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科目与考点
基础数学
微积分、线性代数、复分析、微分方程、傅里叶分析、数论与几何等基础数学内容。
微积分(Calculus)极限、微分、积分与多变量微积分。48
Double-Integral27Constrained-Optimization关联科目运筹与优化21Limit20Improper-Integral16Multivariable-Differentiation12Taylor-Series11Integration-by-Substitution10Definite-Integral9Integration-by-Parts9Differentiation8Gamma-Function关联科目概率与统计8Local-Extrema8Arc-Length6Change-of-Variables-and-Jacobian6Hessian-Test-for-Multivariable-Extrema关联科目运筹与优化6Triple-Integral6Gaussian-Integral关联科目概率与统计5Chain-Rule关联科目数据科学与人工智能3Indefinite-Integral3Infinite-Series3Partial-Fraction-Integration3Power-Series3Sequence-Convergence3Beta-Function关联科目概率与统计2Implicit-Differentiation2LHopital-Rule2Logarithmic-Differentiation2Parametric-Differentiation2Calculus-of-Variations关联科目物理工学基础1Cauchy-Sequence1Continuity-and-Differentiability1Ellipse-Tangent-and-Intercept-Optimization关联科目运筹与优化1Elliptic-Region-Change-of-Variables1Gamma-Function-Log-Derivatives-and-Log-Moments关联科目概率与统计1Geometric-Series-and-Partial-Sum-Remainder1Hyperbolic-Functions-from-Power-Series1Implicit-Function-Local-Power-Series1Integral-of-Inverse-Function1Intermediate-Value-Theorem1Inverse-Hyperbolic-Sine-Integral1Logarithmic-Improper-Integrals-by-Inversion1Multivariable-Taylor-Expansion1Related-Rates关联科目物理工学基础1Sigmoid-and-Hyperbolic-Tangent-Derivatives关联科目数据科学与人工智能1Surface-Area-by-Double-Integral1Tangent-Half-Angle-Substitution1Volume-of-Revolution-by-Cylindrical-Shells1Volume-of-Revolution-by-Washers1
线性代数(Linear-Algebra)矩阵、线性变换、特征值、分解与内积空间。94
Eigenvalues-and-Eigenvectors77Matrix-Diagonalization34Matrix-Power26Kernel-and-Image16Matrix-Inverse15Linear-Independence14Matrix-Determinant14Inner-Product-and-Orthogonality12Matrix-Limit12Matrix-Rank11Linear-Transformation9Projection-Operator9Positive-Semidefinite-Matrix关联科目运筹与优化8Quadratic-Form8Rayleigh-Quotient关联科目运筹与优化8Vector-Space-and-Subspace8Moore-Penrose-Pseudoinverse7Orthogonal-Matrix7Systems-of-Linear-Equations7Matrix-Exponential关联科目电气电子6Matrix-Trace6Nilpotent-Matrix6Orthogonal-Diagonalization-of-Symmetric-Matrices6Singular-Value-Decomposition6Commuting-Matrices5Gram-Schmidt-Orthogonalization5Orthogonal-Decomposition5Unitary-Matrix关联科目物理5Basis-and-Dimension4Skew-Symmetric-Matrix4Affine-Transformation3Companion-Matrix-for-Linear-Recurrences关联科目离散数学3Hermitian-Matrix3Jordan-Normal-Form3Lower-Upper-Decomposition关联科目计算机科学3Matrix-Norm关联科目计算机科学3Rotation-Matrix-and-Axis-Angle关联科目计算机科学工学基础3Subspace-Sum-and-Intersection-Dimension3Cayley-Hamilton-Theorem2Convex-Combination关联科目运筹与优化2Gaussian-Elimination2Gram-Matrix2Householder-Transformation关联科目计算机科学2Parameterized-Eigenvalues-and-Rank2Simultaneous-Diagonalization-of-Commuting-Operators2Stochastic-Matrix关联科目概率与统计2Vandermonde-Determinant2Affine-Solution-Space-of-Linear-System1Best-Fit-Hyperplane-through-Origin关联科目概率与统计数据科学与人工智能1Block-Matrix-Inverse1Centroid-Least-Squares-of-Rotation-Orbit关联科目概率与统计工学基础1Characteristic-Polynomial-Coefficients-from-Eigenvalues1Condition-Number关联科目计算机科学1Courant-Fischer-Minimax-Principle关联科目运筹与优化1Cramers-Rule1Cross-Product-Area-and-Scalar-Triple-Product-Volume关联科目物理工学基础1Determinant-Maximization-at-Fixed-Trace关联科目运筹与优化1Determinant-of-Inverse-Matrix1Determinant-of-Matrix-Exponential1Diagonal-Dominance1Discrete-Linear-Dynamical-System-Convergence关联科目工学基础计算机科学1Distance-from-Point-to-Linear-Subspace关联科目运筹与优化1Fitting-Decomposition1Generalized-Eigenvalue-Characteristic-Polynomial-Recurrence关联科目物理工学基础1Generalized-Eigenvectors-and-Invariant-Subspaces1Inner-Product-Induced-by-Positive-Definite-Matrix1Invariant-Subspace-and-Restricted-Operator1Inverse-of-Identity-plus-Nilpotent-Matrix1Jacobi-Iterative-Method关联科目计算机科学1Kronecker-Product-and-Eigenvalues关联科目物理计算机科学1Least-Squares-and-Minimum-Norm-Solutions关联科目概率与统计运筹与优化1Linear-Operator-on-Polynomial-Space1Low-Rank-Approximation关联科目数据科学与人工智能1Orthogonal-Complement1Orthogonal-Upper-Triangular-Decomposition关联科目计算机科学1PageRank-Teleportation-Fixed-Point-and-Contraction关联科目概率与统计计算机科学离散数学1Parameterization-of-Two-Dimensional-Unitary-and-Special-Unitary-Matrices关联科目物理1Parameterized-Diagonalizability1Permutation-Matrix关联科目离散数学1Permutation-Matrix-and-Minimal-Polynomial关联科目离散数学1Positive-Definite-Matrix关联科目运筹与优化1Positive-Definite-Matrix-Square-Root1Rank-Criterion-for-Linear-System-Consistency1Realification-of-Unitary-Matrix1Rotation-Matrix关联科目工学基础1Simultaneous-Diagonalization-of-Parameterized-Operators1Skew-Symmetric-Subspace-under-Congruence1Smith-Normal-Form关联科目计算机科学1Spectral-Decomposition-of-Hermitian-Matrix关联科目物理1Stationary-Iterative-Method关联科目计算机科学1Sylvester-Equation-with-Positive-Definite-Coefficient1Symmetric-and-Skew-Symmetric-Decomposition1Tridiagonal-Determinant-Recurrence关联科目离散数学1Unitary-Discrete-Fourier-Transform-Matrix关联科目电气电子计算机科学1
实分析(Real-Analysis)实数、序列与函数的极限、连续性、测度与积分基础。12
Functional-Equation2Asymptotics-of-Nonlinear-Sequence-Recurrence关联科目离散数学1Bernstein-Inequality-for-Trigonometric-Polynomials1Differentiability-from-Polynomial-Approximation-Rate1Dirichlet-Test-for-Improper-Integrals1Exponential-Kernel-Sequence-Divergence-and-Continuum-Limit1Frullani-Integral-by-Parameter-Differentiation1Functions-of-Bounded-Variation1Improper-Integrals-with-Floor-and-Fractional-Part1Interchange-of-Limit-Derivative-and-Integral1Uniform-Convergence-by-Supremum-Error1Zero-Gradient-on-Path-Connected-Domain1
复分析(Complex-Analysis)复数、复函数、留数与解析函数。21
Residue-Theorem19Cauchy-Riemann-Equations7Contour-Integration6Real-Integral-by-Residues6Singularities-and-Poles4Complex-Roots3Harmonic-Functions-and-Harmonic-Conjugates3Laurent-Series3Residue-at-Higher-Order-Pole3Complex-Numbers2Contour-Shift-of-Gaussian-Integral2Mobius-Transformation2Argument-Principle-and-Winding-Number1Branch-Cut1Cauchy-Integral-Formula1Complex-Exponential-and-Polar-Form1Conformal-Mapping1Dirichlet-Integral-by-Indented-Contour1Fresnel-Integral-by-Contour-Rotation1Infinite-Series-by-Residues1Taylor-Series-and-Radius-of-Convergence1
微分方程(Differential-Equations)常微分方程、动力系统与相关解析方法。41
Second-Order-Linear-Ordinary-Differential-Equation35First-Order-Ordinary-Differential-Equation13Systems-of-ODEs11Method-of-Undetermined-Coefficients9Separable-Ordinary-Differential-Equation7Initial-Value-Problem6Laplace-Transform关联科目电气电子6Reduction-of-Order5Separation-of-Variables-for-Partial-Differential-Equation关联科目物理工学基础5Homogeneous-First-Order-Ordinary-Differential-Equation4Cauchy-Euler-Equation3Exact-Differential-Equation3Higher-Order-Linear-Ordinary-Differential-Equation3Resonant-Forcing3Riccati-Equation3Wave-Equation3Bernoulli-Equation2Bessel-Equation关联科目物理工学基础2Characteristic-Roots-and-Stability关联科目电气电子2Polynomial-Solutions-of-Ordinary-Differential-Equation2Power-Series-Solution-and-Coefficient-Recurrence2Wronskian2Boundary-Conditions-at-Infinity1Bounded-Solution-of-Forced-Ordinary-Differential-Equation1Clairaut-Equation-and-Singular-Solution1Commuting-Vector-Field-Symmetries1Differential-Galois-Theory1Dirichlet-Heat-Equation-by-Fourier-Sine-Series关联科目物理1Ermakov-Pinney-Equation关联科目物理1First-Order-Ordinary-Differential-Equation-by-Variable-Substitution1Frobenius-Method1Fundamental-Matrix关联科目电气电子1Generalized-Lotka-Volterra-Lyapunov-Stability关联科目运筹与优化1Heat-Kernel-with-Dirac-Initial-Data关联科目物理概率与统计1Helmholtz-Equation关联科目物理工学基础1Hermite-Equation-and-Polynomial-Recurrence关联科目物理1Integrating-Factor1Linear-Ordinary-Differential-Equation-with-Exponential-Forcing1Normal-Modes-of-Coupled-Linear-ODEs关联科目物理工学基础1Orthogonal-Trajectories1Variational-Equation1
向量分析(Vector-Calculus)梯度、散度、旋度、线积分与曲面积分。18
Polar-Coordinates16Divergence-Theorem9Gradient-Divergence-and-Curl关联科目物理9Surface-Integral关联科目物理9Tangent-Plane5Line-Integral关联科目物理4Stokes-Theorem关联科目物理3Parametric-Surface2Scalar-Line-Integral关联科目物理2Surface-Normal2Directional-Derivative1Greens-Identities1Hyperplane-to-Hypersphere-Distance关联科目运筹与优化1Laplacian关联科目物理1Laplacian-in-Polar-Coordinates关联科目物理工学基础1Plane-and-Distance-in-Three-Dimensional-Euclidean-Space1Polar-Coordinate-Differentials1Two-Dimensional-Laplacian-Fundamental-Solution关联科目物理1
抽象代数(Abstract-Algebra)群、环、域、同态与代数结构。13
Finite-Group2Burnside-Lemma-and-Derangement-Proportion关联科目离散数学概率与统计1Endomorphism-Ring-of-an-Ideal-and-Colon-Ideal1Galois-Group-and-Intermediate-Fields-of-Nested-Radicals1Gaussian-Integers1Kernel-Ideal-and-First-Isomorphism-Theorem1Laurent-Polynomial-Ring-as-Quotient-Ring1Nilpotent-Conjugacy-Classes-under-General-Linear-and-Special-Linear-Groups1Quadratic-Integer-Ring1Quaternion-Algebra1Quotient-Ring1Quotient-Ring-Chinese-Remainder-Theorem-Decomposition-and-Unit-Group1Tensor-Square-Vanishing-and-Artinian-Rings1
数论(Number-Theory)整数、整除、最大公约数与数论算法。6
数值分析(Numerical-Analysis)数值微分、数值积分、误差分析与数值稳定性。7
Roundoff-vs-Truncation-Error关联科目计算机科学2Central-Finite-Difference-for-Second-Derivative关联科目计算机科学工学基础1Composite-Trapezoidal-Rule1Exponential-Convergence-of-Trapezoidal-Rule-for-Analytic-Periodic-Functions关联科目计算机科学1Lagrange-Polynomial-Interpolation关联科目计算机科学1Lie-Trotter-Product-Formula-and-Operator-Splitting关联科目物理工学基础1Richardson-Extrapolation-for-Trapezoidal-Error1
傅里叶分析(Fourier-Analysis)傅里叶级数、傅里叶变换与卷积。13
Fourier-Series关联科目电气电子5Infinite-Series-from-Fourier-Series4Convolution关联科目电气电子3Fourier-Sine-and-Cosine-Series关联科目电气电子物理3Fourier-Transform-Differentiation-and-Time-Multiplication关联科目电气电子2Fourier-Transform-Scaling-and-Frequency-Shift关联科目电气电子2Parseval-Identity关联科目电气电子2Fourier-Cosine-Transform关联科目电气电子物理1Fourier-Series-Solution-of-Ordinary-Differential-Equation关联科目电气电子物理1Fourier-Transform关联科目电气电子1Fourier-Transform-Solution-of-Heat-Equation关联科目物理工学基础1Fourier-Transform-Solution-of-Wave-Equation关联科目物理工学基础1Orthogonal-Function-Systems1
拓扑学(Topology)拓扑空间、连续映射、紧致性、连通性与基本拓扑性质。5
几何(Geometry)几何对象、空间结构与计算几何基础。16
Astroid2Involute-of-a-Circle2Arc-Length-Parameter-and-Planar-Curvature1Cardioid1Complex-Plane-Geometry1Concurrency-and-Parallelism-of-Three-Lines关联科目离散数学1Gaussian-Curvature1Gaussian-Curvature-of-Ruled-Surface1Law-of-Cosines1Linear-Image-of-Circular-Arcs-and-Area-Scaling1Maximum-Size-of-Pairwise-Obtuse-Vector-Set关联科目离散数学1Periodic-Line-Coverage-by-Equally-Spaced-Receivers关联科目工学基础1Rigidity-of-Intrinsic-Path-Metric-Isometries1Scaling-of-Differential-Form-Integrals-on-Shrinking-Spheres1Steiner-Formula-for-Convex-Parallel-Body关联科目运筹与优化1Torus-Volume1
泛函分析(Functional-Analysis)赋范空间、内积空间、线性算子与无限维分析。4
离散数学
组合计数、图论、图算法、集合论、数理逻辑与离散结构。
组合数学(Combinatorics)组合计数、二项式系数、卡特兰数与递推关系。7
图论(Graph-Theory)图、树、割、匹配、连通性、平面图、同构、欧拉回路与基础性质。24
Connectivity6Graph-Basics4Planar-Graph4Articulation-Point关联科目计算机科学3Bipartite-Graph3Euler-Circuit3Adjacency-Matrix-and-Walk-Counting关联科目基础数学计算机科学2Clique2Complete-Graph2Graph-Isomorphism2Spanning-Tree2Adjacency-Spectrum-of-Path-and-Complete-Graphs关联科目基础数学1Bipartite-Matching1Consensus-Dynamics-and-Algebraic-Connectivity关联科目基础数学电气电子工学基础1Cut1Extremal-Graph-Construction1Graph-Diameter1Graph-Laplacian关联科目基础数学1Heat-Equation-on-Cycle-Graph-by-Discrete-Fourier-Transform关联科目基础数学电气电子1Laplacian-Positive-Semidefiniteness关联科目基础数学1Matching1Spectral-Diameter-Bound关联科目基础数学1Tree-Metric1Vertex-Degree1
图算法(Graph-Algorithms)图搜索、最短路算法、生成树算法、拓扑排序与图结构判定。8
集合论(Set-Theory)集合、映射、像与逆像、基数及有限集合的基本结构。5
数理逻辑(Mathematical-Logic)命题与谓词逻辑、量词以及离散数学中的基本证明方法。2
概率与统计
概率基础、概率分布与渐近理论、随机过程，以及描述统计、统计推断、统计建模、贝叶斯统计和计算统计。
概率基础(Probability-Basics)条件概率、Bayes 定理、期望与方差、联合分布、相关性、随机变量组合与经典概率问题。31
Expectation-and-Variance17Conditional-Probability14Order-Statistics8Joint-Distribution7Bayes-Theorem关联科目数据科学与人工智能6Conditional-Density6Correlation-Coefficient5Combinatorial-Probability关联科目离散数学4Convolution-of-Independent-Random-Variables关联科目基础数学4Covariance-Matrix关联科目基础数学数据科学与人工智能3Covariance-under-Affine-Transformation关联科目基础数学3Geometric-Probability关联科目基础数学3Uniform-Order-Statistics3Coupon-Collector-Problem2Linear-Combination-of-Independent-Normals2Minimum-Order-Statistic-and-Tail-Sum2Birthday-Collision-Problem关联科目离散数学计算机科学1Collision-Probability-of-Discrete-Distributions关联科目运筹与优化1Conditional-Density-by-Variable-Transformation关联科目基础数学1Copula1Joint-Density-on-Triangular-Support1Marginal-Densities-and-Independence-Test1Marginalization-of-Conditional-Density1Markov-and-Chebyshev-Inequalities1Product-of-Independent-Uniform-Variables1Proportion-and-Base-Rate1Random-Ray-Intersection-with-Polygon关联科目基础数学1Sum-of-Independent-Poisson-Variables1Sum-of-Two-Uniform-Variables1Weighted-Sum-of-Independent-Bernoulli-Variables1Zero-Covariance-does-not-Imply-Independence1
概率分布与渐近理论(Probability-Distributions-and-Asymptotics)常见离散与连续分布、分布变换、生成函数、大数定律、中心极限定理与分布逼近。34
Exponential-Distribution12Binomial-Distribution10Cumulative-Distribution-Function-and-Probability-Density-Function8Geometric-Distribution8Moment-Generating-Function8Normal-Distribution7Gamma-Distribution5Poisson-Distribution5Uniform-Distribution5Exponential-Memoryless-Property4Random-Variable-Transformation关联科目基础数学4Hypergeometric-Distribution关联科目离散数学3Lognormal-Distribution3Minimum-of-Independent-Exponentials3Central-Limit-Theorem2Chi-Square-Distribution2Mixed-Distribution2Negative-Binomial-Distribution2Weibull-Distribution关联科目工学基础2Binomial-Normal-Approximation-via-Stirling关联科目基础数学1Binomial-to-Poisson-Convergence-via-Moment-Generating-Function1Box-Muller-Transform关联科目计算机科学1Cauchy-Distribution1Laplace-Distribution-Moments-Cumulative-Distribution-Function-and-Quantiles1Law-of-Large-Numbers1Levy-Distribution-from-Inverse-Chi-Square关联科目基础数学1Log-Moments-of-Rayleigh-Distribution关联科目基础数学1Moment-Generating-Function-of-Sum-of-Independent-Variables1Normal-Standardization-and-Tail-Probability1Pareto-Distribution1Poisson-Approximation-to-Binomial1Probability-Generating-Function1Probability-Generating-Function-of-Random-Sum1Stable-Law-Sum-Scaling关联科目基础数学1
随机过程(Stochastic-Processes)马尔可夫链、随机游走、计数过程、等待时间、停止时间与其他带时间或状态结构的随机模型。17
Markov-Information-Source10Markov-Chain4Waiting-Time-for-Runs关联科目离散数学2Absorbing-Random-Walk关联科目离散数学1Autoregressive-Order-One-with-Bernoulli-Innovations1Birth-Death-Process关联科目运筹与优化1Exponential-Race-and-Order-of-Arrival关联科目运筹与优化1Exponential-Spacings-and-Poisson-Counting-Process关联科目运筹与优化1Gamblers-Ruin-and-Hitting-Probability关联科目运筹与优化1Pattern-Occurrence-in-Independent-Identically-Distributed-Sequence关联科目计算机科学生物信息学1Pattern-Probability-in-Markov-Sequence1Poisson-Process-Forward-Equations关联科目基础数学1Random-Walk-on-Fourth-Roots-of-Unity关联科目基础数学1Stationary-Pair-Frequencies1Stopping-Time1Two-State-Markov-Chain-Stationary-Reward关联科目运筹与优化1Waiting-Time-for-Runs-via-Probability-Generating-Functions关联科目离散数学1
描述统计与抽样(Descriptive-Statistics-and-Sampling)测量尺度、集中趋势、分位数、样本统计量、标准误与抽样偏差。5
估计与假设检验(Estimation-and-Hypothesis-Testing)点估计与区间估计、最大似然、估计量性质、显著性检验、多重比较、统计功效与样本量。40
Maximum-Likelihood-Estimation21Unbiased-Estimation10Confidence-Interval9Hypothesis-Testing6Statistical-Power4Diagnostic-Test-Positive-Predictive-Value3Minimum-Variance-Unbiased-Estimator3Confidence-Interval-Width-vs-Sample-Size2Exact-Binomial-Test2Family-Wise-Error-Rate2Mean-Squared-Error关联科目数据科学与人工智能2Method-of-Moments2Bonferroni-Correction1Chi-Square-Pivot-for-Normal-Variance1Common-Significance-Interpretation-Errors1Constrained-Maximum-Likelihood-Estimation关联科目运筹与优化1Estimator-Bias1Estimator-Consistency1Exponential-Rate-Maximum-Likelihood-Estimation-and-Bias1Fisher-Exact-Test关联科目生物信息学1Hypothesizing-After-Results-Are-Known1Left-Censored-Exponential-Model1Lognormal-Parameter-Maximum-Likelihood-Estimation1Measurement-Uncertainty关联科目工学基础1Minimum-Variance-Estimator-with-Equicorrelated-Samples1Minimum-Variance-Linear-Unbiased-Combination关联科目运筹与优化1Moment-and-Likelihood-Estimation-with-Censoring1Normal-Mean-Confidence-Interval-with-Known-Variance1Odds-Ratio-and-Confidence-Interval关联科目生物信息学1One-Sample-Proportion-Z-Test1One-Sided-Test-and-Power-for-Laplace-Location1Poisson-Count-Maximum-Likelihood-Estimation-for-Rate1Positive-Predictive-Value-of-Significant-Results1Receiver-Operating-Characteristic-Curve-Interpretation关联科目数据科学与人工智能生物信息学1Sample-Size-for-Target-Power1Simultaneous-Confidence-Intervals1Student-t-Confidence-Interval1Type-II-Error-Interpretation1Uniform-Endpoint-Estimation1Uniform-Scale-Unbiased-Estimator1
统计建模与实验设计(Statistical-Modeling-and-Experimental-Design)线性与多元模型、最小二乘、回归诊断、判别分析、方差分析与实验设计。21
Least-Squares-Method7Analysis-of-Variance4Simple-Linear-Regression3Weighted-Least-Squares关联科目数据科学与人工智能3Effect-Size2Fisher-Linear-Discriminant-Analysis2Mahalanobis-Distance关联科目数据科学与人工智能2Multicollinearity关联科目数据科学与人工智能2Multiple-Regression关联科目数据科学与人工智能2Adjusted-R-Squared关联科目数据科学与人工智能1Expected-Ordinary-Least-Squares-Loss-and-Variance-Trace关联科目基础数学数据科学与人工智能1Experimental-Design1Least-Squares-Residual-Orthogonality关联科目基础数学1Ordinary-Least-Squares-Normal-Equation-and-Singular-Design关联科目基础数学数据科学与人工智能1Orthogonal-Array关联科目工学基础1Polynomial-Regression-via-Maximum-Likelihood-Estimation-and-Least-Squares关联科目数据科学与人工智能1Prediction-Interval关联科目数据科学与人工智能1Regression-Diagnostics关联科目数据科学与人工智能1Regression-through-the-Origin1Ridge-Regularization-for-Singular-Design关联科目运筹与优化数据科学与人工智能1Split-Plot-Design1
贝叶斯统计(Bayesian-Statistics)先验与后验、共轭模型、后验赔率、贝叶斯推断与模型选择。5
计算统计(Computational-Statistics)Bootstrap、Monte Carlo 积分、方差缩减与其他计算型统计方法。3
运筹与优化
优化基础、线性规划、凸优化、非线性优化、组合优化、元启发式、排队论、博弈论、库存管理与决策分析。
优化基础(Optimization-Basics)优化模型、参数化问题、值函数、罚函数与灵敏度分析等基础概念。3
线性规划(Linear-Programming)线性规划建模、对偶、单纯形法、运输问题、互补松弛与内点相关方法。10
凸优化(Convex-Optimization)凸集与凸函数、最优性条件、对偶几何、投影与一阶优化方法。16
Karush-Kuhn-Tucker-Conditions关联科目基础数学8Interior-Point-Method关联科目基础数学2Projected-Gradient-Method关联科目基础数学2Accelerated-Gradient-Flow-and-Discrete-Lyapunov-Rate关联科目基础数学1Arithmetic-Mean-Geometric-Mean-Inequality-via-Optimization关联科目基础数学1Convex-First-Order-Optimality关联科目基础数学1Convexity-of-Power-Compositions关联科目基础数学1Isotonic-Regression-and-Pool-Adjacent-Violators关联科目概率与统计计算机科学1Jensen-Inequality关联科目基础数学1One-Norm-Minimization关联科目数据科学与人工智能1Optimization-over-Convex-Hull关联科目基础数学1Probability-Simplex-Optimization关联科目概率与统计基础数学1Projection-Theorem-for-Closed-Convex-Sets关联科目基础数学1Quadratic-Convexification关联科目基础数学1Separating-Hyperplane-Theorem关联科目基础数学1Strong-Convexity-and-Concavity关联科目基础数学1
非线性优化(Nonlinear-Optimization)二次规划、信赖域、正交约束及一般非线性优化问题。3
组合优化(Combinatorial-Optimization)最大流、匹配、最短路、最小生成树、集合覆盖、旅行商、分支定界与其他离散优化问题。9
Shortest-Path-Problem关联科目计算机科学离散数学22Minimum-Spanning-Tree关联科目计算机科学离散数学13Branch-and-Bound关联科目计算机科学3Maximum-Flow关联科目计算机科学离散数学3Traveling-Salesman-Problem关联科目计算机科学离散数学2Mandatory-Vertex-in-All-Shortest-Paths关联科目计算机科学离散数学1Maximum-Matching关联科目计算机科学离散数学1Minimax-Number-Partitioning-Approximation关联科目计算机科学离散数学1Set-Cover-Problem关联科目计算机科学1
元启发式优化(Metaheuristics)模拟退火等面向复杂搜索空间的随机化近似优化方法。1
排队论(Queueing-Theory)排队模型、到达过程、服务过程与系统性能。5
博弈论(Game-Theory)零和博弈、鞍点、纳什均衡与策略互动。6
库存管理(Inventory-Management)订货批量、补货策略、持有成本与数量折扣。3
计算机科学
算法、数据结构、形式语言、系统、信息论与计算理论。
数据结构(Data-Structures)树、堆、哈希表、链表、队列、栈、字典树与并查集等数据组织结构。26
Binary-Heap7Hash-Table7Binary-Search-Tree5Union-Find-Data-Structure5Priority-Queue4Queue4Binary-Search-Tree-Insertion-and-Deletion3Inorder-Tree-Traversal3Stack3Tree-Data-Structure3Tree-Sort-Complexity2B-Tree1Balanced-Binary-Search-Tree-Height-Bounds关联科目离散数学1Expected-Insertion-Cost-in-Hashing关联科目概率与统计1Expression-Tree1Heap-Order-Assignment-by-Linear-Time-Construction1Linked-List1Linked-List-Reversal1Minimum-Nodes-in-Height-Balanced-Binary-Tree关联科目离散数学1Postorder-Tree-Traversal1Reverse-Polish-Notation1Separate-Chaining-Hashing1Sorted-Linked-List-Insertion1Sparse-Matrix关联科目基础数学数据科学与人工智能1Trie1Union-Find-Path-Compression关联科目离散数学1
算法设计与分析(Algorithm-Design)复杂度、分治、贪心、回溯、排序、搜索、选择与通用算法设计方法。39
Algorithm-Complexity26Merge-Sort14Heap-Sort11Quick-Sort7Binary-Search6Divide-and-Conquer6Bubble-Sort5Recurrence-Relation-Complexity关联科目离散数学4Insertion-Sort3Radix-Sort3Selection-Sort3Backtracking2Greedy-Algorithm关联科目运筹与优化2Master-Theorem2Partitioning2Quick-Select2Asymptotic-Upper-and-Lower-Bound-Proofs关联科目基础数学1Big-O-Equivalence-and-Algebra关联科目基础数学1Binary-Insertion-Sort1Boyer-Moore-Majority-Vote-Algorithm1Bucket-Sort1Comparison-Sorting-Decision-Tree-Lower-Bound1Constrained-Adjacent-Swap-Reachability-Counting关联科目离散数学1Convex-Hull关联科目基础数学1Counting-Sort1Euclidean-Algorithm关联科目基础数学1Horner-Method关联科目基础数学1Karatsuba-Integer-Multiplication关联科目基础数学1Matrix-Multiplication-Algorithms关联科目基础数学1Max-Heapify1Median-of-Medians1Metric-Order-Transfer-with-Minimum-Comparisons关联科目基础数学1Order-Sensitivity-of-Greedy-Algorithms1Randomized-Quickselect关联科目概率与统计1Shell-Sort1Sorting-Algorithm1Sorting-Network-Comparator-Count-and-Depth关联科目离散数学1Tower-of-Hanoi1Two-Pointers1
动态规划(Dynamic-Programming)动态规划方法及背包、子集和、公共子序列、编辑距离等典型问题。20
Maximum-Subarray-Sum6Minimum-Edit-Distance关联科目生物信息学5Knapsack-Problem关联科目运筹与优化4Subset-Sum-Problem关联科目运筹与优化3Dynamic-Programming-Principle2Longest-Common-Subsequence关联科目生物信息学2Counting-Ordered-Pairings关联科目离散数学1Counting-Subset-Sum-Dynamic-Programming1Decision-Tree-Pruning关联科目数据科学与人工智能1Fibonacci-Memoization关联科目离散数学1Greedy-Failure-for-Zero-One-Knapsack1Longest-Increasing-Subsequence1Matrix-Chain-Multiplication关联科目基础数学1Minimum-Cost-Polygon-Triangulation关联科目离散数学1Optimal-Binary-Search-Tree1Optimal-Compression-Encoding1Pattern-Occurrence-Probability关联科目概率与统计生物信息学1Unbounded-Coin-Change-Counting1Unbounded-Minimum-Coin-Change1Zero-One-Knapsack-Recurrence1
字符串算法(String-Algorithms)字符串匹配、模式搜索、回文与滑动窗口等算法。7
程序设计(Programming)程序阅读、实现、语言语义与代码分析。46
Base-Conversion10Bitwise-Operation9Recursion9File-Input-and-Output5Fibonacci-Numbers关联科目基础数学4String-Processing4Integer-Overflow关联科目基础数学3Pointers-and-Arrays3Functional-Programming-Language-Features2NumPy-Array-Operations关联科目数据科学与人工智能2String-Parsing2Approximate-Glyph-Recognition关联科目数据科学与人工智能1Arbitrary-Precision-Arithmetic关联科目基础数学1Binary-File-Format-and-Endianness1C-Operator-Precedence-and-Associativity1C-Short-Circuit-Evaluation1Caesar-Cipher1Call-by-Value-and-Call-by-Reference1Call-by-Value-vs-Call-by-Name1Character-Frequency-Analysis关联科目概率与统计1Closure1Code-Clone-Detection1Connected-Component-Labeling关联科目数据科学与人工智能1Dynamic-Memory-Allocation1Evaluation-Strategy-and-Termination1Garbage-Collection1Higher-Order-Functions1Just-in-Time-Compilation1Lambda-Expression1Linear-Congruential-Generator关联科目基础数学概率与统计1Multibyte-String-Processing1Palindrome-Number关联科目基础数学1Pascal-Triangle关联科目基础数学1Pointer-to-Pointer1Prime-Enumeration关联科目基础数学1Python-Object-Mutability1Referential-Transparency1Reflection1Roman-Numeral-Conversion1Sliding-Window-Pattern-Matching关联科目数据科学与人工智能1Static-Interval-Analysis1Substitution-Cipher1Tail-Recursion1Type-Checking-and-Type-Inference关联科目基础数学1Unicode-Character-Encoding1Variable-Scope1
计算机体系结构(Computer-Architecture)指令、缓存、流水线、内存层次与性能分析。51
Pipelining15Cache10Number-Representation9Performance-Analysis9Data-Hazard8Cache-Address-Mapping6Branch-Prediction4Control-Hazard4Data-Forwarding4Cache-Miss-Types3Floating-Point-Representation3Superscalar-Execution3Average-Memory-Access-Time2Cache-Hit-Rate-Optimization2Endianness2Floating-Point-Rounding-Error关联科目基础数学2IEEE-Standard-754-Floating-Point-Arithmetic2Instruction-Cycle2Locality-of-Reference2Multi-Level-Cache2Out-of-Order-Execution2Parallelism2Pipeline-Hazards2Translation-Lookaside-Buffer2Addressing-Modes1Amdahls-Law1Assembly-Language1Branch-Penalty1Cache-Aware-Loop-and-Register-Reuse1Direct-Mapped-Cache-Conflict-and-Hit-Rate1Hamming-Weight1Hardware-Prefetching1Instruction-Encoding1Instructions-per-Cycle-with-Variable-Latency-Memory-Access1Memory-Alignment1Memory-Level-Parallelism1Microprogrammed-Control1Non-Adjacent-Form-Signed-Binary-Representation关联科目离散数学基础数学1Non-Blocking-Cache1Program-Counter1Reduced-Instruction-Set-Computer-and-Complex-Instruction-Set-Computer-Architectures1Register-Renaming1Sensor-Acquisition-Pipeline-Scheduling关联科目电气电子工学基础1Sequential-Access-Cache-Hit-Rate1Sequential-Random-and-Pointer-Chasing-Access1Single-Instruction-Multiple-Data-Architecture1Snooping-Cache-Coherence1Structural-Hazard1Thread-Level-Speculative-Execution1Two-Way-Set-Associative-Cache-Datapath1Write-Back-Policy1
操作系统(Operating-Systems)进程、内存管理、虚拟内存与系统资源管理。21
Virtual-Memory6Process-Synchronization4Atomic-Operations3Page-Replacement3Page-Table3Semaphore2Central-Processing-Unit-Scheduling1Concurrent-Task-Pool-with-Atomic-Work-Index1Deadlock-and-Starvation1Dining-Philosophers-Problem1Inter-Process-Communication1Message-Passing-Synchronization1Mutual-Exclusion-Primitives1Page-Faults-and-Loop-Order-Locality1Peterson-Algorithm1Priority-Aging1Processes-and-Threads1Real-Time-Systems关联科目工学基础1Round-Robin-Scheduling1Shortest-Job-First-Scheduling1Test-and-Set-and-Swap-Spinlocks1
形式语言与自动机(Formal-Languages)文法、自动机、形式语言与计算理论基础。31
Context-Free-Grammar13Deterministic-Finite-Automaton11Nondeterministic-Finite-Automaton10Regular-Language-Closure-Properties关联科目离散数学8Pumping-Lemma7Regular-Expression7Deterministic-Finite-Automaton-Minimization6Context-Free-Language-Closure-Properties关联科目离散数学5Epsilon-Nondeterministic-Finite-Automaton4Automata-State-Complexity关联科目离散数学3Mealy-Machine关联科目电气电子3Moore-Machine关联科目电气电子2Nondeterministic-Polynomial-Time-Completeness关联科目离散数学运筹与优化2Product-Automaton关联科目离散数学2Regular-Grammar-and-Regular-Language2Backus-Naur-Form1Chomsky-Normal-Form1Context-Free-Grammar-Emptiness-Problem1Context-Free-Language-Regular-Intersection关联科目离散数学1Equal-Length-Prefix-Operation1Finite-State-Transduction1Language-Shuffle关联科目离散数学1Language-Square-Root1Language-Substitution1Left-Quotient1Left-to-Right-Leftmost-Derivation-One-Lookahead-Parsing1Left-to-Right-Rightmost-Derivation-Parsing1Nondeterministic-Finite-Automaton-to-Deterministic-Finite-Automaton-Conversion1Parse-Tree1Regular-Language-Decision-Problems1Turing-Machine1
数据库(Databases)数据库模型、查询、事务与数据管理。5
计算机网络(Networks)网络协议、通信机制与网络系统。16
Protocol-Throughput-and-Utilization4Bandwidth-Delay-Product关联科目基础数学3Reliable-Data-Transfer关联科目概率与统计3Sliding-Window-Protocol3Stop-and-Wait-Automatic-Repeat-Request关联科目概率与统计3Autonomous-System-Numbers1Available-Bandwidth-Estimation1Carrier-Sense-Multiple-Access-with-Collision-Detection1Common-Gateway-Interface1Domain-Name-System1Internet-Protocol-Version-4-and-Version-61Internet-Protocol-Version-4-Subnetting1Packetization-Delay1Server-Concurrency-and-Request-Queueing关联科目运筹与优化1Transmission-Control-Protocol-and-User-Datagram-Protocol1Transparent-Web-Cache-in-Wide-Area-Networks1
图形学(Graphics)计算机图形、几何处理、投影与重建。11
Edge-Line-Detection-in-Grayscale-Images关联科目数据科学与人工智能2Hough-Transform-for-Line-Detection关联科目基础数学数据科学与人工智能2Homogeneous-Coordinates关联科目基础数学1Invariant-Image-Features关联科目数据科学与人工智能1Optical-Flow关联科目数据科学与人工智能1Orthogonal-Vanishing-Point-Camera-Calibration关联科目基础数学1Pinhole-Camera-and-Vanishing-Points关联科目基础数学1Procedural-Modeling1Projection-and-Reconstruction关联科目基础数学1Ray-Tracing关联科目基础数学物理1Robot-Camera-Extrinsic-Calibration关联科目工学基础1
信息安全(Security)认证、公钥基础设施、网络攻击与安全机制。9
分布式系统(Distributed-Systems)分布式计算、客户端服务器、对等网络与资源协同。3
信息论(Information-Theory)熵、互信息、信源编码、信道容量与纠错编码。37
Entropy15Huffman-Coding13Channel-Capacity关联科目电气电子10Entropy-Rate关联科目概率与统计7Mutual-Information6Channel-Coding关联科目电气电子5Conditional-Entropy5Minimum-Distance-Error-Correction关联科目离散数学电气电子5Source-Extension关联科目概率与统计5Cyclic-Code关联科目电气电子3Markov-Source-Stationary-Distribution关联科目概率与统计3Source-Coding3Typical-Sequence3Binary-Symmetric-Channel关联科目电气电子概率与统计2Information-Theoretic-Lower-Bound2Additive-Binary-Channel关联科目电气电子1Additive-Markov-Noise-Channel关联科目电气电子概率与统计1Binary-Linear-Codes关联科目电气电子1Binary-Markov-Source-Run-Length-and-Entropy-Rate关联科目概率与统计1Block-vs-Run-Length-Source-Coding关联科目概率与统计1Channel-Coding-Theorem关联科目电气电子1Coding-Efficiency1Cyclic-Redundancy-Check关联科目电气电子1Differential-Entropy关联科目概率与统计1Entropy-Chain-Rule关联科目概率与统计1Entropy-Lower-Bound-on-Weighted-External-Path-Length关联科目基础数学1Finite-State-Channel-with-Memory关联科目电气电子1Hamming-74-Code-and-Minimum-Distance关联科目离散数学电气电子1Instantaneous-Code1Interleaving-for-Burst-Error关联科目电气电子1Kraft-Inequality-for-Binary-Trees关联科目离散数学1Kullback-Leibler-Divergence关联科目概率与统计数据科学与人工智能1Optimal-Alphabetic-Binary-Tree1Parity-Bit-Single-Error-Detection关联科目电气电子1Pointwise-Mutual-Information关联科目概率与统计1Renyi-Entropy关联科目概率与统计1Self-Information-Axioms关联科目基础数学概率与统计1
量子计算(Quantum-Computing)量子计算模型、量子算法与计算复杂性。1
数据科学与人工智能
数据分析、机器学习、知识表示与智能系统。
数据科学(Data-Science)数据处理、数据分析、特征工程与数据驱动建模。5
机器学习(Machine-Learning)分类、决策树、强化学习与学习模型。36
Backpropagation关联科目基础数学计算机科学4Decision-Tree关联科目计算机科学3K-Nearest-Neighbors关联科目计算机科学3Random-Forest关联科目计算机科学3Curse-of-Dimensionality2Feedforward-Neural-Network关联科目计算机科学2Gaussian-Mixture-Model关联科目概率与统计2Hidden-Markov-Model关联科目概率与统计2K-Means2Naive-Bayes关联科目概率与统计2Nearest-Centroid-Classifier关联科目基础数学2Support-Vector-Machine2Bayesian-Decision-Boundary关联科目概率与统计1Bayesian-Network关联科目概率与统计1Binary-Cross-Entropy关联科目概率与统计1Classification1Covariate-Shift-and-Importance-Weighting关联科目概率与统计1Deep-Learning关联科目计算机科学1Ensemble-Learning1Expectation-Maximization-Algorithm关联科目概率与统计1Feature-Standardization关联科目概率与统计1Gaussian-Generative-Classifier关联科目概率与统计1Linear-Discriminant-Analysis关联科目概率与统计基础数学1Logistic-Regression关联科目概率与统计1Multi-Label-Classification1Neural-Network关联科目计算机科学1Neural-Network-Training-Methods关联科目基础数学计算机科学1Online-Learning-with-Expert-Advice关联科目运筹与优化1Perceptron1Regret-Bound关联科目运筹与优化1Reinforcement-Learning关联科目计算机科学1Sigmoid-Function关联科目基础数学1Softmax-Regression关联科目概率与统计1Stochastic-Gradient-Descent关联科目基础数学运筹与优化1Transformer关联科目计算机科学1Vanishing-Gradient-and-Mitigation1
人工智能基础(Artificial-Intelligence)知识表示、语义网络与智能系统基础。8
电气电子
电路、电子、信号、通信与计算机硬件。
电路与电子电路(Circuits)电路分析、电子电路与模拟/数字硬件基础。25
Phasor-and-Impedance-Analysis关联科目基础数学物理16Circuit-Transient-Response关联科目基础数学13Resistor-Inductor-Capacitor-Resonance关联科目物理8Mutual-Inductance关联科目物理7Maximum-Power-Transfer关联科目运筹与优化6Transformer-Equivalent-Circuit关联科目物理4Alternating-Current-Power-and-Power-Factor关联科目物理3Circuit-Transfer-Function关联科目基础数学3Transmission-Line-and-Impedance-Matching关联科目物理3Two-Port-Network关联科目基础数学3Mesh-Analysis2Metal-Oxide-Semiconductor-Field-Effect-Transistor-Bias-and-Small-Signal-Analysis关联科目物理2Operational-Amplifier2Resistor-Capacitor-Charging-and-Discharging关联科目基础数学物理2Thevenin-and-Norton-Equivalent2Wheatstone-Bridge2Active-Filter1Boost-Converter-Switching-Transient关联科目物理基础数学1Kirchhoff-Laws1Nodal-Analysis1Proximity-Sensor-Principles关联科目物理工学基础1Quarter-Wave-Transformer关联科目物理1Resistor-Inductor-Capacitor-Damping关联科目基础数学物理1Superposition-Theorem1Three-Phase-Circuit1
数字逻辑(Digital-Logic)组合逻辑、时序逻辑、加法器与同步电路。32
Boolean-Function-Minimization关联科目计算机科学11D-Flip-Flop关联科目计算机科学7Half-and-Full-Adders关联科目计算机科学6Not-AND-and-Not-OR-Universal-Gates关联科目计算机科学5Combinatorial-Circuit关联科目计算机科学4Karnaugh-Map-Minimization关联科目离散数学4Sequential-Circuit关联科目计算机科学4Synchronous-Circuit关联科目计算机科学4Counter-Circuit关联科目计算机科学3Ripple-Carry-Adder关联科目计算机科学3Combinational-Binary-Multiplier关联科目计算机科学2Finite-State-Machine-Minimization关联科目计算机科学2Full-Adder-and-Critical-Path关联科目计算机科学2Pulse-Width-Modulation关联科目工学基础2Shift-Register关联科目计算机科学2Signed-Addition-Subtraction-and-Overflow-Detection关联科目计算机科学2Asynchronous-Circuit1Carry-Lookahead-Adder关联科目计算机科学1Comparator-Circuit关联科目计算机科学1Complementary-Metal-Oxide-Semiconductor-Logic-Transistor-Count-Optimization关联科目计算机科学1Critical-Path-Delay关联科目计算机科学1Field-Programmable-Gate-Array关联科目计算机科学1Flip-Flop1Majority-Gate-Logic-Synthesis关联科目计算机科学1Mealy-Sequence-Detector-State-Minimization关联科目计算机科学1Moore-Machine-State-Minimization-and-Encoding关联科目计算机科学1One-Hot-Mealy-Parity-Checker关联科目计算机科学1Periodic-Sequence-Generator1Ripple-vs-Synchronous-Counter-Propagation-Delay1Rising-Edge-Detector关联科目计算机科学1Synchronous-Decade-and-Up-Down-Counter1Synchronous-Modulo-Counter1
信号处理(Signal-Processing)离散信号、变换、滤波与频域分析。31
Sampling-Theorem-and-Aliasing关联科目基础数学7Z-Transform关联科目基础数学5Discrete-Fourier-Transform关联科目基础数学4Continuous-Time-Fourier-Transform关联科目基础数学3Convolution-Theorem关联科目基础数学2Dirac-Comb-Fourier-Transform关联科目基础数学2Autocorrelation-and-Power-Spectral-Density关联科目概率与统计基础数学1Bandlimited-Signal-Reconstruction-from-Samples关联科目基础数学1Bilinear-Transform-for-Analog-to-Digital-Filter关联科目基础数学1Causal-Response-Hilbert-Transform-Relation关联科目基础数学1Cepstrum1Discrete-Cosine-Transform关联科目计算机科学基础数学1Discrete-Fourier-Transform-Time-Reversal-and-Shift关联科目基础数学1Discrete-Time-Filter-Realization1Discrete-Time-System-Transfer-and-Frequency-Response关联科目基础数学1Discrete-Time-Transfer-Function-and-Impulse-Response关联科目基础数学1Fast-Fourier-Transform关联科目计算机科学基础数学1Fourier-Conjugate-Symmetry-and-Modulation关联科目基础数学1Fourier-Slice-Theorem关联科目基础数学数据科学与人工智能1Ideal-Low-Pass-Impulse-Response关联科目基础数学1Impulse-and-Step-Response-Relationship关联科目基础数学1Impulse-Train-Sampling-and-Spectral-Replication关联科目基础数学1Infinite-Impulse-Response-Filter-Transfer-Function-and-Realization关联科目计算机科学1Maximum-Entropy-Quantizer-Boundaries关联科目计算机科学概率与统计1Power-Spectrum-and-Parseval-Energy-Identity关联科目基础数学物理1Scalar-Quantizer-Probability-and-Centroid-Reconstruction关联科目概率与统计计算机科学1Single-Sideband-Modulation1Wavelet-Transform关联科目基础数学1Wiener-Filter关联科目概率与统计数据科学与人工智能1Z-Transform-of-Geometric-Sequence关联科目基础数学1Z-Transform-Time-Shift关联科目基础数学1
控制理论(Control-Theory)系统建模、稳定性、反馈与控制系统分析。22
Step-Response关联科目基础数学5Transfer-Function关联科目基础数学5Bode-Plot-and-Stability-Margins关联科目基础数学4Proportional-Integral-Derivative-and-Integral-Proportional-Derivative-Control4Routh-Hurwitz-Stability关联科目基础数学4Feedback-Control关联科目工学基础运筹与优化3Kalman-Filter关联科目概率与统计数据科学与人工智能2Brushless-Motor关联科目工学基础物理1Collision-Free-Trajectory-Planning关联科目运筹与优化离散数学1Damping-and-Oscillation关联科目物理基础数学1Disturbance-Rejection1Feedback-and-Feedforward-Control1H-Infinity-Control关联科目基础数学1Inverse-Kinematics关联科目基础数学工学基础1Lead-Compensation1Linearization关联科目基础数学1Nyquist-Stability-Criterion关联科目基础数学1Position-and-Torque-Feedback关联科目工学基础1Robot-Arm-Kinematics关联科目工学基础基础数学1Steady-State-Error1Stepping-Motor关联科目工学基础1Three-Dimensional-Position-Sensing关联科目工学基础计算机科学1
通信与编码(Communications)通信信道、编码、信息传输与误差控制。2
物理
力学、电磁学、量子与物理数学。
力学(Mechanics)经典力学、振动、旋转参考系与连续介质基础。23
Lagrangian-Mechanics关联科目基础数学9Cyclic-Coordinate-and-Conserved-Momentum关联科目基础数学5Small-Angle-Pendulum关联科目基础数学3Damped-Harmonic-Motion关联科目基础数学电气电子2Normal-Modes-and-Coupled-Oscillators关联科目基础数学2Two-Body-Central-Force-and-Effective-Potential关联科目基础数学2Action-Integral-and-Adiabatic-Invariant关联科目基础数学1Angular-Momentum-Conservation-and-Areal-Velocity1Beats-in-Coupled-Oscillators1Center-of-Mass-and-Angular-Momentum1Connected-Particles-and-Tension1Coupled-Rigid-Body-Normal-Modes关联科目基础数学1Gyroscopic-Precession1Hamilton-Principle-and-Euler-Lagrange-Equation关联科目基础数学1Involute-Constrained-Motion关联科目基础数学1Lagrangian-and-Hamiltonian-for-Holonomic-Constraints关联科目基础数学1Larmor-Theorem关联科目电气电子1Radial-Small-Oscillation-Frequency关联科目基础数学1Rotating-Frame-Coriolis-and-Centrifugal-Forces关联科目基础数学1Small-Oscillations-of-a-Chain-Pendulum关联科目基础数学1Spring-Pendulum-Coupled-Normal-Modes关联科目基础数学1Time-Dependent-Harmonic-Oscillator关联科目基础数学1Two-Dimensional-Harmonic-Oscillator-Effective-Potential关联科目基础数学1
电磁学(Electromagnetism)电场、磁场、麦克斯韦方程与电磁现象。31
Electromagnetic-Induction-and-Inductance关联科目电气电子6Gauss-Law关联科目基础数学6Biot-Savart-Law关联科目电气电子4Capacitance-and-Electrostatic-Energy关联科目电气电子4Electric-Potential-and-Field关联科目基础数学4Ampere-Law关联科目电气电子3Dielectrics-and-Boundary-Conditions关联科目电气电子3Coaxial-Capacitor-and-Line关联科目电气电子2Conducting-Sphere-in-Uniform-Electric-Field关联科目基础数学2Electric-Dipole-Potential2Electrostatic-Force2Lorentz-Force-and-Charged-Particle-Motion关联科目基础数学2Crossed-Electric-and-Magnetic-Fields关联科目电气电子1Current-Loop-Magnetic-Moment-and-Torque关联科目电气电子1Cyclotron-Motion1Drude-Relaxation-Time关联科目电气电子1Electromagnetic-Wave关联科目电气电子基础数学1Electrostatic-Shielding关联科目电气电子1Fermat-Principle-and-Snells-Law关联科目基础数学1Fields-on-Axis-of-Charged-Rotating-Ring1Hall-Angle关联科目电气电子1Helmholtz-Coil关联科目电气电子1Magnetic-Dipole-Torque1Magnetic-Dipole-Vector-Potential关联科目电气电子1Magnetic-Energy关联科目电气电子1Magnetic-Force1Rectangular-Cavity-Eigenmodes关联科目基础数学电气电子1Rotating-Conductor-Motional-Electromotive-Force关联科目电气电子1Spherical-Capacitor关联科目电气电子1Superposition-Principle关联科目基础数学1Surface-Current-Boundary-Condition关联科目电气电子1
量子力学(Quantum-Mechanics)量子态、算符、自旋与量子统计基础。31
Pauli-Matrices关联科目计算机科学7Creation-and-Annihilation-Operators5Quantum-Observable-Expectation-and-Variance关联科目概率与统计5Harmonic-Oscillator-Ground-State关联科目基础数学4Quantum-State-Time-Evolution关联科目基础数学4Wavefunction-Normalization-and-Energy-Expectation关联科目基础数学化学3Bell-State-Correlation关联科目计算机科学2Canonical-Commutation-Relations2Harmonic-Oscillator-First-Excited-State关联科目化学2Harmonic-Oscillator-Uncertainty2Number-Operator-Spectrum2Pauli-Matrix-Exponential-and-Unitary-Evolution关联科目基础数学计算机科学2Quantum-Measurement关联科目基础数学2Tensor-Product-Separability-and-Entanglement关联科目计算机科学2Time-Evolution-of-Two-Level-System关联科目基础数学2Bell-Inequality-and-Local-Hidden-Variable-Contradiction关联科目概率与统计1Coherent-State-and-Number-Fluctuation关联科目概率与统计1Degenerate-Harmonic-Oscillator-States1Density-Matrix-and-Mixed-State关联科目概率与统计计算机科学1Finite-Dimensional-Hamiltonian关联科目基础数学1First-Order-Perturbation-of-Displaced-Oscillator关联科目基础数学1First-Order-Time-Dependent-Perturbation-Transition-Probability关联科目基础数学1Heisenberg-Uncertainty-and-Minimum-Uncertainty-Gaussian关联科目基础数学1Identical-Fermions-Spin-and-Spatial-Symmetry1Lewis-Riesenfeld-Invariant关联科目基础数学1One-Dimensional-Infinite-Square-Well关联科目基础数学1Particle-in-Circular-Well关联科目基础数学化学1Qubit-State-Tomography关联科目计算机科学1Rectangular-Barrier-Tunneling关联科目基础数学1Two-Level-Tunneling-and-Rabi-Oscillation关联科目基础数学1Wavefunction-Matching-at-Potential-Steps关联科目基础数学1
热力学与统计物理(Thermodynamics)热力学、统计系综、分布函数与物性基础。17
Helmholtz-Free-Energy-Differential关联科目化学2Canonical-Partition-Function关联科目概率与统计化学1Chemical-Equilibrium-and-Vant-Hoff-Relation关联科目化学1Clapeyron-Equation关联科目化学1Classical-Ideal-Gas-Entropy-and-Low-Temperature-Failure关联科目化学1Classical-Ideal-Gas-Partition-Function-and-Gibbs-Factor关联科目化学1Enthalpy-and-Thermodynamic-Relations关联科目化学基础数学1Fermi-Dirac-Grand-Canonical-Distribution关联科目计算机科学1Grand-Canonical-Ideal-Gas关联科目化学1High-Temperature-Fermi-Gas-Classical-Limit关联科目化学1Ideal-Gas-Entropy-of-Mixing关联科目化学1Ideal-Gas-Free-Expansion关联科目化学1Joule-Thomson-Effect关联科目化学工学基础1Langmuir-Adsorption-Isotherm关联科目化学1Low-Temperature-Fermi-Gas-Heat-Capacity-and-Entropy1Maxwell-Relations关联科目化学1Photon-Gas-and-Stefan-Boltzmann-Law关联科目电气电子1
物理海洋学(Ocean-Physics)海洋中的波动、流动、传播与物理过程。1
化学
物理化学、无机化学等化学相关考点。
物理化学(Physical-Chemistry)热化学、反应动力学、量子化学与物理化学基础。11
Einstein-Solid-Heat-Capacity关联科目物理2Consecutive-First-Order-Reaction-Kinetics关联科目基础数学1Entropy-Change关联科目物理1Enzyme-Inhibition-and-Lineweaver-Burk-Plot关联科目生物信息学1Ideal-Gas-Thermodynamics关联科目物理1Langmuir-Hinshelwood-CO-Oxidation关联科目工学基础1Operator-Commutator关联科目物理基础数学1Particle-in-a-Box-and-HOMO-LUMO-Transition关联科目物理基础数学1Planck-Blackbody-Law关联科目物理1Wavefunction-Normalization关联科目物理基础数学1Wien-Displacement-Law关联科目物理1
无机化学(Inorganic-Chemistry)元素、配位化学、无机反应与结构。4
生物信息学
序列分析、计算生物学、医学信息与生命信息处理。
生物信息学(Bioinformatics)序列分析、编辑距离、比对与生命信息处理。1
认知科学与神经科学
认知、神经系统、脑科学与相关信息处理。
认知神经科学(Cognitive-Neuroscience)认知过程、神经系统与脑功能。7
工学基础
机械、材料、土木等工学基础题。
材料力学(Mechanics-of-Materials)应力、应变、梁、材料变形与强度。5
流体力学(Fluid-Mechanics)流体运动、波动、连续介质与工程流动问题。1
机器人学(Robotics)机器人运动学、雅可比矩阵、静力学与执行器控制。8
Forward-and-Inverse-Kinematics-of-Serial-Manipulator关联科目基础数学计算机科学3Zero-Moment-Point关联科目物理基础数学3Simultaneous-Localization-and-Mapping关联科目计算机科学概率与统计2Articulated-Link-Mechanism-Representation关联科目基础数学1Autonomous-Vehicle-Dynamic-Map关联科目计算机科学数据科学与人工智能1Force-Control-Implementation关联科目电气电子1Jacobian-Transpose-Joint-Torque关联科目基础数学物理1Manipulator-Jacobian-and-End-Effector-Velocity关联科目基础数学1