After AMC 10/12 and AIME, the next step for a high school mathematics record is the university invitational circuit. These contests differ from AMC in two ways: they are scored by team, and they include rounds that require a complete written argument rather than an answer. Neither skill comes from solving problems alone.
Sigma Circle Math Club meets every other week, about 18 sessions a year, led jointly by gold-medal competition coaches and current university students with invitational experience. Coaches handle problem types and proof correction; the student leaders run the team rounds.
1. University invitationals: problem sessions and team practice
Every session works through past papers. Members solve under time, then compare approaches problem by problem. Team rounds get their own drills. A relay round passes answers down the line, so each solver’s result is the next solver’s input. A Guts round releases problems in batches, with the next batch withheld until the current one is submitted, which tests division of labor and pacing.
Here is the 2026-27 season for the four target contests, verified against each organizer’s site:
| Contest | Contest dates | Team size | Proof round |
|---|---|---|---|
| Harvard-MIT Mathematics Tournament (HMMT) | 7 Nov, 13 Feb | 4–6 / 6–8 | February team round |
| Berkeley Math Tournament (BMT) | 14 Nov (in person) | up to 6 | Power Round |
| Duke Math Meet (DMM) | 7 Nov | 6 | Power Round |
| Stanford Math Tournament (SMT) | mid-to-late April | team | Power Round |
Three points matter before a family plans the year. HMMT November and the Duke Math Meet are both on 7 November 2026, so a student enters one or the other, and the September assessment settles which. HMMT requires teammates to attend the same in-person school or live within 150 miles of one another, so Irvine members qualify under the second clause and can enter as a club team; BMT and DMM have no geographic restriction. The Stanford Math Tournament has not announced its 2027 date, which in recent years has fallen in mid-to-late April; its in-person edition is limited to students residing in the United States and admits teams by lottery, while a companion online edition is open worldwide and accepts individual entries.
2. Proof writing and LaTeX
Invitational proof rounds and camp application problems both ask for a complete argument, and both award partial credit, so a half-finished line of reasoning still scores. About half of club time goes here: starting from proof by contradiction, induction and the pigeonhole principle, and building toward a self-contained argument of about a page. Every exercise is submitted in writing and returned with corrections for logical gaps and ambiguous phrasing.
LaTeX is the typesetting system used across mathematics and the sciences, generating equations, theorem numbering and bibliographies automatically. Several sessions are given to building a document template from scratch, after which a student can produce a correctly formatted solution for an invitational clean copy, a camp application, or a paper draft.
3. Preparing top math camp applications
Selective American math camps do not screen on standardized scores. They screen on written solutions to a set of hard problems. That set typically takes 40 to 80 hours across multiple drafts, which means the work has to start before the application season.
Timelines for the main programs, which each program adjusts annually:
| Program | Deadline | Core of the application |
|---|---|---|
| Stanford University Mathematics Camp (SUMaC) | early February | take-home proof exam |
| Ross Mathematics Program | early March | problem set, essays, video |
| PROMYS (Boston University) | late February | problem set |
| Canada/USA Mathcamp | early March | Qualifying Quiz |
SUMaC is for students in grades 10 and 11 and opens around January. The Ross Mathematics Program is a six-week residential program; the 2026 program fee was 7,500 US dollars, with need-based aid available. PROMYS runs 27 June to 7 August in 2027. The club starts these problems in the fall term and moves into correction and final drafts over the winter.
4. Open questions and paper structure
Each term includes several discussion sessions on open problems and active directions, concentrating on the small questions in graph theory, combinatorial number theory and discrete geometry that a high school student can actually enter. The goal is not to solve them. It is to see how a mathematics paper is built: how the question is posed, how prior results are surveyed, and where the author’s own contribution sits. Students who want to continue can choose a topic from here and move into independent research.
5. Teaching assistants and volunteer hours
Members with a full year in the club can be selected as teaching assistants, supporting office hours and grading for younger classes. That time counts as volunteer hours, usable for volunteer service awards and for the activities list on a college application. Selection weighs both mathematics and communication, and is confirmed again each term.
The year at a glance
- September: assessment and grouping, target contests chosen, HMMT November and BMT registration opens.
- October: past-paper work and team-round drills; camp application problems begin.
- November: HMMT November, BMT in person and DMM all land this month, each followed by a debrief.
- December to January: proof writing and LaTeX; camp applications finalized.
- February: HMMT February; camp deadlines pass.
- March to April: SMT preparation, discussion sessions, paper topics.
- May to June: camp decisions arrive; summer bridge and next year’s TA selection.
Who it is for
- Students in grades 9-12 who have finished a round of AMC 10/12 training or are ahead in the school math sequence.
- Students applying to selective math camps who need someone alongside them to finish the application problems.
- Students with individual results who need team-round coordination and written proof.
Pairs with AIME Pathway in the math competition track.
How to start
Start with a placement assessment. We use it to set the level and class, then confirm the year plan with the family. For schedules, tuition, and bundle offers, request the 2026-27 program guide through the form below.
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Contact a course advisorFrequently Asked Questions
How is the club different from AIME Pathway?
AIME Pathway is a course. It works through AMC 10/12 and AIME content on a fixed schedule, and the goal is an individual score. Sigma Circle is a club. It teaches no new content and covers the three things a course cannot: team-round coordination, written proof, and the months-long work of a math camp application. The two do not overlap, so most students do both. A student who has finished AIME Pathway or already qualified for AIME can join the club alone.
Can an Irvine student join without an AIME score?
Yes. The placement assessment looks at whether a student can follow the discussion of an invitational problem, not at one test score. The usual reference point is a completed round of AMC 10/12 training, or a strong position in the school math sequence. After the assessment we recommend either joining the club directly or spending a semester in AIME Pathway first.
Is meeting every other week enough?
The club assumes students have other math coursework or independent practice. Meeting time is reserved for what a student cannot do alone: team rounds need a fixed roster, proofs need line-by-line correction, and camp application problems need months of revision. Written work follows every session, and the two-week gap is when that work gets done.
How do Irvine members form teams and register?
The Harvard-MIT Mathematics Tournament (HMMT) requires teammates to attend the same in-person school or live within 150 miles of one another, so Irvine members qualify under the second clause and can enter as a club team; the Berkeley Math Tournament (BMT) and the Duke Math Meet (DMM) have no geographic restriction. Coaches help form teams and guide the registration process, and families pay the organizer directly: HMMT charges 80 US dollars per team, collected in cash or check at check-in on contest day, while BMT charges per student, 15 dollars in the early window and 25 dollars during late registration, through the ContestDojo platform. Prices and capacity change each year, so the official site governs.
How do Irvine members handle the November clash?
In 2026 the Harvard-MIT Mathematics Tournament (HMMT) November contest and the Duke Math Meet (DMM) are both on 7 November, so a student picks one. The September assessment sets the direction first. Teams aiming at HMMT take the November-plus-February route; students who want a reliable team result are better served by DMM. The Berkeley Math Tournament (BMT) is on 14 November and conflicts with neither, so most members enter it as well.
What is LaTeX used for at the high school level?
LaTeX is the typesetting system used across mathematics and the sciences. It generates equations, theorem numbering and bibliographies automatically. Three situations call for it directly: the clean copy of an invitational proof round, the written solutions in a math camp application, and the first draft of a research paper. The club builds a document template from scratch over several sessions, after which a student can submit a properly formatted solution instead of an image or a handwritten page.
When should camp application problems begin?
In the fall term. The take-home exam for the Stanford University Mathematics Camp (SUMaC) and the application problem sets for the Ross Mathematics Program and PROMYS are all proof-based. Strong applicants put in 40 to 80 hours across several drafts. Applications open around January and close between early February and early March, so one month is not enough. The club starts in the fall term and moves into correction and final drafts over the winter.
How do Irvine members earn TA volunteer hours?
Students who have been in the club for a full year and pass a review of their mathematics and their communication can be selected as teaching assistants (TAs), supporting office hours and grading for younger classes. Hours accrue against actual teaching and grading time and can be used for volunteer service awards. Selection is confirmed again each term. Ask a counselor at the assessment for the current record-keeping procedure.
