sealed current ahead
Boot
W1–2 · 15 gatesToolkit
W3–13 · 193 gatesWeek 3 · Toolkit
Analysis: Sequences + Algebra: Polynomials I + LA: Vector Spaces + Comb: Counting Introdue 2026-06-13 · 26–30 hrs · 14 gates · lesson 10 minWeek 4 · Toolkit
Analysis: Continuity + Algebra: Complex Numbers + LA: Linear Maps + Comb: IE + Hidden Tools: Finite Differences + Compactnessdue 2026-06-20 · 26–30 hrs · 19 gates · lesson 10 minWeek 5 · Toolkit
Analysis: Differentiation + Algebra: Inequalities + LA: Eigenvalues + Comb: Bijections + NT: Divisibility + Hidden Tool: Convexity/Jensen/Smoothingdue 2026-06-27 · 26–30 hrs · 17 gates · lesson 10 minWeek 6 · Toolkit
Analysis: Integration + FTC + Algebra: Functional Equations + LA: Inner Products + Comb: Generating Functions + NT: Congruences + Hidden Tools: ODE Recognition + Generating Functionsdue 2026-07-04 · 27–31 hrs · 22 gates · lesson 10 minWeek 7 · Toolkit
Analysis: Uniform Convergence + Algebra: Advanced Inequalities + LA: Spectral Theorem + Comb: Extremal + NT: Diophantine + Geometry begins + Hidden Tools: Auxiliary Functions + Trace/Det Identities + Graph Modelingdue 2026-07-11 · 27–31 hrs · 23 gates · lesson 11 minWeek 8 · Toolkit
Analysis: Power Series + Algebra: Polynomial Advanced + LA: Applications + Comb: Recurrences + NT: Valuations + Hidden Tools: Feynman's Trick + Root-of-Unity Filter + Valuationsdue 2026-07-18 · 26–30 hrs · 27 gates · lesson 10 minWeek 9 · Toolkit
All Tracks: Archive Sprint + Hidden Tools: Abel Summation + LA in Combinatoricsdue 2026-07-25 · 24–28 hrs · 18 gates · lesson 8 minWeek 10 · Toolkit
All Tracks: Consolidation + Identify 2 Weakestdue 2026-08-01 · 25–29 hrs · 19 gates · lesson 8 minWeek 11 · Toolkit
Deep-Dive Week 1: Your 2 Weakest Topicsdue 2026-08-08 · 24–28 hrs · 11 gates · lesson 10 minWeek 12 · Toolkit
Deep-Dive Week 2: Weak Topics Continue + Cross-Topic Synthesisdue 2026-08-15 · 24–28 hrs · 11 gates · lesson 10 minWeek 13 · Toolkit
Full Toolkit Audit + Phase 3 Gatedue 2026-08-22 · 30–36 hrs · 12 gates · lesson 7 minMastery
W14–28 · 252 gatesWeek 14 · Mastery
A1/B1 Slot Masterydue 2026-08-29 · 26–30 hrs · 18 gates · lesson 10 minWeek 15 · Mastery
A2/B2 Slot Masterydue 2026-09-05 · 26–30 hrs · 21 gates · lesson 9 minWeek 16 · Mastery
Mixed A1–B2 Timed Sets + Finish-Clean Drillsdue 2026-09-12 · 28–32 hrs · 21 gates · lesson 10 minWeek 17 · Mastery
Exam Craft + Verification Intensivedue 2026-09-19 · 26–30 hrs · 22 gates · lesson 9 minWeek 18 · Mastery
Advanced Analysis: Feynman + Abeldue 2026-09-26 · 29–33 hrs · 23 gates · lesson 10 minWeek 19 · Mastery
Advanced Algebra: Root-of-Unity Filter + Newton's Identities + Interpolationdue 2026-10-03 · 26–30 hrs · 19 gates · lesson 10 minWeek 20 · Mastery
Advanced Combinatorics: Probabilistic Method + Algebraic Methoddue 2026-10-10 · 26–30 hrs · 22 gates · lesson 10 minWeek 21 · Mastery
Advanced NT + Abstract: LTE + Orders + Burnsidedue 2026-10-17 · 26–30 hrs · 22 gates · lesson 10 minWeek 22 · Mastery
USAMO Bridge: Nightmare Entrydue 2026-10-24 · 28–32 hrs · 19 gates · lesson 9 minWeek 23 · Mastery
Nightmare Ramp Idue 2026-10-31 · 26–30 hrs · 17 gates · lesson 9 minWeek 24 · Mastery
Nightmare Ramp IIdue 2026-11-07 · 26–30 hrs · 21 gates · lesson 9 minWeek 25 · Mastery
Full Mock #1due 2026-11-14 · 18–20 hrs · 9 gates · lesson 8 minWeek 26 · Mastery
Full Mock #2 + Gap Closingdue 2026-11-21 · 18–20 hrs · 6 gates · lesson 7 minWeek 27 · Mastery
Cold Re-Solves + Memory Lockingdue 2026-11-28 · 12–15 hrs (lighter week) · 8 gates · lesson 7 minWeek 28 · Mastery
Taper + Examdue 2026-12-05 · ~6 hrs (taper + exam day) · 4 gates · lesson 6 minThe playbook
Six standing rules for the top of the paper — read them until they are reflexes.
Think like the problem writerAt the high end, many misses are not technical. They are failures to notice the intended pressure point.
- After every hard miss, ask what the setter was trying to force you to see.
- Work backward from elegant official solutions and identify what made the key move natural.
- Keep a 'magic step' log of memorable pivots: unexpected substitutions, bounding choices, extremal reframes, or object redefinitions.
Use discussion, not just solo grindingTop students improve by comparing solution paths, not only by accumulating solved counts.
- Once or twice a week, explain one problem aloud as if presenting in seminar.
- Compare your approach with a stronger or different solver when possible.
- Study multiple official or community solutions for the same problem when a problem supports very different attacks.
Train narrow intuition familiesThe last few Putnam problems are often won by narrow-area familiarity rather than generic heuristics.
- Group problems by mechanism, not just by topic: valuation traps, extremal graph pivots, generating-function recurrences, root-location tricks.
- If you miss two hard problems for the same reason, spend the next session on that exact family.
- Re-solve misses after 3, 10, and 21 days so the pattern becomes reusable.
Use adjacent contests and journalsA mental reset helps when Putnam practice becomes too self-similar.
- Use VTRMC or IMC-style sets for fresh but related problem texture.
- Read hard problems with multiple published solutions from sources like the American Mathematical Monthly or Crux Mathematicorum.
- Steal good solution openings and closing moves from those writeups.
Seminar habits beat passive readingStrong university prep programs usually rely on weekly sheets, selective submission, and proof feedback.
- Do weekly topic sets with a deadline, not an endless queue.
- Only mark a problem 'done' after you can write the solution cleanly.
- Submit or rewrite only your best solutions so quality stays visible.
Train for seminar entry, not just score survivalA strong stretch goal is to arrive in October already able to contribute, not just watch stronger students solve everything.
- Keep one lane of real Putnam exposure every week, even while the main lane is still building foundations.
- Practice presenting one polished solution and one failed attempt diagnosis each week.
- Use MIT/Yufei-style sheets as a standard for problem density, not as rare bonus material.