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3. Body of knowledge of Basic Sciences for Computing
The 15 knowledge areas in Basic Sciences for Computing are:
3.1 Calculus and Analysis (CAN)
- 3.1.1 Line Integrals and Vector Fields
- 3.1.2 Multiple Integrals
- 3.1.3 Multivariable Transformations
- 3.1.4 Surface Integrals and Fundamental Theorems
- 3.1.5 Vector Functions of a Real Variable
- 3.1.6 Limits and Continuity
- 3.1.7 Differential Calculus
- 3.1.8 Integral Calculus and Series
- 3.1.9 Multivariable Differential Calculus
- 3.1.10 Harmonic Analysis and Fourier Theory
- 3.2.1 Linear Algebra
- 3.2.2 Group Theory
- 3.2.3 Rings, Fields, and Galois Theory
- 3.2.4 Cryptography and Coding Theory
- 3.3.1 Enumerative Combinatorics
- 3.3.2 Graph Theory
- 3.3.3 Discrete Optimization
- 3.3.4 Mathematical Logic and Set Theory
- 3.4.1 Probability Axioms and Distributions
- 3.4.2 Limit Theorems
- 3.4.3 Stochastic Processes
- 3.4.4 Estimation Theory
- 3.4.5 Bayesian Inference
- 3.5.1 Approximation Theory and Interpolation
- 3.5.2 Numerical Integration and Quadrature
- 3.5.3 Error Analysis and Floating-Point Arithmetic
- 3.5.4 Root-Finding for Nonlinear Equations
- 3.5.5 Numerical Linear Algebra
- 3.5.6 Numerical Methods for Differential Equations
- 3.5.7 Optimization Algorithms
- 3.6.1 Ordinary Differential Equations
- 3.6.2 Dynamical Systems and Chaos
- 3.6.3 Mathematical Control Theory
- 3.6.4 Stochastic Differential Equations
- 3.7.1 Statistical Learning Theory
- 3.7.2 Optimization for Machine Learning
- 3.7.3 Information Theory
- 3.7.4 Dimensionality Reduction
- 3.7.5 Mathematical Foundations of Deep Learning
- 3.8.1 Quantum Mechanics Foundations for Computing
- 3.8.2 Quantum Circuits and Gates
- 3.8.3 Quantum Algorithms
- 3.8.4 Entanglement and Bell Inequalities
- 3.9.1 Electrostatics: Electric Field and Gauss's Law
- 3.9.2 Electric Current, Circuits, and Kirchhoff's Laws
- 3.9.3 Maxwell's Equations and Gauge Transformations
- 3.10.1 Laws of Thermodynamics and State Functions
- 3.10.2 Kinetic Theory of Gases
- 3.10.3 Heat Engines, Entropy, and the Second Law
- 3.11.1 Numerical Methods for Differential Equations in Physics
- 3.11.2 Monte Carlo Methods and Simulations
- 3.11.3 Machine Learning for Physical Discovery
- 3.12.1 Rotational Motion and Angular Momentum
- 3.12.2 Systems of Particles and Linear Momentum
- 3.12.3 Kinematics and Dynamics of Particles
- 3.12.4 Work, Energy, and Conservation Laws
- 3.12.5 Rigid Body Dynamics
- 3.12.6 Oscillations and Waves
- 3.12.7 Lagrangian and Hamiltonian Mechanics
- 3.13.1 Atomic Structure
- 3.13.2 Chemical Bonding
- 3.13.3 Matter and Energy
- 3.13.4 States of Matter
- 3.13.5 Stoichiometry
- 3.14.1 Molecular Modeling and Simulation
- 3.14.2 Machine Learning in Chemical Discovery
- 3.14.3 Computational Drug Design