# SAT prep:

- Khan academy: You can connect this to your college board account. If you do this, it can see what you got wrong on your PSAT or past SATs and you can practice only what you need to with practices specifically designed for what you got wrong.

# Calculus:

- 3blue1Brown essence of calculus: What are derivatives and integrals and where are they from? Gives you a “feel” for calculus which is EXTREMELY valuable. With stuff like this, getting the right picture in your head makes everything else easy.
- Khan academy’s calculus playlist: Some of the videos are old and low quality, which is annoying.
- Khan Academy/3blue1brown multivariable playlist: By 3blue1brown but on khanacademy for some reason. Really good and in depth
- Khan Academy differential equations: This is a good place to get started on DEs, but if you really want to learn them do the next bullet when you finish this playlist:
- MIT OpenCourseWare Differential equations: Differential equations are basically the most important things in physics, calculus-wise. Once you have a good handle on these, that’s pretty much the extent of any physics math you’ll need for college. It’s important in all sciences including economics as well. Highly recommended. Ordinary differential equations can be done right after single variable
- MathTheBeautiful Tensors: Probably some of the coolest stuff in calculus, maybe tied with differential equations. This can be done right after after multivariable, it doesn’t necessarily have to come after differential equations. Definitely wait a while after learning multivariable so you let it sit and become a part of you. Also, have a good understanding of vectors. Tensors are pretty high up and advanced, so you have to be very comfortable with multivariable and vector calculus. If you watch the 3blue1brown/khan academy multivariable and get it, you should be fine. Tensors are necessary for general relativity, advanced theoretical physics, and coordinate independent analysis
- http://tutorial.math.lamar.edu/ is good for finding practice problems and filling in some of the gaps left by other videos. Basically google something like “double integral” and find something from this site. It might say something about Paul’s online math notes. That’s just the name of the professor who posts notes on this university’s website I guess. After you finish a video, do some problems from here sometimes. I usually look them up before a boring class and do them during it. There are some things the playlists don’t cover that are on this site so go through it and learn what you don’t know after you finish a playlist.

# Here’s what I find helps me:

- Try problems on your own before the video does them. Don’t expect yourself to actually solve it, but just think for a while when you run into a road block like not knowing how to deal with a certain kind of derivative. Interacting with the material independently and thinking of things in your own way to understand them better is really important. If you try to discover something for yourself before being taught it, you retain it better and appreciate it more. Do practice problems. A good place to find them is Paul’s online math notes. Basically google something like “double integral” and find something from this site: http://tutorial.math.lamar.edu/ Weirdly, some important topics are missed in the playlists so just go through all of the topics on this website and learn what you don’t know. Go to wikipedia to find things to learn, DON’T TRY TO LEARN HOW TO DO SOMETHING FROM WIKIPEDIA. For example, look at the article for a vector: https://en.wikipedia.org/wiki/Euclidean_vector There’s so much extra, confusing, overwhelming information and formal definition. It’s good to look over once you know it, but not before or while you are still learning it. You won’t know what’s important and what’s weird formal stuff.
- Look at animations and pictures. These are extremely important. Some very difficult concepts like curved space are just about getting a single picture in your head correctly.
- Geogebra can do 3D graphing. Type something like sin(x)+1/y. This will be useful in multivariable calculus. There’s a lot of things geogebra can do. For example, just google ”geogebra vector field plotter” and it’ll come up.
- Desmos graphing calculator is good too

# Physics:

- PBS SpaceTime General Relativity (conceptual) playlist: I think I remember the math not being too bad, but it’s mostly conceptual anyway, which is nice.
- PBS SpaceTime Origin of Matter and Time playlist:
- PBSSpaceTime channel: Relativity stuff, quantum physics, cosmology, astrophysics, etc. Probably the best channel for theoretical physics. I recommend pretty much every single video from them
- Fermilab quantum physics and a bit of cosmology, string theory, and relativity: I’m not sure if this playlist is complete. The fermilab channel has a lot of unimportant videos, this playlist has the informative ones.
- Sixtysymbols channel: All kinds of physics. Made by the same guy as numberphile
- VSauce channel: Not just physics, pretty much all science and some math. Highly recommended. And for the memes
- Eugene Khutoryansky channel: REALLY good animations.
- Eugene Khutoryansky relativity playlist: I haven’t seen this, but it’s a good channel so this playlist is probably good too
- Eugene Khutoryansky quantum playlist: Watch after learning multivariable calculus and differential equations. There’s some heavy stuff
- Griffiths’ introduction to quantum mechanics 2nd edition: I just started this at the time of writing this, but it seems good. It says you only need multivariable calculus, differential equations, and linear algebra. There’s a solution book too
- Wave function article: Requires some advanced single variable and some multivariable calculus and comfort with them. Highly recommend it though.
- Wave function article footnotes:
- Conceptual quantum mechanics:
- MIT OpenCourseWare Quantum mechanics (an actual MIT course fully available online for free).
- YouTube playlist
- Other course materials:
- This is where I actually learned quantum mechanics and I think it’s the best way. Professor is a great teacher. I recommend doing the problem sets and keeping up with the classwork found on the MIT OCW website.

# Math in general:

- PBSInfiniteSeries: Cool (mostly pure) math stuff with good animations. Very well done videos.
- Numberphile: All kinds of math. Usually pretty cool stuff. Some videos are boring, but you have to find the interesting ones like 1+2+3+4… = -1/12. They try not to get too complicated and every person talking in the videos is a professor in math or physics so they’re qualified.
- 3Blue1Brown: REALLY good animations and explanation. Very in depth. Definitely recommend essence of calculus (linked earlier) and essence of linear algebra
- StandUpMaths: Funny and covers interesting stuff
- Eugene Khutoryansky math playlist: Good animations

# Programming:

- Codecademy: If you’re new to programming, I recommend starting with python. This is a great site for learning any programming language. I don’t think it teaches php well though. If you want to learn php for web development and not just the syntax of the language itself, use w3schools
- Coding train channel:
- Processing intro playlist: Processing and p5js are a lot of fun to make stuff in. they use java and javascript respectively. I recommend learning some java and javascript on codecademy first.
- Coding challenge playlist: If you know a bit of java or javascript, this will teach you the rest in an interesting way. If you know java, watch some of the videos where he codes in javascript and that’ll be enough to teach you javascript. They’re very similar.
- If you want to learn object oriented programming and java really well, take something like AP Computer Science in school. I’m not sure if codecademy teaches you good object oriented programming, but it’ll help anyway. Advanced object oriented programming is the only thing on this document I didn’t have to do on my own so I don’t know where to find it on the internet.
- W3schools: This is really good for web programming. It’s more in depth than codecademy so if you’re serious about web programming, learn from here too. Codecademy has really good jquery, html, and css though.
- StackOverflow and documentation: If you don’t know how to do something, like splitting a string into a list by commas, you could just google “split a string into a list by comma in python” and something will come up. If it’s more complicated or specific, don’t be afraid to ask a question on stack overflow. Also, if you don’t know how to use a specific function, look up the documentation. Stuff like this
- It’s also good to know how to read documentation like this