Learning Path
Master the IMO syllabus topic by topic
Complete Curriculum
Topics are ordered by difficulty within each subject. Click on a topic to access the learning material. Topics with available content are highlighted.
01Expanding and Factoring
02Solving Algebraic Equations
03Algebraic Inequalities
04Functions
05Domain and Range
06Function Composition
07Basic Trigonometry
08Unit Circle
09Complex Numbers
10Sigma Notation
11Product Notation
12Linear Functions
13Quadratic Functions
14Polynomials in One Variable
15Roots of Polynomials
16Vieta's Formulas
17Injective Functions
18Surjective Functions
19Bijective Functions
20Complex Number Arithmetic
21Polar Form
22Euler's Formula
23Fundamental Theorem of Algebra
24AM-GM Inequality
25Polynomials in Two Variables
26Polynomials in Multiple Variables
27Cauchy-Schwarz Inequality
28Limits and Continuity
29Derivatives
30Integrals
31Cauchy's Functional Equation
32Partial Derivatives
33Multiple Integrals
34Hölder's Inequality
35Jensen's Inequality
36Generating Functions
01Multiplication Principle
02Addition Principle
03Permutations
04Factorials
05Sets
06Set Operations
07Functions Between Sets
08Powers of 2
09Combinations
10Binomial Coefficients
11Pascal's Triangle
12Pigeonhole Principle
13Sequences
14Recursion
15Recurrence Relations
16Mathematical Induction
17Strong Induction
18Sample Spaces
19Basic Probability
20Complementary Probability
21Conditional Probability
22Independent Events
23Random Variables
24Expected Value
25Linearity of Expectation
26Graph Theory Basics
27Degree of a Vertex
28Paths and Cycles
29Connectedness
30Trees
31Bipartite Graphs
32Generalized Pigeonhole Principle
33Solving Recurrence Relations
34Convex Sets
35Convex Hull
36Graph Coloring
37Matchings
38Hall's Marriage Theorem
39Turán's Theorem
01Angle Sum
02Isosceles Triangles
03Congruence
04Similarity
05Angle Chasing
06Parallel Lines
07Cyclic Quadrilaterals
08Centroid
09Circumcenter
10Incenter
11Orthocenter
12Euler Line
13Law of Sines
14Law of Cosines
15Excenters
16Stewart's Theorem
17Cartesian Coordinates
18Power of a Point
19Radical Axis
20Radical Center
21Ceva's Theorem
22Menelaus' Theorem
23Homothety
24Nine-Point Circle
25Complex Coordinates
26Barycentric Coordinates
27Conic Sections
28Inversion
29Spiral Similarity
30Projective Geometry
31Cross Ratios
32Harmonic Division
33Poles and Polars
34Pascal's Theorem
01Prime Numbers
02Divisibility
03Prime Factorization
04Infinitude of Primes
05Fundamental Theorem of Arithmetic
06GCD
07LCM
08Modular Arithmetic
09Congruences
10Euclidean Algorithm
11Extended Euclidean Algorithm
12Bézout's Identity
13Coprimality
14Modular Inverses
15Chinese Remainder Theorem
16Euler's Totient Function
17Order Modulo n
18Fermat's Little Theorem
19Euler's Theorem
20p-adic Valuation
21Lifting the Exponent
22Wilson's Theorem
23Primitive Roots
24Quadratic Residues
25Legendre Symbol
26Euler's Criterion
27Sums of Two Squares
28Quadratic Reciprocity
29Dirichlet's Theorem
30Prime Number Theorem