base your worth on your aptitude for math. 

Comet ISON approaching the Sun observed by the spacecraft STEREO. 20 to Nov. 25, 2013.

Credit: NASA

Day 13/100 of productivity · 1/30/21

Some late night notes for today! My boyfriend fell asleep really early and I had nothing better to do, so I decided it was time to study a little bit more. I feel like my motivation has been really high again lately & I am thankful for that, it would be really difficult to be this busy if I wasn't motivated.

problem solving tips that actually worked for me

Hey there!

If you have a math, or science related subject (like I always do), you’ll find that you really can’t escape analysis and problem solving, especially if you’re majoring in something science or maths related. So I am here to share some tips that actually made studying technical subjects a little bit easier and manageable for me in college:

Practice solving. If you have a subject that requires you to solve, you really have to practice solving, there is no easy way out of this one. This allows you to develop your own technique in solving the problem. You can start by doing the problems you did in class, then venture out to some examples in textbooks, then further into the problems in the textbooks until you get the hang of how the concepts and theories are applied. 

Listen during class. I know, it’s boring. But you have to do this. This way, you’ll be able to understand the topic once it is presented to you. In my opinion, it’s better if you let an expert explain it because they know the important bits in the lesson. Then study it afterwards on your own to develop your own techniques.

Ask your professors. Don’t be afraid to ask questions in class. Or if you’re shy, you can ask them after the class. However, it’s important that you ask them about the lesson when you already did your part; meaning: you already studied the material/solution over and over again but there’s just something that you can’t seem to grasp. 

Study before the class. Studying the lesson in advance doesn’t hurt. Plus, it works because you already have an idea about it. However, I don’t do it usually. What I do is that prior the discussion, I study the lessons that are going to be essential to the next topic. Example: Say that our topic later will be about introduction to thermodynamics (which includes derivation of various thermodynamic formulas); what I’m going to study instead is the different integration and derivation techniques, and different basic thermodynamics concepts like laws of thermodynamics. This ensures me that I know the prerequisite lessons of the next topic in class.

Absorb the conceptual parts of the topic first. Before diving into the problems itself, try to digest the concepts or theories behind it first. This way, you can understand which information is important and easily think of a solution because you know the problem’s framework. Even when your professor gives you a problem that seems different from your other sample problems, the concepts will still be the same throughout.

Reverse engineer the solution. Reverse engineering is reading and understanding your solution from bottom to top. I do this to make connections while going through the solution. I usually ask myself “‘where did this come from?’, ‘why did this happen?’, or ‘why is the answer like this?’” It allows me to look into the parts that I missed which are usually concepts or theories that I forgot to apply in solving the problem.

Look for key terms or phrases. There are some problems that put in information that may seem unimportant, but actually is really important. Examples such as the phrases constant velocity, constant acceleration, starting from rest, accelerate uniformly, reversible isothermal, adiabatic conditions, isobaric/isochoric compression/expansion, etc., are easy to miss but actually gives you vital information especially when solving a problem.

Try to ask yourself how or why it happened in every step of the solution. You can do this to gauge your mastery of the lesson. If you can answer yourself confidently, then you’ve studied well enough. But, if you can’t or if you feel that it’s not enough, then you better get your pen, paper, and calculator to practice some more.

If you have to draw it, draw it. Some problems need the use of your imagination, and these problems are the ones that get tricky most of the time. It’s easier to draw each of the time frames that are important so you get the sense of what’s going on between these pictures. This way, you’ll know which information you’re missing and which ones are you failing to take into account.

It’s okay to be messy and slow while practicing. Not all of time you can solve in a tumblr-esque manner because, dude, tumblr notes or solutions are soooo pretty to look at, BUT, what’s more important is that you understand each step of the solution and how the answer came to be 8.0658 m/s directed 32° south of west. So it’s okay to have dashes, strikethroughs, and crosses on your scratch paper, as long as you’re learning, a messy solution on a paper you’re not going to submit to your professor is fine.

IF YOU’VE REALLY GOTTEN THE HANG OF SOLVING IT, try to solve a fresh set of problems as fast and accurately as you can. Try to solve as if you’re in an exam. This is also to gauge how well you’re prepared for it, but you need to do this accurately. I repeat, accurately. It doesn’t work if you’ve finished it in less than an hour but all of your answers are wrong.

Rest. If you know that you’ve done a good job, then take your mind off of everything first and let it wander to wherever it wants to wander. You deserve it ✨

Bless the person who made this. I love it.