Datasets:
ksuinbragimova
/
processed_row_tags

Dataset card Data Studio Files
xet
 Community
aops_id
int64
2
3.62M
tags
listlengths
1
62
100,015
[ "lexicographic_order", "combination", "binomial_coefficient" ]
100,019
[ "permutation", "inclusionexclusion_principle", "factorial" ]
1,000,044
[ "probability", "binomial_distribution", "exponentiation", "binomial_coefficient" ]
100,023
[ "geometric_series", "mathematical_induction", "infinite_product", "power_series" ]
100,010
[ "day", "time", "calendars", "word_problem_mathematics", "arithmetic_progression", "modulo", "relative_change", "mathematical_problem" ]
1,000,141
[ "floor_and_ceiling_functions", "mathematics", "linear_equation", "coin_problem", "generating_function" ]
100,009
[ "differentiation_rules", "trigonometric_functions", "square_root", "cosine", "integrals", "sine", "fundamental_theorem_of_calculus", "list_of_trigonometric_identities", "integral" ]
1,000,136
[ "square_root", "quadratic_equation", "quadratic_formula", "algebra", "completing_the_square", "polynomial" ]
100,026
[ "vietas_formulas", "quadratic_equation", "algebra", "polynomial_root_finding", "polynomial" ]
1,000,249
[ "decision_theory", "non_cooperative_games", "nash_equilibrium", "game_theory", "prisoners_dilemma", "expected_value" ]
100,029
[ "inequality_mathematics", "factorial", "amgm_inequality", "amgm_inequality", "mathematical_induction" ]
100,036
[ "infinite_product", "convergence_mathematics", "divergence", "series_mathematics", "sequence", "absolute_value" ]
1,000,379
[ "power_series", "generating_function", "fibonacci_numbers", "series_mathematics", "radius_of_convergence", "mathematical_induction" ]
1,000,306
[ "remainder", "strategy", "sum_of_squares_function", "divisor_function", "modular_arithmetic", "square", "number_theory", "factorization", "combinatorial_game_theory" ]
100,035
[ "eulers_sum_of_powers_conjecture", "exponentiation", "modular_arithmetic", "diophantine_equation", "inequality_mathematics", "fermats_last_theorem", "number_theory" ]
1,000,440
[ "vietas_formulas", "imaginary_unit", "polynomial_long_division", "polynomial", "polynomial_root_finding", "complex_number" ]
100,046
[ "probability", "random_permutation", "event_probability_theory", "permutation", "playing_cards", "playing_cards", "combinatorics", "conditional_probability" ]
100,047
[ "polynomial", "algebra", "fundamental_theorem_of_algebra", "real_number", "root_of_a_function", "polynomial" ]
100,052
[ "sequence", "functional_equation", "integer_sequence", "mathematical_induction", "square_number", "recurrence_relation" ]
100,067
[ "complex_conjugate", "rational_number", "real_number", "minimal_polynomial_linear_algebra", "sequence", "closed_set", "pisotvijayaraghavan_number" ]
100,071
[ "algebraic_identities", "jensens_inequality", "mathematical_proof", "symmetric_function", "inequality_mathematics", "convex_function", "lagrange_multiplier", "second_partial_derivative_test" ]
100,061
[ "interval_mathematics", "trigonometric_functions", "cosine", "derivative", "inverse_function", "equation", "system_of_equations", "function_mathematics", "monotonic_function", "real_number", "sine", "even_and_odd_functions" ]
100,068
[ "mathematical_proof", "integer_sequence", "sequence", "mathematical_induction", "recurrence_relation", "polynomial" ]
100,073
[ "binomial_coefficient", "wolstenholmes_theorem", "elementary_symmetric_polynomial", "modular_arithmetic", "prime_number", "finite_field", "fermats_little_theorem", "polynomial" ]
100,039
[ "probability", "binomial_coefficient", "probability_theory", "combinatorics", "combination" ]
100,076
[ "trigonometric_functions", "cosine", "right_triangle", "geometry", "angle_bisector_theorem", "tangent_half_angle_formula", "triangle", "law_of_cosines" ]
100,079
[ "probability", "binomial_coefficient", "fair_coin", "probability_theory", "combinatorics", "binomial_distribution" ]
100,075
[ "symmetric_matrix", "projection_linear_algebra", "hilbert_space", "orthogonal_transformation", "eigenvalues_and_eigenvectors", "matrix_norm" ]
100,074
[ "almost_everywhere", "dominated_convergence_theorem", "lp_space", "fatous_lemma", "functional_analysis", "measure_theory", "norm_mathematics", "pointwise_convergence", "positive_and_negative_parts" ]
100,090
[ "interior_topology", "countable_set", "cantor_set", "rational_number", "closed_set", "open_set", "number_line" ]
100,101
[ "integer", "divisibility_rule", "arithmetic_progression", "multiple_mathematics", "natural_number", "repdigit", "number_theory" ]
100,114
[ "jensens_inequality", "mathematical_proof", "real_number", "inequality_mathematics", "concave_function" ]
100,130
[ "exponentiation", "inverse_function", "algebra", "power_law", "inequality_mathematics", "mathematical_problems" ]
100,133
[ "pythagorean_triple", "arithmetic_progression", "quartic_function", "pythagorean_theorem", "rational_root_theorem", "geometric_progression" ]
100,119
[ "subset_sum_problem", "inequality_mathematics", "algebra", "series_mathematics", "abels_identity", "integer", "sumset", "combinatorics", "injective_function" ]
100,160
[ "diameter", "right_triangle", "power_of_a_point", "triangle_inequality", "hypotenuse", "circumcircle" ]
1,001,481
[ "residue_theorem", "complex_plane", "polynomial_interpolation", "lagrange_polynomial", "complex_analysis", "polynomial_root_finding", "contour_integration", "polynomial", "degree_of_a_polynomial" ]
1,001,633
[ "polynomial_mapping", "jacobian_conjecture", "surjective_function", "polynomial_function", "algebraic_geometry", "finite_field", "complex_coordinate_space", "injective_function", "complex_number" ]
100,202
[ "unit_circle", "homogeneous_function", "limit_mathematics", "multivariable_calculus", "continuity_theory", "polynomial" ]
100,172
[ "rectangle", "domino_tiling", "algebra_and_tiling", "modulo", "combinatorics", "parity_mathematics", "integer_partition", "recurrence_relation" ]
100,173
[ "integer", "modular_arithmetic", "integer", "diophantine_equation", "congruence_relation", "modular_arithmetic", "number_theory", "fourth_power" ]
100,226
[ "sum_of_squares_function", "integer", "quadratic_form", "diophantine_equation", "number_theory", "squares_in_number_theory" ]
1,001,604
[ "polynomial", "divisibility_rule", "root_of_unity", "combinatorics", "cyclotomic_polynomial", "prime_power" ]
1,002,173
[ "algebraic_number", "exponentiation", "equation_solving", "polynomial", "nth_root", "radical_of_an_integer", "chebyshev_polynomials", "root_of_unity", "binomial_theorem", "symmetric_polynomial", "complex_number" ]
100,193
[ "trigonometric_functions", "algebraic_identities", "mathematical_proof", "cosine", "inequality_mathematics", "triangle", "sine", "law_of_cosines", "inequalities_mathematics", "symmetric_polynomial" ]
100,233
[ "pigeonhole_principle" ]
100,235
[ "proof_by_contradiction", "exponentiation", "modular_arithmetic", "division_algorithm", "divisibility_rule", "number_theory" ]
100,255
[ "pigeonhole_principle", "modular_arithmetic", "combinatorics", "number_theory", "congruence_relation" ]
100,250
[ "equation", "logarithm", "algebra", "exponential_function", "exponential_decay" ]
100,241
[ "hexomino", "triangular_number", "tessellation", "polyiamond", "combinatorial_geometry_in_the_plane", "equilateral_triangle", "geometric_dissection" ]
100,229
[ "residue_number_system", "sum_of_squares_function", "divisibility_rule", "digit_sum", "modular_arithmetic", "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", "golden_ratio", "continued_fraction" ]
100,274
[ "divisor", "mersenne_prime", "prime_number", "euclideuler_theorem", "number_theory", "perfect_number" ]
100,259
[ "remainder", "polynomial", "polynomial_long_division", "interpolation", "polynomial_remainder_theorem" ]
1,002,802
[ "power_set", "binomial_coefficient", "set_mathematics", "mathematical_induction", "union_set_theory", "expected_value" ]
100,277
[ "polynomial_root_finding", "triangle_inequality", "complex_analysis", "inequality_mathematics", "polynomial", "absolute_value", "complex_number" ]
1,002,828
[ "integer", "factorial", "geometric_series", "generating_function", "natural_number", "series_mathematics", "multinomial_theorem" ]
1,002,871
[ "binomial_coefficient", "summation", "arithmetic_mean", "exponentiation", "binomial_theorem", "inequality_mathematics" ]
100,287
[ "jensens_inequality", "logarithm", "real_number", "inequality_mathematics", "convex_function" ]
1,002,900
[ "sequence", "floor_and_ceiling_functions", "inequality_mathematics", "mathematical_analysis", "proof_by_contradiction", "functional_equation", "riemann_zeta_function", "natural_number", "mathematical_induction" ]
100,294
[ "mathematical_proof", "summation", "harmonic", "series_mathematics", "inequality_mathematics", "sequence" ]
100,297
[ "fundamental_theorem_of_arithmetic", "function_mathematics", "multiplicative_function", "prime_number", "unique_factorization_domain", "natural_number" ]
100,299
[ "polynomial", "inequality_mathematics", "mathematical_proof", "unit_circle", "complex_plane", "root_of_unity", "polynomial", "triangle_inequality", "limit_of_a_sequence", "rotation", "absolute_value", "complex_number" ]
1,002,990
[ "integer", "binomial_coefficient", "permutation", "divisibility_rule", "cyclic_group", "necklace_combinatorics", "combinatorics", "greatest_common_divisor" ]
1,002,911
[ "tuple", "integer", "pigeonhole_principle", "proof_truth", "summation", "integer_sequence", "mathematical_induction", "greatest_common_divisor", "difference_of_two_squares" ]
1,002,943
[ "square", "point_geometry", "rectangle", "acute_and_obtuse_triangles", "pigeonhole_principle", "cyclic_quadrilateral", "planes_geometry", "rhombus", "distance", "angle", "similarity_system_of_triangles", "equilateral_triangle", "quadrilateral", "circle", "perpendicular_bisector", "para...
100,300
[ "square", "similarity_system_of_triangles", "power_of_a_point", "triangle", "chord_geometry", "circumcircle" ]
1,002,994
[ "chinese_remainder_theorem", "integer", "dirichlets_theorem_on_arithmetic_progressions", "legendre_symbol", "modular_arithmetic", "arithmetic_progression", "prime_number", "square", "square_free_integer", "natural_number", "quadratic_residue", "quadratic_reciprocity", "congruence_relation" ]
1,003,005
[ "square", "similarity_system_of_triangles", "straightedge_and_compass_construction", "perpendicular", "cyclic_quadrilateral", "angle", "triangle", "altitude", "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", "combinatorics", "mathematical_induction", "binomial_distribution", "geometric_distribution" ]
1,003,040
[ "muirheads_inequality", "area_of_a_triangle", "schurs_inequality", "circumradius", "triangle_inequality", "feuerbach_point", "amgm_inequality", "triangle", "nine_point_circle", "inequality_mathematics", "substitution_method", "inradius" ]
100,332
[ "square_root", "integer", "floor_and_ceiling_functions", "real_number", "inequality_mathematics", "piecewise_function" ]
100,336
[ "modular_arithmetic", "divisibility_rule", "prime_number", "diophantine_equation", "natural_number", "number_theory", "greatest_common_divisor" ]
100,318
[ "concyclic_points", "radical_axis", "euclidean_geometry", "angle_bisector_theorem", "incenter", "central_angle", "triangle", "inscribed_angle", "tangent", "circumcircle", "orthocenter", "circumcenter", "isosceles_triangle" ]
10,035
[ "divide_and_conquer_algorithm", "binary_search", "information_theory", "combinatorial_search", "decision_tree", "weighing_scales", "weighing_scales" ]
100,350
[ "pedal_triangle", "perpendicular", "concurrent_lines", "orthogonal_transformation", "triangle", "isogonal_conjugate", "circle", "circumcircle" ]
100,340
[ "determinant", "complex_plane", "perpendicular", "excenter", "concurrent_lines", "symmetry_geometry", "foot_of_a_perpendicular", "cevas_theorem", "triangle", "geometry", "incircle_and_excircles", "altitude", "circumcircle", "orthocenter", "complex_number" ]
1,003,750
[ "integrals", "algebra", "binomial_theorem", "power_rule", "integral", "polynomial" ]
100,370
[ "complex_plane", "absolute_value", "pythagorean_theorem", "complex_number" ]
1,003,681
[ "integer", "exponentiation", "function_mathematics", "divisibility_rule", "prime_number", "diophantine_equation", "natural_number", "number_theory" ]
1,003,591
[ "dilation_operator_theory", "centrosymmetry", "polygon", "center_of_mass", "area", "parallel_geometry", "continuity_theory", "line_geometry", "reflection_mathematics" ]
1,003,557
[ "integer", "combinatorial_proof", "binomial_coefficient", "summation", "enumerative_combinatorics", "mathematical_induction", "binomial_theorem", "combinatorial_number_system", "binomial_coefficient", "combinatorics", "counting", "a_group", "binomial_distribution" ]
100,382
[ "line_integral", "complex_plane", "entire_function", "moreras_theorem", "sine", "complex_analysis", "fubinis_theorem", "integral" ]
100,378
[ "algebraic_number", "recurrence_relation", "integer", "fundamental_solution", "diophantine_equation", "integer", "square_number", "pells_equation" ]
100,383
[ "sequence", "derivative", "borels_theorem", "real_number", "differentiable_function" ]
1,003,940
[ "clock_angle_problem", "degree_angle", "angle" ]
100,386
[ "liouvilles_theorem_complex_analysis", "complex_plane", "entire_function", "maximum_modulus_principle", "compact_space" ]
100,388
[ "cauchyschwarz_inequality", "inequality_mathematics", "positive_real_numbers", "amgm_inequality", "inequality_mathematics", "symmetric_polynomial" ]
100,394
[ "square_root", "jensens_inequality", "inequality_mathematics", "mathematical_proof", "logarithm", "positive_real_numbers", "amgm_inequality", "convex_function" ]
1,004,076
[ "transitive_relation", "conversion_of_units", "ratio", "equation" ]
1,004,096
[ "inclusionexclusion_principle", "indian_buffet_process", "set_theory", "venn_diagram" ]
1,004,058
[ "arithmetic", "geometric_series", "geometric_series", "ratio", "series_mathematics" ]
100,413
[ "interval_mathematics", "riemann_integral", "zero_function", "integrals", "darboux_integral", "continuous_function", "real_analysis", "fundamental_theorem_of_calculus", "integral" ]
100,419
[ "square_root", "mathematical_proof", "algebra", "amgm_inequality", "real_number", "inequality_mathematics" ]
100,415
[ "identity_element", "dihedral_group", "order_group_theory", "group_theory", "direct_product_of_groups", "cyclic_group", "group_mathematics" ]
100,428
[ "infinite_product", "convergence_mathematics", "exponentiation", "decimal_floating_point", "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", "bernoullis_inequality" ]