Optimization - Linear programming - Simplex method - Duality theory - Sensitivity analysis - Interior point methods - Ellipsoid method - Integer programming - Branch and bound - Cutting plane methods - Lagrangian relaxation - Knapsack problems - Traveling salesman problem - Nonlinear programming - Unconstrained optimization - Constrained optimization - Karush-Kuhn-Tucker (KKT) conditions - Penalty methods - Augmented Lagrangian methods - Convex optimization - Convex sets and functions - Convex programming - Duality in convex optimization - Semidefinite programming - Conic programming - Stochastic optimization - Stochastic programming - Chance-constrained programming - Robust optimization - Sample average approximation - Stochastic gradient descent - Optimal control theory - Pontryagin's maximum principle - Hamilton-Jacobi-Bellman equation - Dynamic programming - Calculus of variations - Infinite-dimensional optimization - Game theory - Nash equilibrium - Stackelberg equilibrium - Evolutionary game theory - Cooperative game theory - Mechanism design Dynamical Systems and Chaos Theory - Discrete dynamical systems - Difference equations - Iterated maps - Cobweb diagrams - Bifurcation theory - Sarkovskii's theorem - Continuous dynamical systems - Flows and vector fields - Equilibrium points - Limit cycles - Poincaré-Bendixson theorem - Bifurcation theory - Bifurcation theory - Saddle-node bifurcation - Pitchfork bifurcation - Hopf bifurcation - Period-doubling bifurcation - Bifurcation diagrams - Chaos theory - Sensitive dependence on initial conditions - Lyapunov exponents - Strange attractors - Horseshoe map - Symbolic dynamics - Ergodic theory - Measure-preserving transformations - Ergodic theorems - Mixing and weak mixing - Entropy - Invariant measures - Fractals - Self-similarity - Fractal dimension - Iterated function systems - L-systems - Multifractals Mathematical Physics - Classical mechanics - Lagrangian mechanics - Hamiltonian mechanics - Noether's theorem - Poisson brackets - Canonical transformations - 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Stochastic differential equations - Feynman-Kac formula - Option pricing theory - Black-Scholes model - Binomial options pricing model - Lévy processes - Stochastic volatility models - Interest rate models - Portfolio optimization - Mean-variance optimization - Capital asset pricing model (CAPM) - Arbitrage pricing theory (APT) - Sharpe ratio - Risk measures - Risk management - Value at risk (VaR) - Expected shortfall - Credit risk modeling - Operational risk - Stress testing - Interest rate modeling - Short rate models - Heath-Jarrow-Morton (HJM) framework - LIBOR market model - Affine term structure models - Forward rate agreements (FRAs) - Credit risk modeling - Structural models - Reduced-form models - Copula models - Credit default swaps (CDS) - Collateralized debt obligations (CDOs) - Algorithmic trading - High-frequency trading - Statistical arbitrage - Pairs trading - Market microstructure - Limit order books Cryptography and Coding Theory - Public-key cryptography - RSA cryptosystem - 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Pole placement - Kalman filter - Linear quadratic regulator (LQR) - Robust control - H-infinity control - Structured singular value (μ) analysis - Lyapunov stability theory - Linear matrix inequalities (LMIs) - Sliding mode control - Adaptive control - Model reference adaptive control (MRAC) - Self-tuning regulators - Adaptive pole placement - Adaptive backstepping - Extremum seeking control - Optimal control - Pontryagin's maximum principle - Dynamic programming - Hamilton-Jacobi-Bellman equation - Calculus of variations - Model predictive control (MPC) - Stochastic control - Stochastic dynamic programming - Markov decision processes (MDPs) - Partially observable MDPs (POMDPs) - Stochastic optimal control - Stochastic model predictive control - Nonlinear control - Lyapunov stability theory - Feedback linearization - Backstepping - Sliding mode control - Singular perturbation theory Signal Processing - Fourier analysis - Fourier series - Fourier transform - Discrete Fourier transform (DFT) - 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Deep learning architectures - Probabilistic graphical models Mathematical Modeling - Deterministic modeling - Ordinary differential equations (ODEs) - Partial differential equations (PDEs) - Difference equations - Cellular automata - Agent-based models - Stochastic modeling - Markov chains - Stochastic differential equations (SDEs) - Poisson processes - Brownian motion - Lévy processes - Agent-based modeling - Individual-based models - Swarm intelligence - Evolutionary algorithms - Cellular automata - Network models - Partial differential equation modeling - Finite difference methods - Finite element methods - Spectral methods - Boundary element methods - Level set methods - Optimization modeling - Linear programming - Integer programming - Nonlinear programming - Stochastic programming - Multiobjective optimization - Statistical modeling - Regression analysis - Time series analysis - Bayesian modeling - Hierarchical models - Generalized linear models - Computational modeling - Numerical simulation - 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Behavioral game theory - Bounded rationality - Prospect theory - Quantal response equilibrium - Level-k thinking - Evolutionary game theory Actuarial Science - Life contingencies - Survival models - Life tables - Annuities and pensions - Life insurance - Multiple state models - Risk theory - Individual risk models - Collective risk models - Ruin theory - Reinsurance - Risk measures - Credibility theory - Bühlmann model - Bühlmann-Straub model - Empirical Bayes credibility - Hierarchical credibility - Bayesian credibility - Loss models - Frequency distributions - Severity distributions - Aggregate loss models - Compound distributions - Extreme value theory - Ruin theory - Classical ruin theory - Lundberg's inequality - Cramér-Lundberg approximation - Gerber-Shiu discounted penalty function - Markov-modulated risk processes - Pension mathematics - Defined benefit plans - Defined contribution plans - Funding methods - Asset-liability management - Stochastic pension fund modeling - Health insurance mathematics - Morbidity models - Long-term care insurance - Disability insurance - Health expense models - Risk adjustment and equalization Mathematical Economics - Microeconomic theory - Consumer theory - Producer theory - General equilibrium theory - Welfare economics - Social choice theory - Macroeconomic theory - Growth theory - Business cycle theory - Monetary economics - Fiscal policy - Open economy macroeconomics - Econometrics - Linear regression - Time series analysis - Panel data analysis - Instrumental variables - Generalized method of moments (GMM) - Game theory - Nash equilibrium - Bayesian games - Evolutionary game theory - Mechanism design - Cooperative game theory - Welfare economics - Pareto efficiency - Social welfare functions - Income distribution - Externalities - Public goods - Public economics - Optimal taxation - Public expenditure - Fiscal federalism - Social insurance - Political economy - International trade theory - Ricardian model - Heckscher-Ohlin model - Gravity model of trade - New trade theory - Economic integration Mathematical Finance - Asset pricing theory - Capital asset pricing model (CAPM) - Arbitrage pricing theory (APT) - Consumption-based asset pricing - Factor models - Intertemporal CAPM - Derivative pricing - Black-Scholes model - Binomial options pricing model - Stochastic volatility models - Jump-diffusion models - Interest rate models - Portfolio optimization - Mean-variance optimization - Risk measures - Stochastic portfolio theory - Robust portfolio optimization - Asset-liability management - Risk management - Value at risk (VaR) - Expected shortfall - Credit risk modeling - Operational risk - Liquidity risk - Market microstructure - Limit order books - Market making - High-frequency trading - Algorithmic trading - Market efficiency - Algorithmic trading - Statistical arbitrage - Pairs trading - Machine learning for trading - Reinforcement learning for trading - Execution algorithms - Quantitative finance - Numerical methods for finance - Monte Carlo methods - Finite difference methods - Fourier methods - Quasi-Monte Carlo methods Mathematical Biology - Population dynamics - Malthusian growth model - Logistic growth model - Lotka-Volterra equations - Age-structured models - Spatial population models - Epidemiology - SIR model - SEIR model - Stochastic epidemic models - Network models of disease spread - Vaccination strategies - Ecology - Predator-prey models - Competition models - Mutualism and symbiosis - Food web dynamics - Metapopulation models - Neuroscience - Hodgkin-Huxley model - FitzHugh-Nagumo model - Integrate-and-fire models - Neural network models - Synaptic plasticity models - Physiology - Cardiac electrophysiology - Respiratory mechanics - Renal function - Endocrine system modeling - Musculoskeletal modeling - Genetics - Population genetics - Quantitative genetics - Coalescent theory - Genetic algorithms - Gene regulatory networks - Evolutionary biology - Fitness landscapes - Adaptive dynamics - Evolutionary game theory - Phylogenetic inference - 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Geophysics - Seismic wave propagation - Gravity and magnetic methods - Electrical and electromagnetic methods - Geodynamics - Geophysical inverse problems - Geodynamics - Mantle convection - Plate tectonics - Lithosphere dynamics - Earthquake modeling - Volcanic processes - Seismology - Seismic wave equations - Ray theory - Seismic tomography - Earthquake source mechanisms - Seismic hazard assessment - Hydrology - Groundwater flow - Surface water hydrology - Porous media flow - Multiphase flow - Stochastic hydrology - Atmospheric science - Atmospheric dynamics - Numerical weather prediction - Climate modeling - Atmospheric chemistry - Atmospheric radiation - Oceanography - Ocean circulation models - Tidal dynamics - Wave modeling - Coastal processes - Biogeochemical cycles - Climate modeling - General circulation models (GCMs) - Earth system models - Paleoclimate modeling - Climate change projections - Uncertainty quantification