Datasets:
ksuinbragimova
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row_tags

Dataset card Data Studio Files
xet
 Community
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aops_id
int64
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3.62M
tags
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74
100,015
[ "Alphabetical order", "Combination", "Binomial coefficient", "License plate" ]
100,019
[ "Permutation", "Inclusion–exclusion principle", "Factorial" ]
1,000,044
[ "Probability", "Binomial distribution", "Exponentiation", "Binomial coefficient" ]
100,023
[ "Geometric series", "Mathematical induction", "Infinite product", "Power series" ]
100,010
[ "Snail", "Day of the week", "Date and time", "Calendar", "Word problem", "Arithmetic progression", "Modulo operation", "Rate of change", "Problem solving" ]
1,000,141
[ "Nickel (United States coin)", "Floor function", "Dime", "Casework (mathematics)", "Penny (United States coin)", "Quarter (United States coin)", "Linear equation", "Coin problem", "Generating function" ]
100,009
[ "Differentiation", "Trigonometric functions", "Square root", "Cosine", "Definite integral", "Sine", "Fundamental theorem of calculus", "Trigonometric identities", "Integral" ]
1,000,136
[ "Square root", "Quadratic equation", "Quadratic formula", "Algebra", "Completing the square", "Polynomial" ]
100,026
[ "Vieta's formulas", "Quadratic equation", "Algebra", "Root of a polynomial", "Polynomial" ]
1,000,249
[ "Decision theory", "Non-cooperative game", "Dominant strategy", "Nash equilibrium", "Game theory", "Prisoner's dilemma", "Expected value" ]
100,029
[ "Inequality", "Factorial", "Arithmetic mean–geometric mean inequality", "AM–GM inequality", "Mathematical induction" ]
100,036
[ "Infinite product", "Convergence (mathematics)", "Divergence (mathematics)", "Infinite series", "Sequence (mathematics)", "Absolute value" ]
1,000,379
[ "Power series", "Generating function", "Fibonacci number", "Infinite series", "Radius of convergence", "Induction (mathematics)" ]
1,000,306
[ "Remainder", "Winning strategy", "Sum of squares", "Divisor function", "Modular arithmetic", "Perfect square", "Locker problem", "Number theory", "Factorization", "Combinatorial game theory" ]
100,035
[ "Euler's sum of powers conjecture", "Exponents", "Modular arithmetic", "Diophantine equation", "Inequality (mathematics)", "Fermat's Last Theorem", "Number theory" ]
1,000,440
[ "Vieta's formulas", "Imaginary unit", "Polynomial division", "Polynomial", "Root of a polynomial", "Complex number" ]
100,046
[ "Probability", "Random permutation", "Event (probability theory)", "Permutation", "Deck of cards", "Playing card", "Combinatorics", "Conditional probability" ]
100,047
[ "Polynomial equation", "SAT Subject Tests", "Algebra", "Fundamental theorem of algebra", "TI-83", "Real number", "Root of a function", "Polynomial" ]
100,052
[ "Sequence", "Functional equation", "Integer sequence", "Mathematical induction", "Square number", "Recurrence relation" ]
100,067
[ "Algebraic conjugate", "Rational number", "Real number", "Minimal polynomial", "Sequence (mathematics)", "Closed set", "Pisot number" ]
100,071
[ "Algebraic identity", "Jensen's inequality", "Mathematical proof", "Symmetric function", "Inequality (mathematics)", "Convex function", "Lagrange multipliers", "Second derivative test" ]
100,061
[ "Interval (mathematics)", "Trigonometric functions", "Cosine", "Derivative", "Inverse function", "Equation", "System of equations", "Function (mathematics)", "Monotonic function", "Real number", "Sine", "Odd function" ]
100,068
[ "Proof (mathematics)", "Integer sequence", "Sequence (mathematics)", "Mathematical induction", "Recurrence relation", "Polynomial" ]
100,073
[ "Binomial coefficient", "Wolstenholme's theorem", "Elementary symmetric polynomial", "Modular arithmetic", "Prime number", "Finite field", "Fermat's little theorem", "Polynomial" ]
100,039
[ "Probability", "Binomial coefficient", "Probability theory", "Combinatorics", "Combination" ]
100,076
[ "Trigonometric functions", "Cosine", "Right triangle", "Geometry", "Angle bisector", "Half-angle formula", "Triangle", "Law of cosines" ]
100,079
[ "Probability", "Binomial coefficient", "Fair coin", "Probability theory", "Combinatorics", "Binomial distribution" ]
100,075
[ "Positive-semidefinite matrix", "Real symmetric matrix", "Projection (linear algebra)", "Non-negative definite matrix", "Hilbert space", "Orthogonal projection", "Eigenvalues and eigenvectors", "Matrix norm", "Frobenius norm" ]
100,074
[ "Almost everywhere", "Dominated convergence theorem", "Lp space", "Fatou's lemma", "Convergence in norm", "Functional analysis", "Measure theory", "Real part and imaginary part", "Norm (mathematics)", "Pointwise convergence", "Positive and negative parts of a function" ]
100,090
[ "Interior (topology)", "Countable set", "Measure zero", "Cantor set", "Rational number", "Closed set", "Open interval", "Real number line" ]
100,101
[ "Integer", "Divisibility rule", "Arithmetic progression", "Multiple (mathematics)", "Natural number", "Repdigit", "Number theory" ]
100,114
[ "Jensen's inequality", "Mathematical proof", "Real number", "Cyclic sum", "Inequality (mathematics)", "Concave function" ]
100,130
[ "Exponents", "Inverse function", "Algebra", "Power law", "Inequality (mathematics)", "Mathematical problem solving" ]
100,133
[ "Pythagorean triple", "Arithmetic progression", "Quartic function", "Pythagorean theorem", "Rational root theorem", "Geometric progression" ]
100,119
[ "Subset sum problem", "Inequality", "Algebra", "Partial sum", "Abel's identity", "Positive integer", "Sumset", "Combinatorics", "Injective function" ]
100,160
[ "Diameter (geometry)", "Right triangle", "Power of a point", "Triangle inequality", "Hypotenuse", "Circumcircle" ]
1,001,481
[ "Residue theorem", "Complex plane", "Polynomial interpolation", "Lagrange polynomial", "Complex analysis", "Root of a polynomial", "Contour integral", "Polynomial", "Degree of a polynomial" ]
1,001,633
[ "Polynomial map", "Jacobian conjecture", "Surjective function", "Polynomial function", "Algebraic geometry", "Finite field", "Complex Euclidean space", "Injective function", "Complex number" ]
100,202
[ "Unit circle", "Homogeneous function", "Limit (mathematics)", "Multivariable calculus", "Continuity", "Polynomial" ]
100,172
[ "Rectangle", "Domino tiling", "Tiling (mathematics)", "Modulo operation", "Combinatorics", "Parity (mathematics)", "Integer partition", "Recurrence relation" ]
100,173
[ "Non-negative integer", "Modular arithmetic", "Integer solution", "Diophantine equation", "Congruence (number theory)", "Modular arithmetic properties", "Number theory", "Fourth power" ]
100,226
[ "Sum of squares", "Integer solution", "Quadratic form", "Diophantine equation", "Number theory", "Representation of numbers as sums of squares" ]
1,001,604
[ "Polynomial (mathematics)", "Divisibility", "Primitive root of unity", "Combinatorics", "Cyclotomic polynomial", "Prime power" ]
1,002,173
[ "Algebraic number", "Exponents", "Equation solving", "Polynomial equation", "Surd", "Radical (mathematics)", "Chebyshev polynomials", "Root of unity", "Binomial theorem", "Symmetric polynomial", "Complex number" ]
100,193
[ "Trigonometric functions", "Algebraic identity", "Mathematical proof", "Cosine", "Inequality (mathematics)", "Triangle", "Sine", "Law of cosines", "Cyclic sum", "Inequalities in mathematics", "Symmetric polynomial" ]
100,233
[ "Pigeonhole principle" ]
100,235
[ "Proof by contradiction", "Exponentiation", "Modular arithmetic", "Division algorithm", "Divisibility", "Number theory" ]
100,255
[ "Pigeonhole principle", "Modular arithmetic", "Combinatorics", "Number theory", "Congruence (mathematics)" ]
100,250
[ "Half-life", "Equation", "Logarithm", "Algebra", "Exponential function", "Exponential decay" ]
100,241
[ "Hexomino", "Triangular number", "Tessellation", "Polyiamond", "Combinatorial geometry", "Equilateral triangle", "Mathematical tiling", "Geometric dissection" ]
100,229
[ "Residue class", "Sum of squares function", "Divisibility rule", "Digit sum", "Modular arithmetic", "Integer square", "Quadratic residue", "Sum of two squares theorem", "Number theory" ]
100,257
[ "Euclidean algorithm", "Irrational number", "Pi", "Rational number", "Real number", "Limit of a sequence", "Sequence (mathematics)", "Golden ratio", "Continued fraction" ]
100,274
[ "Divisor", "Mersenne prime", "Prime number", "Euclid–Euler theorem", "Number theory", "Perfect number" ]
100,259
[ "Remainder (polynomial)", "Polynomial (mathematics)", "Polynomial division", "Lagrange interpolation", "Polynomial remainder theorem" ]
1,002,802
[ "Power set", "Binomial coefficient", "Set (mathematics)", "Strong induction", "Union (set theory)", "Expected value" ]
100,277
[ "Polynomial root", "Triangle inequality", "Complex analysis", "Inequality (mathematics)", "Polynomial", "Absolute value", "Complex number" ]
1,002,828
[ "Non-negative integer", "Factorial", "Geometric series", "Generating function", "Natural number", "Infinite series", "Multinomial theorem" ]
1,002,871
[ "Binomial coefficient", "Summation", "Arithmetic mean", "Exponentiation", "Binomial theorem", "Inequality (mathematics)" ]
100,287
[ "Jensen's inequality", "Logarithm", "Real number", "Inequality (mathematics)", "Convex function" ]
1,002,900
[ "Sequence", "Floor function", "Inequality", "Mathematical analysis", "Proof by contradiction", "Functional equation", "Riemann zeta function", "Natural number", "Mathematical induction" ]
100,294
[ "Mathematical proof", "Summation", "Harmonic series", "Infinite series", "Inequality (mathematics)", "Sequence (mathematics)" ]
100,297
[ "Fundamental theorem of arithmetic", "Function (mathematics)", "Multiplicative function", "Prime number", "Unique factorization domain", "Natural number" ]
100,299
[ "Complex polynomial", "Inequality", "Mathematical proof", "Unit circle", "Complex plane", "Root of unity", "Polynomial (mathematics)", "Triangle inequality", "Limit of a sequence", "Rotation (mathematics)", "Absolute value", "Complex number" ]
1,002,990
[ "Integer", "Binomial coefficient", "Permutation", "Divisibility (mathematics)", "Cyclic group", "Necklace (combinatorics)", "Combinatorics", "Greatest common divisor" ]
1,002,911
[ "Tuple", "Integer", "Pigeonhole principle", "Proof", "Summation", "Integer sequence", "International Mathematical Olympiad", "Mathematical induction", "Greatest common divisor", "Difference (mathematics)" ]
1,002,943
[ "Square (geometry)", "Point (geometry)", "Rectangle", "Obtuse angle", "Pigeonhole principle", "Cyclic quadrilateral", "Plane (geometry)", "Rhombus", "Distance", "Angle", "Triangle similarity", "Equilateral triangle", "Quadrilateral", "Circle (geometry)", "Perpendicular bisector", "Para...
100,300
[ "Square (geometry)", "Similar triangles", "Power of a point", "Triangle", "Chord (geometry)", "Circumcircle" ]
1,002,994
[ "Chinese remainder theorem", "Integer", "Dirichlet's theorem on arithmetic progressions", "Quadratic nonresidue", "Legendre symbol", "Modular arithmetic", "Arithmetic progression", "Prime number", "Perfect square", "Squarefree integer", "Natural number", "Quadratic residue", "Law of quadrati...
1,003,005
[ "Square (geometry)", "Similar triangles", "Straightedge and compass construction", "Perpendicular", "Cyclic quadrilateral", "Angle", "Triangle", "Altitude (triangle)", "Orthocenter" ]
1,003,043
[ "Functional equation", "Function (mathematics)", "Contradiction", "Real number", "Cubic function" ]
1,003,111
[ "Transposition (mathematics)", "Permutation", "Triangle", "Area", "Inequality (mathematics)", "Combinatorics", "Quadrilateral" ]
10,032
[ "Probability", "Binomial coefficient", "Playoff (sports)", "Combinatorics", "Mathematical induction", "Binomial distribution", "Geometric distribution" ]
1,003,040
[ "Muirhead inequality", "Area of a triangle", "Schur's inequality", "Circumradius", "Feuerbach's theorem", "Triangle inequality", "Feuerbach point", "Arithmetic mean–geometric mean inequality", "Triangle", "Nine-point circle", "Inequality (mathematics)", "Substitution (mathematics)", "Inradiu...
100,332
[ "Square root", "Integer", "Floor function", "Real number", "Inequality (mathematics)", "Piecewise function" ]
100,336
[ "Modular arithmetic", "Divisibility", "Prime number", "Diophantine equation", "Natural number", "Number theory", "Greatest common divisor" ]
100,318
[ "Concyclic points", "Radical axis (geometry)", "Euclidean geometry", "Angle bisector", "Incenter", "Central angle", "Triangle", "Inscribed angle", "Tangent line", "Circumcircle", "Orthocenter", "Circumcenter", "Isosceles triangle" ]
10,035
[ "Divide and conquer algorithm", "Binary search algorithm", "Information theory", "Combinatorial search", "Decision tree", "Weighing scale", "Coin weighing problem", "Balance scale" ]
100,350
[ "Pedal triangle", "Perpendicular", "Concurrency (geometry)", "Orthogonal projection", "Triangle", "Isogonal conjugate", "Circle (geometry)", "Circumcircle" ]
100,340
[ "Determinant", "Complex plane", "Perpendicular (geometry)", "Excenter", "Concurrent lines", "Symmetry (geometry)", "Foot of perpendicular", "Ceva's theorem", "Triangle", "Geometric proof", "Excircle", "Altitude (triangle)", "Circumcircle", "Orthic triangle", "Complex number" ]
1,003,750
[ "Definite integral", "Algebra", "Binomial theorem", "Power rule for integration", "Integral", "Polynomial" ]
100,370
[ "Complex plane", "Absolute value", "Pythagorean theorem", "Complex number" ]
1,003,681
[ "Integer", "Exponentiation", "Function (mathematics)", "Divisibility", "Prime number", "Diophantine equation", "Natural number", "Number theory" ]
1,003,591
[ "Dilation (mathematics)", "Central symmetry", "Polygon", "Center of mass", "Area", "Parallel (geometry)", "Continuity", "Line (geometry)", "Reflection (mathematics)" ]
1,003,557
[ "Integer", "Combinatorial proof", "Binomial coefficient", "Summation", "Combinatorial enumeration", "Mathematical induction", "Binomial identity", "Binomial theorem", "Combinatorial number system", "Binomial coefficient#Identities", "Combinatorics", "Counting", "Committee (disambiguation)", ...
100,382
[ "Line integral", "Complex plane", "Entire function", "Morera's theorem", "Sine", "Complex analysis", "Fubini's theorem", "Integral" ]
100,378
[ "Algebraic number", "Recurrence relation", "Integer solution", "Fundamental solution (Pell's equation)", "Diophantine equation", "Positive integer", "Square number", "Pell's equation" ]
100,383
[ "Sequence", "Derivative", "Borel's theorem", "Real number", "Infinitely differentiable function" ]
1,003,940
[ "Minute hand", "Clock angle problem", "Degree (angle)", "Hour hand", "Angle" ]
100,386
[ "Liouville's theorem (complex analysis)", "Complex plane", "Entire function", "Maximum modulus principle", "Compact space" ]
100,388
[ "Cauchy–Schwarz inequality", "Algebraic inequality", "Positive real numbers", "AM–GM inequality", "Inequality (mathematics)", "Symmetric polynomial" ]
100,394
[ "Square root", "Jensen's inequality", "Inequality", "Mathematical proof", "Logarithm", "Positive real numbers", "Arithmetic mean–geometric mean inequality", "Convex function" ]
1,004,076
[ "Transitive property", "Unit conversion", "Ratio", "Equation" ]
1,004,096
[ "Inclusion–exclusion principle", "Buffet", "Set theory", "Venn diagram" ]
1,004,058
[ "Arithmetic operations", "Sum of a geometric series", "Geometric series", "Common ratio", "Infinite series" ]
100,413
[ "Interval (mathematics)", "Riemann integral", "Identically zero function", "Definite integral", "Darboux integral", "Continuous function", "Real analysis", "Fundamental theorem of calculus", "Integral", "Non-negative function" ]
100,419
[ "Square root", "Mathematical proof", "Algebra", "Arithmetic mean–geometric mean inequality", "Real number", "Inequality (mathematics)" ]
100,415
[ "Identity element", "Dihedral group", "Order of an element", "Group order", "Conjugation (group theory)", "Direct product of groups", "Cyclic group", "Group (mathematics)" ]
100,428
[ "Infinite product", "Convergence (mathematics)", "Exponentiation", "Decimal representation", "Real number", "Limit of a sequence", "Mathematical induction" ]
1,004,329
[ "Natural number", "Irreducible fraction", "Greatest common divisor", "Euclidean algorithm" ]
100,434
[ "Mathematical proof", "Exponential function", "Real number", "Inequality (mathematics)", "Bernoulli's inequality" ]