Update index.md

Author: mtian8

docs/index.md

@@ -69,7 +69,7 @@ SciCode sources challenging and realistic research-level coding problems across
 
 | **Fields**           | **Subfields**                                                                                                 |
 |----------------------|---------------------------------------------------------------------------------------------------------------|
-| **Mathematics**      | [Numerical Linear Algebra](#numerical-linear-algebra) (7), [Computational Mechanics](#computational-mechanics) (6), [Computational Finance](#computational-finance) (1) |
+| **Mathematics**      | [Numerical Linear Algebra](#numerical-linear-algebra) (8), [Computational Mechanics](#computational-mechanics) (5), [Computational Finance](#computational-finance) (1) |
 | **Physics**          | [Condensed Matter Physics](#condensed-matter-physics) (13), [Optics](#optics) (10), [Quantum Information/Computing](#quantum-informationcomputing) (6), [Computational Physics](#computational-physics) (5), [Astrophysics](#astrophysics) (2), [Particle Physics](#particle-physics) (1) |
 | **Chemistry**        | [Quantum Chemistry](#quantum-chemistry) (5), [Computational Chemistry](#computational-chemistry) (3)          |
 | **Biology**          | [Ecology](#ecology) (6), [Biochemistry](#biochemistry) (1), [Genetics](#genetics) (1)                         |
@@ -78,90 +78,143 @@ SciCode sources challenging and realistic research-level coding problems across
 Nobel prized related problems:
 
 ### Numerical Linear Algebra
-1_CG
+1_Conjugate_Gradient
+
 3_Gauss_Seidel
-4_IncomChol
+
+4_Incomplete_Cholesky
+
 5_Lanczos
+
 9_Weighted_Jacobi
+
 29_Gram_Schmidt_orthogonalization
+
 31_independent_component_analysis
+
 74_Householder_QR
+
 ### Computational Mechanics
 18_NURBS
+
 24_Burgers_equation
+
 40_Spliting_Operator
+
 54_SUPG
+
 78_Chaotic_Dynamics_Pendulum
 
 ### Computational Finance
 63_Estimating_Stock_Option_Price
 
 ### Condensed Matter Physics
 17_linear_tetrahedron_method
+
 20_phonon_angular_momentum
+
 33_phase_diagram_chern_haldane_model
+
 38_Reciprocal_lattice_vector
+
 48_MEELS_conversion
+
 50_Replica_symmetry_breaking
+
 62_dmrg
+
 67_LEG_Dyson_equation_bulk
+
 69_LEG_Dyson_equation_semi_infinite
+
 72_ising_model
+
 73_Xray_conversion_II
+
 75_graphene_tight_binding
 
 ### Optics
 2_Gaussian_Beam_Focus
+
 6_Spatial_filters_I
+
 7_Spatial_filters_II
+
 8_Spatial_filters_III
+
 14_Brownian_motion_in_the_optical_tweezer
+
 22_Beam_translation_reexpansion
+
 28_Gaussian_Beam_Intensity
+
 32_Multiparticle_dynamics_in_the_optical_tweezer_array
+
 37_ray_optics_spherical_aberration
+
 43_two_end_fiber_laser_generator
 
 ### Quantum Information/Computing
 11_GADC_entanglement
+
 19_n_tangle
+
 23_Blahut_Arimoto
+
 59_VQE
+
 65_GHZ_protocol_fidelity
+
 71_GADC_rev_coherent_info
 
 ### Computational Physics
 13_Maxwell_Equation_Solver
+
 15_Crank_Nicolson_for_time_dependent_Schrodinger
+
 45_finite_difference_heat_equation
+
 52_Shooting_algo_H_atom
+
 57_1D_harmonic_oscillator_numerov_shooting
 
 ### Astrophysics
 49_nbody
+
 58_Tolman_Oppenheimer_Volkoff_star
 
 ### Particle Physics
 70_neutrino_oscillation
 
 ### Quantum Chemistry
 12_Schrodinger_DFT_with_SCF
+
 30_helium_slater_jastrow_wavefunction
+
 46_helium_atom_vmc
+
 66_kolmogorov_crespi_potential
+
 68_helium_atom_dmc
 
 ### Computational Chemistry
 10_ewald_summation
+
 16_Davidson_method
+
 60_Widom_particle_insertion
 
 ### Ecology
 25_CRM_in_chemostat
+
 26_CRM_in_serial_dilution
+
 41_Structural_stability_in_serial_dilution
+
 53_Stochastic_Lotka_Volterra
+
 55_Swift_Hohenberg
+
 56_temporal_niches
 
 ### Biochemistry
@@ -172,19 +225,30 @@ Nobel prized related problems:
 
 ### Semiconductor Materials
 21_Absorption_coefficient_for_alloy_GaAlAs
+
 27_Design_trade_offs_for_high_speed_photodetectors
+
 34_PN_diode_band_diagram
+
 35_Quantum_Dot_Absorption_Spectrum
+
 36_Quasi_Fermi_levels_of_photo_resistor_out_of_equilibrium
+
 39_Reflection_spectra_for_a_Distributed_Bragg_Reflector
+
 42_The_threshold_current_for_multi_quantum_well_lasers
 
 ### Molecular Modeling
 47_Internal_Energy
+
 51_Simple_Molecular_Dynamics
+
 64_GCMC
+
 77_Berendsen_thermostat
+
 79_Nose_Hoover_chain_thermostat
+
 80_Anderson_thermostat
 
 ## Example: Calculate Chern numbers for the Haldane Model