# Units

## Synopsis

You choose the units you do based on what you think is most beneficial for you. Request your units (which can be changed at any time for any reason) through the Unit Request Form. You can request them sequentially, request what you want to do the whole year, or just put all of the units in a specific order and do however many you can. (First-timers/less experienced competitors: I recommend the first option to make it all a little less overwhelming.)

Two units will be unlocked for you at a time - you can do them in whatever order you feel. This is so you can stay focused on what you want to work on. There are two units and not one unit unlocked so you can move off of a subject if you need a break from it but want to finish it eventually, and so you have something to do when you turn in one of the units and I haven't gotten back to you yet.

You may choose, for whatever reason, at whatever time, to drop/add units. Just let me know through the request form or by email.

## Recommended Units

These are recommended - if you feel like you know better than me what you want to do, you're probably right. And if you change your mind, you can change the unit you're doing. That being said, doing these units will probably benefit you and are a good place to start if you're not sure what to do. You can choose whether to follow this strictly, follow this loosely, or completely ignore it - and all are valid options. Whatever floats your boat (and helps you learn).

Difficulty levels are rough. If you had a bad day on the AIME, or were going to take AIME II in 2020, higher levels are okay. But don't hold too much credence to a mock score of a 14 on an AIME from the 1990s.

### General must-takes

I think nearly everyone should take the following units.

Perspectives

Logarithms

### Beginners: <5 on AIME

Do the Intro to Combo and Intro to Modular Arithmetic units first, in whatever order makes you happy. (You can also do both at the same time.) Then do Logarithms, if you aren't already familiar with them, and do Areas and Lengths in Triangles.

### Intermediate: 6-9 on AIME

Start with Areas and Lengths in Triangles. Do Logarithms if unfamiliar with them. Then do Sequences in the AIME, Telescoping, and States.

### Advanced: >9 on AIME

Start with Radical Axes. You are probably familiar with Logarithms, but if not, do them. Then do Sequences in the AIME, States, and Fake Algebra. Go for the harder problems in your handouts.

## Codes

Each unit has a 3 letter code. The first letter is subject, the second letter is difficulty, and the third letter is relevance (to the AIME). Codes are non-unique.

### Subject

There are 5 letters for 5 subjects.

A - Algebra

C - Combinatorics

G - Geometry

N - Number Theory

M - Miscellaneous

The Miscellaneous topic is a catch-all for stuff that doesn't fit under the first four categories. (An example would be "problems easy to mess up on," which is in progress.)

### Difficulty

P - The generally recommended difficulty for those who got <5 on the AIME. Problems will be early to mid-AIME (think difficulty of 5-8, with few 9s and 10s thrown in).

Q - The generally recommended difficulty for those who got 6-9 on the AIME. This should be the average unit difficulty for a lot of people. Problems will be mid AIME with a few hard problems (think difficulty 7-11, with late AIME problems sprinkled in consistently).

R - Do a few of these handouts if you got >9 on the AIME. You probably will still be doing a non-zero amount of level Q handouts. The subject material is usually in late AIME problems, though I will try to ease you in with a couple of easier problems.

### Relevance

T - Tangential. These are the "for fun" units.

U - Useful. Good to know stuff. Helps with quality of life.

V - Vital. These are the main things you should know for the AIME.

## Submissions

### A few guidelines.

Please send a PDF and use LaTeX to typeset your solutions. Overleaf is a simple way to do this. If you absolutely cannot type it up, please make sure I can clearly read what you are scanning/taking a picture of.

Solution sketches are fine. Full solutions are also fine.

Do around 2/3 of the problems.

Email me for hints if you've been stuck on a problem with no progress.

Feedback is encouraged! Include it in the email so I can separate feedback from solutions. (Unless it is a rating, in which case include it in your solutions file - see below.)

### And a request.

For each problem you do, please rate it 0-3 in two categories: Difficulty and instructiveness. Decimals are fine, but I would encourage using them sparely.

Difficulty is how hard it was to solve, and how likely you think you'd be able to replicate something similar in competition.

Instructiveness is how much you think it will help you with future questions.

Alternatively, you may just do one rating of 0-3 that includes both difficulty and instructiveness and reflects how much you got out of the problem.

You may switch between both styles of rating depending on how much time and energy you have, but I'd appreciate consistency for each unit submission.

I'm considering this my tuition for the first few seasons I'm running MAST. Please take this seriously - future students will be impacted by the scores you send and I will redesign units based off of your feedback.

## Upcoming

Generating Functions (AQT) - Generating functions.

Careful! (MPU) - A selection of problems where you'll

*feel*you did it right but might miss something. Better to mess up in practice so you don't do it in competition.Games and Friends (CRT) - Problems you can show your friends that don't do math. The average person who watches some math/science videos should be able to understand the problem and the solution. Includes "game" problems, such as the 21 game.

Bases (NQU) - Interpreting problems in different bases. Usually useful for problems involving floor functions.