Theory and assigned exercises
The first 90-minute lesson develops the coursebook's central ideas and introduces six core exercises, followed by optional extensions.
August 17–September 17, 2026 · Live via Zoom
Lyran Polynomial
and Trigonometry
Masterclasses.
A five-week, author-led program in mathematical problem solving. Develop the theory in a live lesson, work through carefully selected exercises, and return for a rigorous solution workshop.
Polynomial structureP(x² − 2) = P(x)² − 2
Infinite processessin x = sin(x/3ⁿ) ∏(1 + 2 cos(2x/3ʲ))
Curved spacecos c = cos a cos b + sin a sin b cos C
Author-led
Olympiad
Masterclasses
Olympiad
Masterclasses
12coursebook-based masterclasses
24live teaching sessions
2parallel time streams
20assessed-student capacity per title
$18–35individual masterclass fee
A complete two-session learning cycle
From core theory
to a finished proof.
Each masterclass extends beyond the live lessons. Course materials, an examination, private feedback, and one scored correction round are all included.
Review and complete solutions
The second 90-minute lesson examines common errors and develops rigorous solutions. The full solution packet is released after every stream for the title has ended.
Examination and correction
Submit an open-book examination worth 60 core marks plus 10 bonus marks, receive private red-ink feedback, and complete one scored correction on up to two core problems.
Five teaching weeks
Live teaching schedule.
Trigonometry is taught on Mondays and Wednesdays; polynomials are taught on Tuesdays and Thursdays. Pass holders select one time stream for all included titles.
| Coursebook | Live classes | Registration | Paperback | Hardcover |
|---|---|---|---|---|
| Trigonometry masterclassLyran Trigonometry Coursebook 1: Three Geometries and Ancient AlgebraMasterclass · $20 USD | TheoryExercise review | 220 pagesOrder on Amazon View contents (PDF) | 238 pagesOrder on Amazon View contents (PDF) | |
| Polynomial masterclassLyran Polynomial Coursebook 1: Polynomial Foundations and FactorizationMasterclass · $20 USD | TheoryExercise review | 281 pagesOrder on Amazon View contents (PDF) | 298 pagesOrder on Amazon View contents (PDF) | |
| Trigonometry masterclassLyran Trigonometry Coursebook 2: Sexagesimal Fields, Reciprocals, and Power TablesMasterclass · $20 USD | TheoryExercise review | 254 pagesOrder on Amazon View contents (PDF) | 268 pagesOrder on Amazon View contents (PDF) | |
| Polynomial masterclassLyran Polynomial Coursebook 2: Roots, Equations, and Algebraic StructureMasterclass · $20 USD | TheoryExercise review | 272 pagesOrder on Amazon View contents (PDF) | 286 pagesOrder on Amazon View contents (PDF) | |
| Trigonometry masterclassLyran Trigonometry Coursebook 3: Polyarcs, Periods, and Logarithmic TablesMasterclass · $20 USD | TheoryExercise review | 218 pagesOrder on Amazon View contents (PDF) | 228 pagesOrder on Amazon View contents (PDF) | |
| Polynomial masterclassLyran Polynomial Coursebook 3: Integer Polynomials and Arithmetic MethodsMasterclass · $20 USD | TheoryExercise review | 350 pagesOrder on Amazon View contents (PDF) | 372 pagesOrder on Amazon View contents (PDF) | |
| Trigonometry masterclassLyran Trigonometry Coursebook 4: Triangle TrigonometryMasterclass · $20 USD | TheoryExercise review | 258 pagesOrder on Amazon View contents (PDF) | 274 pagesOrder on Amazon View contents (PDF) | |
| Trigonometry masterclassLyran Trigonometry Coursebook 5: Contest Trigonometry and Infinite ProcessesMasterclass · $20 USD | TheoryExercise review | 294 pagesOrder on Amazon View contents (PDF) | 307 pagesOrder on Amazon View contents (PDF) | |
| Polynomial masterclassLyran Polynomial Coursebook 4: Functional Methods and Polynomial DynamicsMasterclass · $20 USD | TheoryExercise review | 284 pagesOrder on Amazon View contents (PDF) | 298 pagesOrder on Amazon View contents (PDF) | |
| Trigonometry masterclassLyran Trigonometry Coursebook 6: Spherical Trigonometry and Curved-Space MethodsMasterclass · $20 USD | TheoryExercise review | 283 pagesOrder on Amazon View contents (PDF) | 299 pagesOrder on Amazon View contents (PDF) | |
| Trigonometry masterclassLyran Trigonometry Coursebook 7: Global Contest Synthesis and Worldwide ProblemsMasterclass · $20 USD | TheoryExercise review | 454 pagesOrder on Amazon View contents (PDF) | 484 pagesOrder on Amazon View contents (PDF) | |
| Polynomial masterclassLyran Polynomial Coursebook 5: Olympiad Polynomial SynthesisMasterclass · $20 USD | TheoryExercise review | 347 pagesOrder on Amazon View contents (PDF) | 368 pagesOrder on Amazon View contents (PDF) |
Times are shown for every title inside its registration links. Most international sessions begin at 9:00 AM Pacific, and most North American evening sessions begin at 3:00 PM Pacific. Where simultaneous trigonometry titles require a later start, the precise later time is shown directly—no separate schedule column is needed.
Included with every masterclass
Rigorous instruction with a permanent record of progress.
Lyran-formatted course materialsReceive a theory packet, selected exercises, complete review solutions, and a private examination prepared specifically for the title.
Proof StudioWrite mathematics with an immediate KaTeX preview. Full LaTeX and TikZ compilation remains in beta until the safety corpus passes; PDF and image upload remain available throughout.
Private teacher feedbackReceive red annotations, rubric marks, and a permanent first-attempt score visible only to you.
One scored revisionCorrect up to two core problems and earn a separate revised-mastery score while preserving the original attempt.
The complete program
Twelve coursebooks.
One focused series.
Individual masterclass fees are approximately half the corresponding paperback list price. Subject passes offer additional savings, and the complete pass saves $64.
Trigonometry$20
Lyran Trigonometry Coursebook 1: Three Geometries and Ancient Algebra
Identities, transformations, and geometric models
Polynomial$20
Lyran Polynomial Coursebook 1: Polynomial Foundations and Factorization
Expressions, division, and factorization
Trigonometry$20
Lyran Trigonometry Coursebook 2: Sexagesimal Fields, Reciprocals, and Power Tables
Ancient tables, exact computation, and reconstruction
Polynomial$20
Lyran Polynomial Coursebook 2: Roots, Equations, and Algebraic Structure
Complex roots and equation methods
Trigonometry$20
Lyran Trigonometry Coursebook 3: Polyarcs, Periods, and Logarithmic Tables
Cyclic structures, reciprocal periods, and table geometry
Polynomial$20
Lyran Polynomial Coursebook 3: Integer Polynomials and Arithmetic Methods
Congruences, divisibility, and finite differences
Register early · select books later
Attend the masterclasses. Then choose the books that suit you.
Active students with a delivery address in Canada or the United States may request one consolidated package of signed author copies through September 17. When the teacher verifies that Setmore payment was completed before 12:00 AM Pacific on August 10, 2026, the campaign rate—50% of the applicable paperback list price—is applied automatically.
Automatic early-book rate
The verified Setmore payment timestamp determines eligibility. After enrollment, select or revise your titles and confirm the package country in your student workspace until September 17 at 11:59 PM Pacific. Availability, tracked shipping charges, and fulfillment timing are confirmed separately; an arrival date is not guaranteed.
You may instead order unsigned retail copies directly from Amazon at the price and delivery terms shown there. Amazon does not sign or fulfill the author-sent package.
Register for a masterclassRegistration opens August 6
Choose the mathematics you want to master.
Live teaching concludes on September 17. All corrections and final results are locked by 6:00 PM Pacific on September 27.