Mark's Handouts
This page lists all the handouts I've written for my classes at the ORMC, arguably the best math circle in the western world. We teach students mathematics far beyond the regular school curriculum, much like AOPS and the BMC.
For my students:
Don't look at solutions we haven't discussed,
and don't start any handouts before class. That spoils all the fun!
For everyone else:
If you're using any of these, please let me know---especially
if you find errors, mistakes, or a poorly designed section.
Such things must be fixed!
Overview & Context
Our classes are two hours long, with a ten-minute break in between. The lessons below
are written with this in mind.
I do not expect the average student to finish all problems during this two-hour session.
If the class finishes early, the lesson is either too short or too easy.
The sources for all these handouts are available here.
Some are written in LaTeX, some are in Typst.
The latter is vastly superior.
Warm-Ups
Students never show up on time. Some come early, some come late. Warm-ups are my solution to this problem: we hand these out as students walk in, giving them something to do until we can start the lesson.
- A Familiar Concept [ handout ]
- Adders [ handout | solutions ]
- Big-Tac-Toe [ handout ]
- Flip-Flops [ handout | solutions ]
- Fuse Timers [ handout ]
- Ivan the Electrician [ handout ]
- Jump Chess [ handout | solutions ]
- Mario Kart [ handout | solutions ]
- Odd Dice [ handout | solutions ]
- Partition Products [ handout | solutions ]
- Passing Balls [ handout | solutions ]
- Prime Factors [ handout ]
- Regex [ handout ]
- Rootbound [ handout ]
- Somewhat Random Numbers [ handout | solutions ]
- The Gallery [ handout | solutions ]
- The Painting [ handout | solutions ]
- The Sysadmin's Warm-Up [ handout ]
- Travellers [ handout | solutions ]
- Tuesday [ handout | solutions ]
- What's an AST? [ handout ]
- Wild Tic-Tac-Toe [ handout ]
- Zeno's Furniture [ handout | solutions ]
- fmod [ handout ]
Advanced
The highest level of the ORMC, and the group I spend most of my time with. Students in ORMC Advanced are in high school, which means they're ~14-18 years old.
- Compression [ handout | solutions ]
- Continued Fractions [ handout | solutions ]
- Cryptography [ handout | solutions ]
- De Bruijn [ handout | solutions ]
- Definable Sets [ handout | solutions ]
- Error-Correcting Codes [ handout | solutions ]
- Fast Inverse Square Root [ handout | solutions ]
- Finite Automata [ handout | solutions ]
- Generating Functions [ handout | solutions ]
- Geometric Optimization [ handout ]
- Geometry of Masses [ handout ]
- Gods, Demons, and Mortals [ handout | solutions ]
- Graph Algorithms [ handout | solutions ]
- Intro to Proofs [ handout ]
- Lambda Calculus [ handout | solutions ]
- Lattices [ handout | solutions ]
- Mock a Mockingbird [ handout | solutions ]
- Origami [ handout | solutions ]
- Pidgeonhole Problems [ handout | solutions ]
- Quantum Computing [ handout | solutions ]
- Random Walks [ handout | solutions ]
- Retrograde Analysis [ handout | solutions ]
- Stopping Problems [ handout | solutions ]
- Symmetric Groups [ handout | solutions ]
- The Size of Sets [ handout ]
- Wallpaper Symmetries [ handout | solutions ]