Here are a bunch of miscellaneous resources from high school notes to Princeton notes.

Table of Contents


MAT 201 - Multivariable Calculus

Taught by Dr. Jon Fickenscher at Princeton University.

PHY 104 - E&M

Precept with Professor NP Ong. Lectures by Professor Christopher Tully.

PHY 103 - Mechanics

Precept with Dr. Aurelien Fraisse. Lectures by Professor Isobel Ojalvo.



I got an internship at Boise State University's (BSU) 2022 Data-driven Security REU. I worked with Cassi Chen (UC Berkeley) and Paul Vanderveen (BSU).

Professor Liljana Babinkostova, Professor Edoardo Serra, and Ph.D. student Aparna Sankaran oversaw our research.

We researched deep-learning power analysis attacks on SCHWAEMM and GIFT, two lightweight cryptosystems.

The following files are notes I/we took during the REU.

American Mathematics Competition

The American Mathematics Competition is a group of competitions for secondary students. The AMC 10 and 12 are tests for students in grade 10 and 12, respectively, or below.

You can find past AMCs here.

Below are notes that are helpful for AMC 10/12:

Linear Algebra

Linear algebra is essential foundational knowledge for almost anything in applied mathematics. Here are the notes I took based on MATH 301 - Introduction to Linear Algebra with Professor Stephen Brill at Boise State University.

Multivariable Calculus

Below are notes I took in MATH 275 - Multivariable and Vector Calculus with Professor Shari Ultman at Boise State University.

Standardized Tests


I do not encourage people to look for private tutoring for the SAT. Learning is a very individualized activity in that you have to put in the effort. No matter how good the material is, if you're not working on it, you won't get results. (This is not to say that private tutoring is absolutely a "no." You know yourself better than I do.)

For most people, I suggest going to Khan Academy's practice tests and mini-sections. They have ample amounts of material for anyone (10 practice tests & a legion of mini-sections).

If you're struggling with Reading & Writing, do a reading passage and a writing passage each day. If you're struggling with Math, do a mini-section each day. I recommend you start studying at least a month ahead of your test date. Again, specialize your studying schedule to your needs.


All of the difficulty levels and review recommendations are my opinions. Please adjust your expectations for each course and studying plan to suit your skill set.
Do not be discouraged from taking a course if I give it a hard rating. With enough perseverance and studying, you can get a 5!

My ratings go as follows:
1/5 - Easy. You probably won't need to study much for a good score.
2/5 - Moderately easy. Most concepts are simple, and it's just rote memorization. Not much studying is needed.
3/5 - Mildly hard. Some concepts are hard to understand, and the course requires more than rote memorization. A decent amount of studying is required.
4/5 - Hard. Most concepts are difficult to grasp, and the course requires an in-depth understanding of each concept. You should set a good portion of time to study.
5/5 - Very challenging. This is essentially a 4/5, but I feel like the course is harder.

AP Recommendations

Each class has a brief synopsis, difficulty rating, review book recommendation, and how-to-study. You can go to AP Pass to look at the curves for each test and decide how much you need to study based on those.


AP Calculus AB/BC

Synopsis: AP Calculus teaches the absolute fundamentals of the math of continuities. You'll learn about differentiation and integration in AB. In BC, you'll learn about more abstract concepts, like sequences and series (which are at the crux of the arithmetic your calculators do), and apply differentiation and integration to parametric and polar equations.

How-to-Study: Pick up Princeton Review's textbook and go over the topics you're weak on. Then, it's just a matter of seeing and doing as many problems as you can before the test date.

Difficulty Rating: 4/5. Your ability to learn calculus is a measurement of how well you know the fundamentals of high school math. Most school systems are horrible at teaching the inspiration behind problem-solving, which makes calculus a fairly hard class. If you've studied for math competitions before, this most likely will be easy for you.

AP Statistics

Synopsis: AP Statistics, in my opinion, is more of an English class than a Statistics class (at least on the FRQs). You'll learn about types of distributions and sampling, probability, confidence intervals, and hypothesis testing. As long as you're able to follow a general formula for doing each type of problem, you're set.

How-to-Study: Honestly, this course doesn't require a textbook. If you use the College Board daily videos and their practice problems, you're on your way to a 5 (I only used College Board to review). Nonetheless, if you really want a review book, Princeton Review seems good.

Difficulty Rating: 3/5. You can get all of the problems correct on the test by following a general formula for each type of problem. Thus, this course is more about memorizing around 8 general concepts, garnering it a semi-hard rating.


AP Physics 1

Synopsis: AP Physics 1 is an algebra-based physics course that emphasizes Newtonian mechanics. None of the math is particularly hard. However, the concepts make Physics 1 a challenging course.

How-to-Study: Use a review book to go over the content that you're unsure about. If you're cramming, prioritize College Board practice problems over those in your review book (Barron's or Princeton Review).

Difficulty Rating: 4/5. AP Physics 1 is a conceptually challenging class. Many of the multiple-choice problems and FRQs require knowledge about special cases of physics. If you're able to memorize all these special cases and solve the problems from there, you're good to go. Thus, AP Physics 1 gets a hard rating.

AP Physics C: Mechanics

Synopsis: Mechanics is an extension of Newtonian physics from AP Physics 1. You'll go over kinematics, dynamics, simple harmonic motion, etc. with a bit of calculus sprinkled in.

How-to-Study: Don't buy a review book. Most review books are too hard for the exam. Instead, watch the AP Daily Videos and do the MCQ progress checks. Don't do FRQ progress checks. Rather, do past FRQs. If necessary, take full practice tests after all of that. Flipping Physics has good videos on review content and equations to memorize.

Difficulty Rating: 3/5. Mechanics is conceptually less rigorous than AP Physics 1 as it doesn't introduce many foreign concepts. Instead, it adds in calculus at the expense of Physics 1's rigor. The hardest part may be the differential equations for pendulums.

AP Physics C: Electricity & Magnetism

Synopsis: E&M serves as an extension of the very last units of AP Physics 1. You'll learn about electricity, magnetism, and electromagnetism.

How-to-Study: Don't buy a review book. Most review books are too hard for the exam. Instead, watch the AP Daily Videos and do the MCQ progress checks. Don't do FRQ progress checks. Rather, do past FRQs. If necessary, take full E&M practice tests after all of that.

Difficulty Rating: 4.5/5. E&M is a pretty hard class. Most of the information you'll learn hasn't been covered in prior classes, and if they have, at a very shallow level compared to E&M. Like AP Physics 1, the class is also conceptually challenging, requiring familiarity with common derivations.

AP Chemistry

Synopsis: AP Chemistry teaches you the very basics of chemistry, but requires you to know them well. You can expect first semester to cover all content from "regular" or "accelerated" chemistry. Second semester will include kinetics, acids and bases (much harder than what you've learned), thermodynamics, and more.

How-to-Study: Don't buy a review book. It's 100% not worth it. Watch all of the AP Daily videos and do all of the MCQ Progress Checks for each unit. If you want extra practice, do past FRQs (not FRQs given on myAP). You'll be well on your way to a 5 if you thoroughly understand only what's in the Daily Videos.

Difficulty Rating: 5/5. AP Chemistry is a very hard science course. You're expected to know all the rules of chemistry and their exceptions. Sometimes, it's easy to mix up different justifications of different principles. Plus, you should be familiar with elements' natural state (e.g. Hydrogen appears as Hydrogen gas, H2) and some of their properties.

AP Environmental Science

Synopsis: AP Environmental Science covers a legion of topics but does so very superficially. You can expect to learn about biogeochemical cycles, air and water pollution, ecosystem interactions, and climate change.

How-to-Study: Buying a review book isn't necessary, but you could do it if you have the time and energy to use it. Otherwise, AP Daily Videos are very helpful in combination with the MCQ progress checks on myAP. I wouldn't do the FRQ progress checks. Just do past FRQs.

Difficulty Rating: 2/5. Most people have a good understanding of what the test covers. There just isn't enough time on the test to go in-depth into the concepts you learn, so the test essentially acts as a common-sense test. If you memorize some key concepts, you'll do well without much studying.

Humanities, History, & Social Sciences

AP English Language & Composition

Synopsis: AP Lang is essentially a harder SAT with a long essay portion. If you do well on the SAT, you should do well on this test.

How-to-Study: For the multiple choice questions, I recommend going through the SAT practice on Khan Academy. For the essays, just practice writing lots of synthesis, rhetorical analysis, and argument essays.

Difficulty Rating: 2.5/5. You need to know basic grammar structures and essay-writing skills. Those don't take too much effort to learn if you're also studying for the SAT.

AP United States History

Synopsis: AP US History starts from when Columbus sailed the ocean blue up to the 2010s. Although you don't need to remember every detail from each period of time, you should remember some important events in history to use as evidence in your FRQs.

How-to-Study: Heimler's History is a great aid. If you're looking for Barron's or Princeton Review, I wouldn't get their prep books. Instead, you can buy Barron's flashcards. Practice writing FRQs based on past released APUSH prompts.

Difficulty Rating: 4/5. You need to know a lot of history to be comfortable on the day of the test. Unlike psychology or human geography, you really need to know your timeline. Otherwise, it'll be hard to answer the FRQs.

AP Human Geography

Synopsis: AP Human Geography is about human influence on the landscape. You'll learn about population patterns, agricultural developments, cultural patterns, and more. Think of Human Geography as a high-level intro to history class.

How-to-Study: If you're looking for a prep book, I would go for Barron's. The progress checks for multiple-choice questions are fairly similar to the ones you'll get on the test. To practice the free-response section, I would use past released FRQs.

Difficulty Rating: 3/5. You should have general knowledge of each of the topics, but you don't need to know every detail. As you go through the course, you'll see patterns emerge in how we affect each other and our landscape.

AP Psychology

Synopsis: AP Psychology is the study of human behavior. You'll learn about perception, learning, cognition, personality, and more.

How-to-Study: Unfortunately, I don't think College Board's daily videos are the best way to study. AP Psychology is basically a vocabulary-memorizing course, so you should invest in a review book. Barron's is amazing for AP Psychology—it concisely covers everything you need to know to get a 5. If it's possible, you should create or buy Barron's flashcards, since your understanding of the vocabulary is the crux of your score.

Difficulty Rating: 2.5/5. AP Psychology is one of the "introductory" AP classes. Because the course requires memorization of vocabulary and basic applications of concepts, it isn't too hard.