Olympiad Algebra Lessons Book 1
Fundamentals of Polynomials
The first lessons volume in the Olympiad Algebra sequence.
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Lyran Math Books
Browse Lyran Math books published in 2026. New books will be added here as they are released.
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Four-volume series
The Olympiad Algebra Series
Two substantial lesson books, one in polynomials and one in trigonometry, each with a complete solutions manual. For easier reading, their material is also divided across five polynomial coursebooks and seven trigonometry coursebooks. Selected coursebooks include supplementary material beyond the main volumes.
4 paperback volumes
Olympiad Algebra Solutions Manual for Book 1
Fundamentals of Polynomials: Solutions Manual
The companion solutions manual for Lessons Book 1.
Olympiad Algebra Lessons Book 2
Fundamentals of Trigonometry
The second lessons volume in the Olympiad Algebra sequence.
Olympiad Algebra Solutions Manual for Book 2
Fundamentals of Trigonometry: Solutions Manual
The companion solutions manual for Lessons Book 2.
Five-book coursebook series
Lyran Polynomial Coursebooks
The Polynomial Lessons Book and Solutions Manual are divided across five shorter coursebooks for easier reading, from foundations and factorization through olympiad-level synthesis. Selected volumes also include supplementary material.
5 books · 10 print editions
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Lyran Polynomial Coursebook 1/5
Polynomial Foundations and Factorization
Polynomial foundations, roots, identities, Viète's formulas, polynomial expressions, systematic factorization, division, remainders, and the Euclidean algorithm.
Lyran Polynomial Coursebook 2/5
Roots, Equations, and Algebraic Structure
Advanced polynomial structure through complex numbers, symmetric sums, discriminants, resultants, interpolation, algebraic systems, and reciprocal and irrational equations.
Lyran Polynomial Coursebook 3/5
Integer Polynomials and Arithmetic Methods
Integer and arithmetic methods using finite differences, interpolation, congruences, divisibility, finite fields, power sums of roots, and discrete equation techniques.
Lyran Polynomial Coursebook 4/5
Functional Methods and Polynomial Dynamics
Composition, iteration, functional equations, symmetry, Chebyshev methods, modular reduction, irreducibility, algebraic numbers, and structural contest problems.
Lyran Polynomial Coursebook 5/5
Olympiad Polynomial Synthesis
A cumulative synthesis course combining factorization, root bounds, congruences, interpolation, complex methods, mock contests, past competition problems, and original synthesis problems.
Seven-book coursebook series
Lyran Trigonometry Coursebooks
The Trigonometry Lessons Book and Solutions Manual are divided across seven shorter coursebooks for easier reading. Selected volumes add supplementary material; Coursebook 7 includes an extensive worldwide problem collection beyond the main volumes.
7 books · 14 print editions
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Lyran Trigonometry Coursebook 1/7
Three Geometries and Ancient Algebra
An identity-focused coursebook connecting Euclidean, spherical, and hyperbolic geometry with ancient-algebra themes.
Lyran Trigonometry Coursebook 2/7
Sexagesimal Fields, Reciprocals, and Power Tables
A historical-table laboratory for sexagesimal notation, field plans, metrology, reciprocals, power tables, and structured mathematical bookkeeping.
Lyran Trigonometry Coursebook 3/7
Polyarcs, Periods, and Logarithmic Tables
A continuation of the historical-table sequence through polyarcs, reciprocal periods, logarithmic table geometry, and related olympiad structures.
Lyran Trigonometry Coursebook 4/7
Triangle Trigonometry
A focused coursebook on triangle trigonometry with lessons, exercises, complete solutions, and olympiad-oriented methods.
Lyran Trigonometry Coursebook 5/7
Contest Trigonometry and Infinite Processes
Contest trigonometry paired with sums, products, limits, roots of unity, Fourier methods, and other infinite-process techniques.
Lyran Trigonometry Coursebook 6/7
Spherical Trigonometry and Curved-Space Methods
Great circles, spherical triangles, polar duality, navigation, solid angles, and spatial methods for olympiad geometry.
Lyran Trigonometry Coursebook 7/7
Global Contest Synthesis and Worldwide Problems
The final synthesis volume, with extensive additional problems from around the world beyond the Trigonometry Lessons Book and Solutions Manual.