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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。

315

微积分(Calculus)极限、微分、积分与多变量微积分。50

Double-Integral82 Limit67 Integration65 Differentiation61 Multivariable-Differentiation43 Definite-Integral38 Taylor-Series34 Change-of-Variables-and-Jacobian27 Constrained-Optimization关联科目运筹与优化26 Improper-Integral25 Local-Extrema24 Integration-by-Parts19 Extrema16 Hessian-Test-for-Multivariable-Extrema关联科目运筹与优化14 Gamma-Function关联科目概率与统计13 Integration-by-Substitution12 Indefinite-Integral11 Implicit-Differentiation10 Infinite-Series10 Triple-Integral9 Arc-Length8 Gaussian-Integral关联科目概率与统计7 Power-Series7 Chain-Rule关联科目数据科学与人工智能5 Sequence-Convergence5 Beta-Function关联科目概率与统计4 Continuity-and-Differentiability4 Parametric-Differentiation4 Partial-Fraction-Integration3 Logarithmic-Differentiation2 Multivariable-Taylor-Expansion2 Volume-of-Revolution-by-Washers2 Calculus-of-Variations关联科目物理工学基础1 Cauchy-Sequence1 Ellipse-Tangent-and-Intercept-Optimization关联科目运筹与优化1 Elliptic-Region-Change-of-Variables1 Gamma-Function-Log-Derivatives-and-Log-Moments关联科目概率与统计1 Geometric-Series-and-Partial-Sum-Remainder1 Hyperbolic-Functions-from-Power-Series1 Implicit-Function-Local-Power-Series1 Integral-of-Inverse-Function1 Intermediate-Value-Theorem1 Inverse-Hyperbolic-Sine-Integral1 LHopital-Rule1 Logarithmic-Improper-Integrals-by-Inversion1 Related-Rates关联科目物理工学基础1 Sigmoid-and-Hyperbolic-Tangent-Derivatives关联科目数据科学与人工智能1 Surface-Area-by-Double-Integral1 Tangent-Half-Angle-Substitution1 Volume-of-Revolution-by-Cylindrical-Shells1

线性代数(Linear-Algebra)矩阵、线性变换、特征值、分解与内积空间。96

Eigenvalues-and-Eigenvectors203 Matrix-Diagonalization75 Matrix-Determinant50 Matrix-Power47 Matrix-Inverse45 Basis-and-Dimension43 Inner-Product-and-Orthogonality42 Linear-Independence35 Kernel-and-Image26 Linear-Transformation26 Matrix-Rank23 Orthogonal-Matrix22 Quadratic-Form22 Matrix-Exponential关联科目电气电子14 Matrix-Limit13 Orthogonal-Diagonalization-of-Symmetric-Matrices13 Projection-Operator11 Systems-of-Linear-Equations11 Positive-Semidefinite-Matrix关联科目运筹与优化10 Rayleigh-Quotient关联科目运筹与优化9 Vector-Space-and-Subspace9 Affine-Transformation7 Gram-Schmidt-Orthogonalization7 Matrix-Norm关联科目计算机科学7 Matrix-Trace7 Nilpotent-Matrix7 Positive-Definite-Matrix关联科目运筹与优化7 Unitary-Matrix关联科目物理7 Commuting-Matrices6 Moore-Penrose-Pseudoinverse6 Singular-Value-Decomposition6 Affine-Solution-Space-of-Linear-System5 Characteristic-Polynomial5 Hermitian-Matrix5 Jordan-Normal-Form5 Subspace-Sum-and-Intersection-Dimension5 Cayley-Hamilton-Theorem4 Invariant-Subspace-and-Restricted-Operator4 Orthogonal-Decomposition4 Rotation-Matrix-and-Axis-Angle关联科目计算机科学工学基础4 Simultaneous-Diagonalization-of-Commuting-Operators4 Skew-Symmetric-Matrix4 Companion-Matrix-for-Linear-Recurrences关联科目离散数学3 Linear-Operator-on-Polynomial-Space3 Lower-Upper-Decomposition关联科目计算机科学3 Rotation-Matrix关联科目工学基础3 Convex-Combination关联科目运筹与优化2 Diagonal-Dominance2 Discrete-Linear-Dynamical-System-Convergence关联科目工学基础计算机科学2 Gaussian-Elimination2 Gram-Matrix2 Householder-Transformation关联科目计算机科学2 Jacobi-Iterative-Method关联科目计算机科学2 Least-Squares-and-Minimum-Norm-Solutions关联科目概率与统计运筹与优化2 Matrix-Operations2 Parameterized-Diagonalizability2 Parameterized-Eigenvalues-and-Rank2 Rank-Criterion-for-Linear-System-Consistency2 Stationary-Iterative-Method关联科目计算机科学2 Stochastic-Matrix关联科目概率与统计2 Symmetric-and-Skew-Symmetric-Decomposition2 Vandermonde-Determinant2 Best-Fit-Hyperplane-through-Origin关联科目概率与统计数据科学与人工智能1 Block-Matrix-Inverse1 Centroid-Least-Squares-of-Rotation-Orbit关联科目概率与统计工学基础1 Characteristic-Polynomial-Coefficients-from-Eigenvalues1 Condition-Number关联科目计算机科学1 Courant-Fischer-Minimax-Principle关联科目运筹与优化1 Cramers-Rule1 Cross-Product-Area-and-Scalar-Triple-Product-Volume关联科目物理工学基础1 Determinant-Maximization-at-Fixed-Trace关联科目运筹与优化1 Determinant-of-Inverse-Matrix1 Determinant-of-Matrix-Exponential1 Distance-from-Point-to-Linear-Subspace关联科目运筹与优化1 Fitting-Decomposition1 Generalized-Eigenvalue-Characteristic-Polynomial-Recurrence关联科目物理工学基础1 Generalized-Eigenvectors-and-Invariant-Subspaces1 Inner-Product-Induced-by-Positive-Definite-Matrix1 Inverse-of-Identity-plus-Nilpotent-Matrix1 Kronecker-Product-and-Eigenvalues关联科目物理计算机科学1 Low-Rank-Approximation关联科目数据科学与人工智能1 Orthogonal-Complement1 Orthogonal-Upper-Triangular-Decomposition关联科目计算机科学1 PageRank-Teleportation-Fixed-Point-and-Contraction关联科目概率与统计计算机科学离散数学1 Parameterization-of-Two-Dimensional-Unitary-and-Special-Unitary-Matrices关联科目物理1 Permutation-Matrix关联科目离散数学1 Permutation-Matrix-and-Minimal-Polynomial关联科目离散数学1 Positive-Definite-Matrix-Square-Root1 Realification-of-Unitary-Matrix1 Simultaneous-Diagonalization-of-Parameterized-Operators1 Skew-Symmetric-Subspace-under-Congruence1 Smith-Normal-Form关联科目计算机科学1 Spectral-Decomposition-of-Hermitian-Matrix关联科目物理1 Sylvester-Equation-with-Positive-Definite-Coefficient1 Tridiagonal-Determinant-Recurrence关联科目离散数学1 Unitary-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

Interchange-of-Limit-Derivative-and-Integral4 Uniform-Convergence-by-Supremum-Error3 Functional-Equation2 Asymptotics-of-Nonlinear-Sequence-Recurrence关联科目离散数学1 Bernstein-Inequality-for-Trigonometric-Polynomials1 Differentiability-from-Polynomial-Approximation-Rate1 Dirichlet-Test-for-Improper-Integrals1 Exponential-Kernel-Sequence-Divergence-and-Continuum-Limit1 Frullani-Integral-by-Parameter-Differentiation1 Functions-of-Bounded-Variation1 Improper-Integrals-with-Floor-and-Fractional-Part1 Zero-Gradient-on-Path-Connected-Domain1

复分析(Complex-Analysis)复数、复函数、留数与解析函数。21

微分方程(Differential-Equations)常微分方程、动力系统与相关解析方法。42

向量分析(Vector-Calculus)梯度、散度、旋度、线积分与曲面积分。18

Polar-Coordinates20 Gradient-Divergence-and-Curl关联科目物理12 Surface-Integral关联科目物理11 Divergence-Theorem10 Line-Integral关联科目物理8 Tangent-Plane8 Stokes-Theorem关联科目物理4 Surface-Normal4 Directional-Derivative3 Greens-Identities2 Parametric-Surface2 Scalar-Line-Integral关联科目物理2 Hyperplane-to-Hypersphere-Distance关联科目运筹与优化1 Laplacian关联科目物理1 Laplacian-in-Polar-Coordinates关联科目物理工学基础1 Plane-and-Distance-in-Three-Dimensional-Euclidean-Space1 Polar-Coordinate-Differentials1 Two-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-Group2 Quaternion-Algebra2 Burnside-Lemma-and-Derangement-Proportion关联科目离散数学概率与统计1 Endomorphism-Ring-of-an-Ideal-and-Colon-Ideal1 Galois-Group-and-Intermediate-Fields-of-Nested-Radicals1 Gaussian-Integers1 Kernel-Ideal-and-First-Isomorphism-Theorem1 Laurent-Polynomial-Ring-as-Quotient-Ring1 Nilpotent-Conjugacy-Classes-under-General-Linear-and-Special-Linear-Groups1 Quadratic-Integer-Ring1 Quotient-Ring1 Quotient-Ring-Chinese-Remainder-Theorem-Decomposition-and-Unit-Group1 Tensor-Square-Vanishing-and-Artinian-Rings1

数论(Number-Theory)整数、整除、最大公约数与数论算法。6

Greatest-Common-Divisor关联科目计算机科学6 Divisor-Counting-Function关联科目计算机科学1 Mobius-Inversion关联科目离散数学1 Prime-Diophantine-Equation1 Prime-Factorization关联科目计算机科学1 Unit-Fraction-Decomposition关联科目离散数学1

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4 Central-Finite-Difference-for-Second-Derivative关联科目计算机科学工学基础3 Composite-Trapezoidal-Rule1 Exponential-Convergence-of-Trapezoidal-Rule-for-Analytic-Periodic-Functions关联科目计算机科学1 Lagrange-Polynomial-Interpolation关联科目计算机科学1 Lie-Trotter-Product-Formula-and-Operator-Splitting关联科目物理工学基础1 Richardson-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19 Fourier-Transform关联科目电气电子15 Infinite-Series-from-Fourier-Series6 Convolution关联科目电气电子5 Fourier-Transform-Scaling-and-Frequency-Shift关联科目电气电子5 Parseval-Identity关联科目电气电子5 Fourier-Transform-Differentiation-and-Time-Multiplication关联科目电气电子4 Fourier-Sine-and-Cosine-Series关联科目电气电子物理3 Fourier-Cosine-Transform关联科目电气电子物理1 Fourier-Series-Solution-of-Ordinary-Differential-Equation关联科目电气电子物理1 Fourier-Transform-Solution-of-Heat-Equation关联科目物理工学基础1 Fourier-Transform-Solution-of-Wave-Equation关联科目物理工学基础1 Orthogonal-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

Hausdorff-Space3 Compactness-Preserving-Injections-and-Continuity1 Hausdorff-Closure-and-Connectedness-in-a-Custom-Topology1 Homology-of-a-Projective-Subspace-and-Nontrivial-Loop1 Locally-Constant-Functions-on-Connected-Spaces1

几何(Geometry)几何对象、空间结构与计算几何基础。16

Arc-Length-Parameter-and-Curvature2 Astroid2 Involute-of-a-Circle2 Cardioid1 Complex-Plane-Geometry1 Concurrency-and-Parallelism-of-Three-Lines关联科目离散数学1 Gaussian-Curvature1 Gaussian-Curvature-of-Ruled-Surface1 Law-of-Cosines1 Linear-Image-of-Circular-Arcs-and-Area-Scaling1 Maximum-Size-of-Pairwise-Obtuse-Vector-Set关联科目离散数学1 Periodic-Line-Coverage-by-Equally-Spaced-Receivers关联科目工学基础1 Rigidity-of-Intrinsic-Path-Metric-Isometries1 Scaling-of-Differential-Form-Integrals-on-Shrinking-Spheres1 Steiner-Formula-for-Convex-Parallel-Body关联科目运筹与优化1 Torus-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

Uniform-Convergence3 Bounded-Linear-Operator1 Normed-Space1 Uniform-Convergence-of-Iterated-Sine-and-LogSumExp关联科目数据科学与人工智能1

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

Recurrence-Relation关联科目计算机科学8 Binomial-Coefficient关联科目计算机科学4 Fibonacci-Recurrence关联科目基础数学计算机科学4 Binomial-Inversion关联科目基础数学1 Catalan-Number关联科目计算机科学1 Matroid-Theory关联科目基础数学计算机科学1 Reconstruction-from-Pairwise-Sums1

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。25

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。9

Depth-First-Search关联科目计算机科学12 Breadth-First-Search关联科目计算机科学10 Dijkstra-Algorithm关联科目计算机科学7 Kruskal-Algorithm关联科目计算机科学6 Prim-Algorithm关联科目计算机科学4 Bellman-Ford-Algorithm关联科目计算机科学3 Topological-Sort关联科目计算机科学3 A-Star-Shortest-Path-Search关联科目计算机科学2 Shortest-Path-Counting关联科目计算机科学2

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。6

Binary-Relations7 Cardinality7 Composition-of-Injective-and-Surjective-Maps5 Image-and-Preimage5 Partially-Ordered-Sets-and-Chains2 Image-of-Intersection1

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

Predicate-Logic9 Mathematical-Induction7

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。

162

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。33

Expectation-and-Variance90 Independence-of-Random-Variables49 Conditional-Probability34 Joint-Distribution17 Order-Statistics12 Bayes-Theorem关联科目数据科学与人工智能11 Covariance11 Marginal-Densities-and-Independence-Test9 Correlation-Coefficient8 Combinatorial-Probability关联科目离散数学7 Conditional-Density7 Convolution-of-Independent-Random-Variables关联科目基础数学4 Covariance-Matrix关联科目基础数学数据科学与人工智能3 Covariance-under-Affine-Transformation关联科目基础数学3 Geometric-Probability关联科目基础数学3 Uniform-Order-Statistics3 Coupon-Collector-Problem2 Linear-Combination-of-Independent-Normals2 Markov-and-Chebyshev-Inequalities2 Minimum-Order-Statistic-and-Tail-Sum2 Zero-Covariance-does-not-Imply-Independence2 Birthday-Collision-Problem关联科目离散数学计算机科学1 Collision-Probability-of-Discrete-Distributions关联科目运筹与优化1 Conditional-Density-by-Variable-Transformation关联科目基础数学1 Copula1 Joint-Density-on-Triangular-Support1 Marginalization-of-Conditional-Density1 Product-of-Independent-Uniform-Variables1 Proportion-and-Base-Rate1 Random-Ray-Intersection-with-Polygon关联科目基础数学1 Sum-of-Independent-Poisson-Variables1 Sum-of-Two-Uniform-Variables1 Weighted-Sum-of-Independent-Bernoulli-Variables1

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

Cumulative-Distribution-Function-and-Probability-Density-Function47 Normal-Distribution34 Exponential-Distribution31 Moment-Generating-Function16 Binomial-Distribution13 Poisson-Distribution13 Geometric-Distribution9 Uniform-Distribution8 Central-Limit-Theorem7 Random-Variable-Transformation关联科目基础数学7 Gamma-Distribution6 Exponential-Memoryless-Property4 Negative-Binomial-Distribution4 Chi-Square-Distribution3 Hypergeometric-Distribution关联科目离散数学3 Law-of-Large-Numbers3 Lognormal-Distribution3 Minimum-of-Independent-Exponentials3 Mixed-Distribution3 Weibull-Distribution关联科目工学基础3 Normal-Standardization-and-Tail-Probability2 Binomial-Normal-Approximation-via-Stirling关联科目基础数学1 Binomial-to-Poisson-Convergence-via-Moment-Generating-Function1 Box-Muller-Transform关联科目计算机科学1 Cauchy-Distribution1 Laplace-Distribution-Moments-Cumulative-Distribution-Function-and-Quantiles1 Levy-Distribution-from-Inverse-Chi-Square关联科目基础数学1 Log-Moments-of-Rayleigh-Distribution关联科目基础数学1 Moment-Generating-Function-of-Sum-of-Independent-Variables1 Pareto-Distribution1 Poisson-Approximation-to-Binomial1 Probability-Generating-Function1 Probability-Generating-Function-of-Random-Sum1 Stable-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。16

Markov-Information-Source10 Markov-Chain8 Stopping-Time2 Waiting-Time-for-Runs关联科目离散数学2 Absorbing-Random-Walk关联科目离散数学1 Autoregressive-Order-One-with-Bernoulli-Innovations1 Birth-Death-Process关联科目运筹与优化1 Exponential-Race-and-Order-of-Arrival关联科目运筹与优化1 Exponential-Spacings-and-Poisson-Counting-Process关联科目运筹与优化1 Gamblers-Ruin-and-Hitting-Probability关联科目运筹与优化1 Pattern-Occurrence-in-Independent-Identically-Distributed-Sequence关联科目计算机科学生物信息学1 Pattern-Probability-in-Markov-Sequence1 Random-Walk-on-Fourth-Roots-of-Unity关联科目基础数学1 Stationary-Pair-Frequencies1 Two-State-Markov-Chain-Stationary-Reward关联科目运筹与优化1 Waiting-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

Mean-Median-and-Quartiles3 Standard-Error-of-Sample-Mean2 Affine-Transformation-of-Sample-Mean1 Measurement-Scales-and-Summary-Statistics1 Selection-Bias关联科目数据科学与人工智能1

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-Estimation36 Hypothesis-Testing21 Confidence-Interval15 Unbiased-Estimation10 Statistical-Power5 Diagnostic-Test-Positive-Predictive-Value3 Estimator-Consistency3 Confidence-Interval-Width-vs-Sample-Size2 Exact-Binomial-Test2 Family-Wise-Error-Rate2 Mean-Squared-Error关联科目数据科学与人工智能2 Method-of-Moments2 Minimum-Variance-Unbiased-Estimator2 Odds-Ratio-and-Confidence-Interval关联科目生物信息学2 Sample-Size-for-Target-Power2 Bonferroni-Correction1 Chi-Square-Pivot-for-Normal-Variance1 Common-Significance-Interpretation-Errors1 Constrained-Maximum-Likelihood-Estimation关联科目运筹与优化1 Estimator-Bias1 Exponential-Rate-Maximum-Likelihood-Estimation-and-Bias1 Fisher-Exact-Test关联科目生物信息学1 Hypothesizing-After-Results-Are-Known1 Left-Censored-Exponential-Model1 Lognormal-Parameter-Maximum-Likelihood-Estimation1 Measurement-Uncertainty关联科目工学基础1 Minimum-Variance-Estimator-with-Equicorrelated-Samples1 Minimum-Variance-Linear-Unbiased-Combination关联科目运筹与优化1 Moment-and-Likelihood-Estimation-with-Censoring1 Normal-Mean-Confidence-Interval-with-Known-Variance1 One-Sample-Proportion-Z-Test1 One-Sided-Test-and-Power-for-Laplace-Location1 Poisson-Count-Maximum-Likelihood-Estimation-for-Rate1 Positive-Predictive-Value-of-Significant-Results1 Receiver-Operating-Characteristic-Curve-Interpretation关联科目数据科学与人工智能生物信息学1 Simultaneous-Confidence-Intervals1 Student-t-Confidence-Interval1 Type-II-Error-Interpretation1 Uniform-Endpoint-Estimation1 Uniform-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

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

Bayesian-Inference关联科目数据科学与人工智能5 Beta-Bernoulli-Model关联科目数据科学与人工智能5 Bayesian-Model-Selection-for-Sequence-Sources关联科目计算机科学1 Independent-Replication-and-Posterior-Odds1 Poisson-Gamma-Conjugacy关联科目数据科学与人工智能1

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

Monte-Carlo-Integration4 Antithetic-Variates关联科目计算机科学1 Bootstrap-Method关联科目数据科学与人工智能1

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

Parametric-Optimization-and-Value-Function关联科目基础数学2 Penalty-Method关联科目基础数学1 Sensitivity-Analysis1

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。11

Linear-Programming-Duality25 Simplex-Method16 Linear-Programming-Problem9 Production-Planning6 Complementary-Slackness3 Parametric-Linear-Programming关联科目基础数学2 Affine-Scaling-Method关联科目基础数学1 Farkas-Lemma关联科目基础数学1 Stepping-Stone-Method1 Total-Unimodularity-and-Integrality关联科目离散数学1 Transportation-Problem1

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

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

Quadratic-Programming关联科目基础数学5 Orthogonal-Procrustes-via-Singular-Value-Decomposition关联科目基础数学数据科学与人工智能1 Trust-Region-Subproblem关联科目基础数学1

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

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

Simulated-Annealing关联科目计算机科学概率与统计1

排队论(Queueing-Theory)排队模型、到达过程、服务过程与系统性能。5

Average-Waiting-Time关联科目概率与统计2 Finite-Capacity-Queue关联科目概率与统计计算机科学1 Littles-Law关联科目概率与统计1 M-M-1-Queue关联科目概率与统计1 Packet-Loss关联科目计算机科学1

博弈论(Game-Theory)零和博弈、鞍点、纳什均衡与策略互动。6

Nash-Equilibrium3 Best-Response-in-One-Shot-Game关联科目概率与统计2 Prisoners-Dilemma2 Saddle-Point2 Backward-Induction1 Chain-Store-Paradox1

库存管理(Inventory-Management)订货批量、补货策略、持有成本与数量折扣。3

Newsvendor-Problem关联科目概率与统计2 Economic-Order-Quantity1 Quantity-Discount1

决策分析(Decision-Analysis)多准则决策、层次分析法与判断一致性。7

Analytic-Hierarchy-Process4 Pairwise-Comparison-Consistency4 Sensitivity-Analysis3 Conditional-Value-at-Risk-and-Coherent-Risk-Measure关联科目概率与统计1 Decision-Under-Uncertainty关联科目概率与统计1 Pareto-Dominance关联科目基础数学1 Secretary-Problem-and-One-over-e-Rule关联科目概率与统计1

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。

340

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。29

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

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-Sum7 Minimum-Edit-Distance关联科目生物信息学7 Dynamic-Programming-Principle6 Knapsack-Problem关联科目运筹与优化6 Subset-Sum-Problem关联科目运筹与优化3 Longest-Common-Subsequence关联科目生物信息学2 Longest-Increasing-Subsequence2 Matrix-Chain-Multiplication关联科目基础数学2 Optimal-Binary-Search-Tree2 Zero-One-Knapsack-Recurrence2 Counting-Ordered-Pairings关联科目离散数学1 Counting-Subset-Sum-Dynamic-Programming1 Decision-Tree-Pruning关联科目数据科学与人工智能1 Fibonacci-Memoization关联科目离散数学1 Greedy-Failure-for-Zero-One-Knapsack1 Minimum-Cost-Polygon-Triangulation关联科目离散数学1 Optimal-Compression-Encoding1 Pattern-Occurrence-Probability关联科目概率与统计生物信息学1 Unbounded-Coin-Change-Counting1 Unbounded-Minimum-Coin-Change1

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

Knuth-Morris-Pratt-Algorithm2 String-Matching2 Hash-Collision-Verification-and-Worst-Case关联科目概率与统计1 Knuth-Morris-Pratt-Failure-and-Shift-Table1 Longest-Palindromic-Substring1 Minimum-Window-Substring1 Rabin-Karp-Rolling-Hash1

程序设计(Programming)程序阅读、实现、语言语义与代码分析。46

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

Pipelining16 Cache15 Number-Representation14 Performance-Analysis13 Data-Hazard8 Cache-Address-Mapping7 Average-Memory-Access-Time4 Branch-Prediction4 Control-Hazard4 Data-Forwarding4 Cache-Miss-Types3 Direct-Mapped-Cache-Conflict-and-Hit-Rate3 Floating-Point-Representation3 Floating-Point-Rounding-Error关联科目基础数学3 Superscalar-Execution3 Assembly-Language2 Cache-Aware-Loop-and-Register-Reuse2 Cache-Hit-Rate-Optimization2 Endianness2 IEEE-Standard-754-Floating-Point-Arithmetic2 Instruction-Cycle2 Locality-of-Reference2 Multi-Level-Cache2 Out-of-Order-Execution2 Parallelism2 Pipeline-Hazards2 Sequential-Access-Cache-Hit-Rate2 Translation-Lookaside-Buffer2 Addressing-Modes1 Amdahls-Law1 Branch-Penalty1 Hamming-Weight1 Hardware-Prefetching1 Instruction-Encoding1 Instructions-per-Cycle-with-Variable-Latency-Memory-Access1 Memory-Alignment1 Memory-Level-Parallelism1 Microprogrammed-Control1 Non-Adjacent-Form-Signed-Binary-Representation关联科目离散数学基础数学1 Non-Blocking-Cache1 Program-Counter1 Reduced-Instruction-Set-Computer-and-Complex-Instruction-Set-Computer-Architectures1 Register-Renaming1 Sensor-Acquisition-Pipeline-Scheduling关联科目电气电子工学基础1 Sequential-Random-and-Pointer-Chasing-Access1 Single-Instruction-Multiple-Data-Architecture1 Snooping-Cache-Coherence1 Structural-Hazard1 Thread-Level-Speculative-Execution1 Two-Way-Set-Associative-Cache-Datapath1 Write-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

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-Grammar24 Deterministic-Finite-Automaton21 Deterministic-Finite-Automaton-Minimization12 Pumping-Lemma12 Nondeterministic-Finite-Automaton11 Regular-Expression9 Regular-Language-Closure-Properties关联科目离散数学9 Context-Free-Language-Closure-Properties关联科目离散数学7 Epsilon-Nondeterministic-Finite-Automaton5 Automata-State-Complexity关联科目离散数学3 Mealy-Machine关联科目电气电子3 Parse-Tree3 Product-Automaton关联科目离散数学3 Regular-Grammar-and-Regular-Language3 Chomsky-Normal-Form2 Moore-Machine关联科目电气电子2 Nondeterministic-Polynomial-Time-Completeness关联科目离散数学运筹与优化2 Backus-Naur-Form1 Context-Free-Grammar-Emptiness-Problem1 Context-Free-Language-Regular-Intersection关联科目离散数学1 Equal-Length-Prefix-Operation1 Finite-State-Transduction1 Language-Shuffle关联科目离散数学1 Language-Square-Root1 Language-Substitution1 Left-Quotient1 Left-to-Right-Leftmost-Derivation-One-Lookahead-Parsing1 Left-to-Right-Rightmost-Derivation-Parsing1 Nondeterministic-Finite-Automaton-to-Deterministic-Finite-Automaton-Conversion1 Regular-Language-Decision-Problems1 Turing-Machine1

数据库(Databases)数据库模型、查询、事务与数据管理。5

Query-Optimization1 Relational-Algebra关联科目基础数学1 Relational-Database-Normalization1 Relational-Model-and-Structured-Query-Language1 Schema-Design-and-Aggregation1

计算机网络(Networks)网络协议、通信机制与网络系统。20

Protocol-Throughput-and-Utilization9 Transmission-Control-Protocol-and-User-Datagram-Protocol6 Bandwidth-Delay-Product关联科目基础数学5 Carrier-Sense-Multiple-Access-with-Collision-Detection5 Distance-Vector-and-Link-State-Routing5 Reliable-Data-Transfer关联科目概率与统计5 Stop-and-Wait-Automatic-Repeat-Request关联科目概率与统计5 Sliding-Window-Protocol4 Internet-Protocol-Version-4-Subnetting3 Autonomous-System-Numbers2 Domain-Name-System2 Hidden-Terminal-Problem-and-Request-to-Send-Clear-to-Send2 Internet-Protocol-Version-4-and-Version-62 Transparent-Web-Cache-in-Wide-Area-Networks2 Available-Bandwidth-Estimation1 Common-Gateway-Interface1 Hypertext-Transfer-Protocol1 Packetization-Delay1 Server-Concurrency-and-Request-Queueing关联科目运筹与优化1 Transmission-Control-Protocol-Congestion-Control1

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2 Hough-Transform-for-Line-Detection关联科目基础数学数据科学与人工智能2 Homogeneous-Coordinates关联科目基础数学1 Invariant-Image-Features关联科目数据科学与人工智能1 Optical-Flow关联科目数据科学与人工智能1 Orthogonal-Vanishing-Point-Camera-Calibration关联科目基础数学1 Pinhole-Camera-and-Vanishing-Points关联科目基础数学1 Procedural-Modeling1 Projection-and-Reconstruction关联科目基础数学1 Ray-Tracing关联科目基础数学物理1 Robot-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

Public-Key-Cryptography关联科目基础数学3 Public-Key-Infrastructure2 Buffer-Overflow1 Cross-Site-Scripting1 Network-Security-Protocols1 Phishing-Attack1 Secure-Sockets-Layer1 Targeted-Email-Attack1 User-Authentication-Methods1

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

Client-Server-and-Peer-to-Peer-Comparison1 Distributed-Hashing关联科目概率与统计1 Grid-Computing1

信息论(Information-Theory)熵、互信息、信源编码、信道容量与纠错编码。37

量子计算(Quantum-Computing)量子计算模型、量子算法与计算复杂性。1

Quantum-Computing关联科目物理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

Principal-Component-Analysis关联科目概率与统计基础数学2 Vector-Quantization关联科目电气电子2 Image-Color-Quantization关联科目计算机科学1 Image-Filtering-and-Moments关联科目计算机科学基础数学1 Term-Frequency-Inverse-Document-Frequency关联科目计算机科学1

机器学习(Machine-Learning)分类、决策树、强化学习与学习模型。36

人工智能基础(Artificial-Intelligence)知识表示、语义网络与智能系统基础。8

Minimax-Algorithm关联科目计算机科学运筹与优化2 A-Star-Algorithm关联科目计算机科学运筹与优化1 Alpha-Beta-Pruning关联科目计算机科学运筹与优化1 Best-First-Search关联科目计算机科学运筹与优化1 Knowledge-Representation关联科目计算机科学1 Morphological-Analysis关联科目计算机科学1 Natural-Language-Morphology-and-Morphemes关联科目计算机科学1 Semantic-Network关联科目计算机科学1

电气电子

电路、电子、信号、通信与计算机硬件。

116

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16 Circuit-Transient-Response关联科目基础数学13 Resistor-Inductor-Capacitor-Resonance关联科目物理8 Mutual-Inductance关联科目物理7 Maximum-Power-Transfer关联科目运筹与优化6 Transformer-Equivalent-Circuit关联科目物理4 Alternating-Current-Power-and-Power-Factor关联科目物理3 Circuit-Transfer-Function关联科目基础数学3 Transmission-Line-and-Impedance-Matching关联科目物理3 Two-Port-Network关联科目基础数学3 Mesh-Analysis2 Metal-Oxide-Semiconductor-Field-Effect-Transistor-Bias-and-Small-Signal-Analysis关联科目物理2 Operational-Amplifier2 Resistor-Capacitor-Charging-and-Discharging关联科目基础数学物理2 Thevenin-and-Norton-Equivalent2 Wheatstone-Bridge2 Active-Filter1 Boost-Converter-Switching-Transient关联科目物理基础数学1 Kirchhoff-Laws1 Nodal-Analysis1 Proximity-Sensor-Principles关联科目物理工学基础1 Quarter-Wave-Transformer关联科目物理1 Resistor-Inductor-Capacitor-Damping关联科目基础数学物理1 Superposition-Theorem1 Three-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

信号处理(Signal-Processing)离散信号、变换、滤波与频域分析。31

控制理论(Control-Theory)系统建模、稳定性、反馈与控制系统分析。22

通信与编码(Communications)通信信道、编码、信息传输与误差控制。2

Code-Division-Multiple-Access关联科目基础数学计算机科学1 Spread-Spectrum-Communication关联科目计算机科学1

物理

力学、电磁学、量子与物理数学。

112

力学(Mechanics)经典力学、振动、旋转参考系与连续介质基础。23

电磁学(Electromagnetism)电场、磁场、麦克斯韦方程与电磁现象。32

量子力学(Quantum-Mechanics)量子态、算符、自旋与量子统计基础。32

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。18

Fermi-Dirac-Grand-Canonical-Distribution关联科目计算机科学2 Helmholtz-Free-Energy-Differential关联科目化学2 Canonical-Partition-Function关联科目概率与统计化学1 Chemical-Equilibrium-and-Vant-Hoff-Relation关联科目化学1 Clapeyron-Equation关联科目化学1 Classical-Ideal-Gas-Entropy-and-Low-Temperature-Failure关联科目化学1 Classical-Ideal-Gas-Partition-Function-and-Gibbs-Factor关联科目化学1 Enthalpy-and-Thermodynamic-Relations关联科目化学基础数学1 Grand-Canonical-Ideal-Gas关联科目化学1 High-Temperature-Fermi-Gas-Classical-Limit关联科目化学1 Ideal-Gas-Entropy-of-Mixing关联科目化学1 Ideal-Gas-Free-Expansion关联科目化学1 Joule-Thomson-Effect关联科目化学工学基础1 Langmuir-Adsorption-Isotherm关联科目化学1 Low-Temperature-Fermi-Gas-Heat-Capacity-and-Entropy1 Maxwell-Relations关联科目化学1 Mean-Field-Ising-Model-and-Phase-Transition关联科目基础数学1 Photon-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

Group-Velocity-and-Wave-Packets关联科目基础数学工学基础1

天体物理(Astrophysics)天文观测、光子统计、恒星事件与天体信号分析。3

Central-Limit-Theorem-Based-Simulation-of-Observation-Noise关联科目概率与统计计算机科学1 Exposure-Time-Signal-to-Noise-with-Readout-Noise关联科目概率与统计电气电子1 Photon-Counting-Poisson-Process关联科目概率与统计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。13

Consecutive-First-Order-Reaction-Kinetics关联科目基础数学2 Einstein-Solid-Heat-Capacity关联科目物理2 Entropy-Change关联科目物理2 Electrochemical-Cell-Potential-from-Gibbs-Free-Energy关联科目电气电子1 Enzyme-Inhibition-and-Lineweaver-Burk-Plot关联科目生物信息学1 Gibbs-Free-Energy-and-Non-PV-Work关联科目物理1 Ideal-Gas-Thermodynamics关联科目物理1 Langmuir-Hinshelwood-CO-Oxidation关联科目工学基础1 Operator-Commutator关联科目物理基础数学1 Particle-in-a-Box-and-HOMO-LUMO-Transition关联科目物理基础数学1 Planck-Blackbody-Law关联科目物理1 Wavefunction-Normalization关联科目物理基础数学1 Wien-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

Coordination-Compound-Composition1 Oxygen-Vacancies-in-Stabilized-Zirconia关联科目工学基础1 Radius-Ratio-Rule-and-Ionic-Coordination1 Stepwise-Complex-Formation-and-Ligand-Field关联科目物理1

有机化学(Organic-Chemistry)有机反应机理、合成、立体化学与结构鉴定。6

Arene-Oxide-NIH-Shift关联科目生物信息学1 Cyclohexane-Trans-Diaxial-E2-Elimination1 Diels-Alder-and-Amino-Claisen-Rearrangements1 Friedel-Crafts-Acylation-to-Alkylbenzene1 Robinson-Annulation1 Stork-Enamine-Alkylation1

地球科学

地质年代、地貌、构造地质及地球表层过程。

地球年代学(Geochronology)利用放射性核素等方法测定地质事件与地貌的年代。1

Radiocarbon-Decay-and-Dating-Limit关联科目基础数学物理1

冰缘地貌学(Periglacial-Geomorphology)永久冻土、冻融作用及其形成的地貌。1

Active-Layer-Permafrost-and-Pingo关联科目物理1

河流地貌学(Fluvial-Geomorphology)河流侵蚀、堆积、下切与阶地形成。1

Fluvial-Terraces-and-River-Incision1

构造地质学(Structural-Geology)断层、褶皱、地壳变形及其地貌证据。1

Active-Fault-Geomorphology1

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

Sequence-Alignment关联科目计算机科学4

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

Attentional-Orienting1 Dissociation-Methods1 Magnetoencephalography-vs-Functional-Magnetic-Resonance-Imaging关联科目工学基础1 Reaction-Time-Experiment-Design关联科目概率与统计1 Sensory-Processing-and-Illusions1 Speed-Accuracy-Tradeoff1 Voxel-Based-Morphometry-and-Diffusion-Tensor-Imaging关联科目数据科学与人工智能1

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

Beam-Deflection关联科目基础数学1 Euler-Buckling关联科目基础数学物理1 Strain-Gauge关联科目电气电子1 Thermal-Deformation-Compatibility关联科目物理1 Yielding关联科目物理1

流体力学(Fluid-Mechanics)流体运动、波动、连续介质与工程流动问题。1

Logarithmic-Wind-Profile-and-Wind-Power-Scaling关联科目基础数学物理1

材料科学(Materials-Science)材料结构、性质、相变与材料工程基础。1

Piezoelectric-Effect-and-Element关联科目电气电子物理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3 Zero-Moment-Point关联科目物理基础数学3 Simultaneous-Localization-and-Mapping关联科目计算机科学概率与统计2 Articulated-Link-Mechanism-Representation关联科目基础数学1 Autonomous-Vehicle-Dynamic-Map关联科目计算机科学数据科学与人工智能1 Force-Control-Implementation关联科目电气电子1 Jacobian-Transpose-Joint-Torque关联科目基础数学物理1 Manipulator-Jacobian-and-End-Effector-Velocity关联科目基础数学1

经济学

研究资源配置、经济增长、公共政策、国际交换与经济制度演变。

微观经济学(Microeconomics)研究个人、家庭与企业的选择，以及市场中的价格形成和资源配置。3

Adverse-Selection-and-Lemons-Market1 Consumer-and-Producer-Surplus1 Gender-and-Labor-Economics关联科目工商管理社会学1

计量经济学(Econometrics)

运用统计模型与数据识别、估计和检验经济关系。

财政学(Public-Finance)研究税收、公共支出、政府预算及公共部门的资源配置。1

Health-Economics-and-Nursing-Services关联科目工商管理1

工商管理

研究组织的战略、结构、人才、市场、会计、金融与科学决策。

人力资源管理(Human-Resource-Management)研究人员招聘、配置、培养、评价、激励与劳动关系。1

Nursing-Workforce关联科目经济学1

市场营销(Marketing)研究消费者、市场分析、产品、定价、渠道、传播与品牌。1

Tourism-Marketing-and-Destination-Management关联科目经济学社会学2

金融(Finance)研究企业融资、投资决策、资本结构、资产定价与风险管理。4

Efficient-Market-Hypothesis关联科目经济学1 Market-Price-of-Risk关联科目经济学概率与统计1 One-Period-Binomial-Model-and-State-Prices关联科目经济学概率与统计1 Put-Call-Parity关联科目经济学1

社会学

研究社会关系、制度、结构、不平等、共同体与文化变迁。

家庭与性别(Family-and-Gender)研究家庭结构、亲密关系、照护、性别规范与性别不平等。1

Gendered-Division-of-Labor关联科目工商管理经济学1

都市社会学(Urban-Sociology)研究城市空间、社区、迁移、住房、治理与都市生活。1

Overtourism-and-Regional-Dispersion关联科目工商管理经济学2

文化与媒体(Culture-and-Media)研究意义、身份、文化生产、传播媒介与大众文化。1

Individualism-and-Collectivism关联科目心理学1

心理学

研究心理过程与行为，涵盖基础、认知、社会、发展、临床、研究方法、评估与伦理。

基础心理学(Basic-Psychology)研究学习、条件作用、动机、情绪、感觉及其他基本心理机制。1

Punishment-and-Aversive-Learning1

认知心理学(Cognitive-Psychology)研究知觉、注意、记忆、语言、思维与决策等信息处理过程。1

Stroop-Effect关联科目认知科学与神经科学1

社会心理学(Social-Psychology)研究个体如何受到他人、群体、规范、身份与社会情境的影响。3

Cultural-Individualism-and-Collectivism关联科目社会学1 Ingroup-Bias-and-Social-Identity1 Self-Esteem-and-Culture关联科目社会学1

发展心理学(Developmental-Psychology)研究从婴幼儿期到老年期的认知、情绪、社会性与人格发展。1

Successful-Aging1

临床心理学(Clinical-Psychology)研究心理健康、精神病理、预防、心理治疗及面向个人与社区的支持。3

Eating-Disorders1 Psychodynamic-Theory1 Suicide-Prevention-and-Gatekeeping1

研究方法与统计(Research-Methods-and-Statistics)研究实验与调查设计、测量、数据分析、推断及研究结果的解释。3

Measurement-Error关联科目概率与统计1 Multiple-Comparisons关联科目概率与统计1 Nonverbal-Behavioral-Measurement1

伦理(Ethics)研究心理学研究与实践中的知情同意、保密、专业边界、责任与权益保护。3

Confidentiality1 Informed-Assent1 Multiple-Relationships1

法学

研究法律规范、权利义务、公共权力及法律制度的解释与适用。

民法(Civil-Law)研究私人之间的财产关系、债权债务、合同、侵权及相关救济。1

Creditors-Subrogation-Right1

行政法(Administrative-Law)研究行政权的法律依据、行政活动、程序、救济与司法控制。1

Principle-of-Statutory-Reservation1

待归类

Computer-Science.Digital-Logic.Flip-Flop1 Computer-Science.Digital-Logic.Sequential-Circuit1