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119 lines
No EOL
7.9 KiB
JSON
119 lines
No EOL
7.9 KiB
JSON
{
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"Topology": null,
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"Space-filling_curves_and_the_relationship_between_infinite_and_finite_mathematics": null,
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"The_inscribed_square_or_rectangle_problem_in_topology": null,
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"Planar_graph_duality_and_Eulers_Characteristic_Formula": null,
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"The_Borsuk-Ulam_theorem_and_stolen_necklace_problem": null,
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"Space-filling_curves": null,
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"Fractal_dimension": null,
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"Linear_transformations_and_matrices": null,
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"Cross_products_and_their_relationship_to_geometric_intuition_and_linear_transformations": null,
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"Geometric_interpretation_of_non-square_matrices_as_transformations_between_dimensions": null,
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"Eigenvectors_eigenvalues_and_eigenbasis": null,
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"Change_of_basis": null,
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"Basics_of_linear_algebra_and_vectors": null,
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"Dot_products_and_duality": "Dot_products_and_duality.jpg",
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"Three-dimensional_linear_transformations": null,
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"Geometric_interpretation_of_linear_systems_inverse_matrices_column_space_and_null_space": null,
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"Abstract_vector_spaces": null,
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"Superposition_and_quantum_states_in_quantum_mechanics": "Superposition_and_quantum_states_in_quantum_mechanics.jpg",
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"Matrix_multiplication_as_composition_of_linear_transformations": null,
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"Geometric_intuition_in_linear_algebra": null,
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"The_determinant": null,
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"Eigenvalues_of_2x2_matrices": null,
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"Span_linear_combinations_linear_dependence_and_bases": null,
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"History_and_definition_of_π": "History_and_definition_of_π.jpg",
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"Eulers_formula_and_e{pi_i}_=_-1": "Eulers_formula_and_e{pi_i}_=_-1.jpg",
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"Riemann_zeta_function": "Riemann_zeta_function.jpg",
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"Numerical_algorithms_for_solving_2D_equations_winding_numbers_and_domain_coloring": "Numerical_algorithms_for_solving_2D_equations_winding_numbers_and_domain_coloring.jpg",
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"Uncertainty_Principle_in_the_Context_of_Fourier_Transforms": "Uncertainty_Principle_in_the_Context_of_Fourier_Transforms.jpg",
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"Infinite_sums_convergence_and_divergence_2-adic_metric_in_mathematics": null,
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"Eulers_Formula_and_eπi_=_-1": "Eulers_Formula_and_eπi_=_-1.jpg",
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"Holomorphic_dynamics_and_iterated_complex_functions": "Holomorphic_dynamics_and_iterated_complex_functions.jpg",
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"Basel_problem_and_its_geometric_proof": null,
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"Origin_of_π_in_the_normal_distribution_and_the_Gaussian_integral": "Origin_of_π_in_the_normal_distribution_and_the_Gaussian_integral.jpg",
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"Pure_Fourier_series": "Pure_Fourier_series.jpg",
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"Prime_patterns_pi_approximations_and_Dirichlets_theorem": "Prime_patterns_pi_approximations_and_Dirichlets_theorem.jpg",
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"Alternate_notation_for_powers_logarithms_and_roots": "Alternate_notation_for_powers_logarithms_and_roots.jpg",
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"Interconnections_in_number_theory_π_primes_complex_numbers_and_prime_regularities": null,
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"Newtons_method_and_Newtons_fractal_in_root-finding": "Newtons_method_and_Newtons_fractal_in_root-finding.jpg",
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"Eulers_formula_e{iπ}": "Eulers_formula_e{iπ}.jpg",
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"Fourier_Transform": "Fourier_Transform.jpg",
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"Fourier_series_and_their_connection_to_the_heat_equation_and_circular_representations": "Fourier_series_and_their_connection_to_the_heat_equation_and_circular_representations.jpg",
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"Central_Limit_Theorem": "Central_Limit_Theorem.png",
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"Bayes_theorem_and_the_geometry_of_changing_probabilistic_beliefs": "Bayes_theorem_and_the_geometry_of_changing_probabilistic_beliefs.jpg",
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"Information_theory_and_entropy_in_solving_Wordle": null,
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"Binomial_distributions": "Binomial_distributions.png",
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"256-bit_hash_security": null,
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"Likelihood_Ratios_and_Bayes_Factors_in_Medical_Testing": null,
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"Bayes_theorem_and_independence_in_probability": "Bayes_theorem_and_independence_in_probability.png",
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"Sum_of_normal_distributions_Gaussian_+_Gaussian_=_Gaussian": null,
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"Adding_Random_Variables_and_Convolution_in_Probability": null,
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"Probability_density_functions": null,
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"Intuition_for_eπi_=_-1_using_group_theory_and_Eulers_formula": null,
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"Exponential_growth_and_logistic_growth": null,
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"SIR_models_and_epidemic_simulation": null,
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"DP-3T_algorithm_for_contact_tracing": null,
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"Attention_mechanism_in_transformers_and_large_language_models": null,
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"Neural_networks_structure_neurons_layers_underlying_mathematics": null,
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"How_multilayer_perceptrons_in_transformers_may_store_facts": null,
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"Neural_network_learning_and_intuitive_backpropagation": null,
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"Discrete_convolutions_and_their_applications": null,
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"Cost_functions_and_gradient_descent_in_neural_network_training": null,
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"Large_Language_Models_and_Transformers_in_Deep_Learning": null,
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"Backpropagation_calculus": null,
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"Diffusion_models_CLIP_and_the_mathematics_of_text-to-image_generation_in_AI": null,
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"Mathematical_principles_of_cryptocurrencies_and_Bitcoin": null,
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"Qubits_state_vectors_and_Grovers_algorithm_in_quantum_computing": null,
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"Error_correction_codes_and_Hamming_codes": null,
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"Hamming_error_correction_codes": null,
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"Large_Language_Models": null,
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"Ternary_counting_constrained_Towers_of_Hanoi_and_Sierpinski_triangle_graph_traversal": null,
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"High-dimensional_spheres": null,
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"Grovers_algorithm_in_quantum_computing": null,
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"The_Brachistochrone_Problem": null,
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"Binary_counting_and_its_application_to_the_Towers_of_Hanoi_puzzle": null,
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"Criteria_for_effective_mathematical_explanation": null,
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"Optimal_Wordle_starting_strategies_and_algorithmic_analysis": null,
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"Generating_functions_and_complex_numbers_in_combinatorial_counting": null,
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"Impossible_chessboard_puzzle_and_information_theory": null,
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"Music_and_Measure_Theory": null,
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"Mosers_circle_problem": null,
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"Putnam_mathematics_competition_problem-solving": null,
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"Geometry_puzzles_involving_dimensional_shifts": null,
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"Dandelin_spheres_and_conic_sections": "Dandelin_spheres_and_conic_sections.jpg",
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"Windmill_problem": null,
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"Cross_products_in_2D_and_3D": null,
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"Pythagorean_triples_and_their_connection_to_complex_numbers": null,
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"Wallis_product_for_pi": null,
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"Sphere_surface_area_and_its_relationship_to_projected_shadow": null,
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"How_wiggling_charges_give_rise_to_light_and_the_barber_pole_effect": "How_wiggling_charges_give_rise_to_light_and_the_barber_pole_effect.png",
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"Fundamental_constants_and_mathematical_structure_in_turbulence": null,
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"Proof_of_Snells_law": "Proof_of_Snells_law.png",
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"Refraction_and_the_behavior_of_light_in_different_media": "Refraction_and_the_behavior_of_light_in_different_media.png",
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"Block_collision_problem_and_its_relation_to_calculating_digits_of_pi": null,
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"Origin_and_color_dependence_of_the_index_of_refraction": "Origin_and_color_dependence_of_the_index_of_refraction.png",
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"The_physics_of_pi_arising_from_colliding_blocks": null,
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"Barber_pole_effect_with_polarized_light_in_sugar_water": null,
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"Unexpected_answer_to_a_counting_puzzle_involving_collisions_and_pi": null,
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"Principles_of_Holography_and_Diffraction": null,
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"Partial_differential_equations": null,
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"Boundary_conditions_and_Fourier_series_in_solving_the_heat_equation": null,
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"Ordinary_Differential_Equations": null,
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"Matrix_exponentials": null,
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"The_essence_of_calculus": "The_essence_of_calculus.jpg",
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"Implicit_differentiation": null,
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"Borwein_integrals_and_their_surprising_patterns": "Borwein_integrals_and_their_surprising_patterns.jpg",
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"Limits_LHpitals_rule_and_epsilon-delta_definitions": null,
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"Higher_order_derivatives": null,
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"Transformational_view_of_derivatives": null,
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"Instantaneous_rate_of_change_and_the_derivative": null,
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"Chain_rule_and_product_rule_in_calculus": null,
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"Divergence_and_curl_in_vector_calculus": null,
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"Taylor_polynomials_and_Taylor_series": null,
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"Relationship_between_integrals_and_derivatives": "Relationship_between_integrals_and_derivatives.jpg",
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"Derivative_formulas_and_geometric_intuition": null,
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"Eulers_number_e_and_exponential_functions_in_calculus": null,
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"Cramers_rule_explained_geometrically": null,
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"Integration_the_Fundamental_Theorem_of_Calculus_and_the_inverse_relationship_between_integrals_and_derivatives": "Integration_the_Fundamental_Theorem_of_Calculus_and_the_inverse_relationship_between_integrals_and_derivatives.jpg"
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} |