Caltech Math Meet Preparation: CMM Formerly CHMMC

Caltech Math Meet preparation has to begin with a correction, because most material about this competition is out of date in two specific ways that affect how a team should train.

The competition formerly called CHMMC

If you are looking for the Caltech Harvey Mudd Math Competition, this is it under its current name. The event now runs as the Caltech Math Meet, organised by Caltech students, and its own site refers to previous Caltech Math Meets and CHMMC together. Harvey Mudd is no longer reflected in the name or the stated organiser.

This matters for more than labelling. Older material describes a Power Round that no longer exists: it has been replaced by a Guts Round. A team that prepares a week-long proof paper for this competition is preparing for the wrong event entirely.

Seven proof-style questions with the marks printed on them

The Team Round is 7 proof-style questions in 60 minutes, set in increasing difficulty, and each question is labelled with its point value.

That last detail is a gift and most teams waste it. The paper tells you where the marks are before you start, so a team can decide in the first two minutes which questions to commit to, rather than discovering at minute fifty that they spent half the round on a cheap one.

We practise reading the paper as a whole and allocating it deliberately, because sixty minutes across seven questions does not survive working straight through in order.

Calculus is on the paper, and that is an opening

The Individual Rounds are 10 questions in 50 minutes, short answer with no justification required, in four subjects: Algebra and Number Theory, Combinatorics, Geometry, and Calculus. Most students take two.

Calculus is unusual at this level. Olympiad-track students typically arrive with strong algebra, combinatorics and geometry and no competition calculus at all, because the olympiad syllabus excludes it.

For a Class 11 or 12 student who has covered calculus at school, that frequently makes it the least crowded of the four subjects and often the better of their two choices. A real part of Caltech Math Meet preparation goes to calculus specifically for competition use — limits, differentiation, integration, series, and the optimisation and area problems these tournaments actually set, which are not the problems a school textbook sets.

Guts, and the live leaderboard

The Guts Round is 9 sets of 3 problems across 75 minutes, worked as a team, submitted one set at a time, with a live leaderboard.

The leaderboard is the part teams handle badly. It is information, and it is also a distraction that arrives at exactly the moment a team is deciding whether to submit an incomplete set.

Teams that have practised this agree a rule beforehand and stop re-litigating it under pressure. Teams that have not spend the final twenty minutes making decisions based on other teams' scores rather than on their own remaining problems.

Scoring, and why team size matters

The meet is scored 40 per cent from the Team Round and 60 per cent from the Individual Rounds. The individual component is six times the team's average individual score when a team has four or more members, but the plain sum of scores when it has fewer than four.

That is a structural penalty for a small team and it is worth understanding before registering rather than after. A team of three strong students is scored on three results; a team of four is scored on an average multiplied up to six. Teams are capped at six members.

What to cover beyond calculus

Algebra and number theory: polynomials, functional equations, modular arithmetic. Combinatorics: bijective counting, recursion, invariants — our combinatorics course covers the systematic methods these reward. Geometry: cyclic configurations, power of a point, and coordinate methods, as covered in our geometry course.

The Team Round draws across all of it and asks for proof-style answers, so a team collectively needs every area covered even though each individual sits only two subjects.

Preparing the proof-style Team Round

Proof-style is not quite the same as a full olympiad proof, but it is considerably more than a final answer. The questions want reasoning set out clearly enough to be followed and awarded.

Teams coming from short-answer tournaments find this the hardest adjustment, exactly as they do at HMMT February. The remedy is the same: write solutions during practice, have them critiqued on whether a reader could follow them, and do it months before the competition rather than weeks.

Choosing your two individual subjects

Because each student sits only two of the four, the choice is worth making deliberately rather than by preference.

The useful question is not which subject you enjoy most but which two give you the best expected score against the field. Calculus is frequently under-contested among olympiad-track students, as noted above. Geometry tends to attract students who are genuinely strong at it, so a middling geometer gains little by choosing it.

Within a team there is a second consideration: the Team Round draws on everything, so a team whose six members have collectively chosen only two subjects will have gaps nobody can fill. Coordinating the choices across the team is worth a conversation before registration.

Who should enter

Students aged 19 or younger enrolled full-time in high school, in teams of at most six. A student intending to take the Calculus subject test needs the school groundwork in place, since competition calculus builds technique on top of it rather than teaching it from nothing.

The meet is held at Caltech, most recently in January, with registration opening the previous August. Dates, fees and format are set each year by the organisers, so confirm them at caltechmathmeet.org. Note that the old chmmc.caltech.edu address still appears in search results and should not be treated as current.