A factorization approach to grouping

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数学词汇中英文对照（初中部分）方程与代数

数学词汇中英文对照（初中部分）方程与代数数学词汇中英文对照（初中部分）二、方程与代数代数（学）：algebra字母表示数：Use letters to indicate numbers代数式：algebraic expression单项式：monomial系数：coefficient次数：degree多项式：polynomial二项式：binomial三项式：trinomial二次三项式：second degree trinomial项：term常数项：constant term整式：integral expression升幂：in ascending order of the power降幂：in descending order of the power同类项：like terms合并：combine等式：equality, equation等号：sign of equality二次方：(x)squared三次方：(x)cubedn次方：(x)to the power of n/to the n-th power乘法公式：multiplication formula平方差：difference of squares平方差公式：formula for the difference of squares 完全平方：perfect square完全平方公式：formula for the perfect square分解因式：factorizing公因式：common factor提公因式法：method of extracting common factors 十字相乘法：method of cross multiplication分组分解法：method of regrouping长除法：long division分离系数法：method of detached coefficients分式：algebraic fraction无意义：illegal有意义：legal有理式：rational expression约分：reduction of a fraction最简分式：simplest fraction通分：turn fractions to a common denominator最简公分母：simplest common denominator根式：radical根指数：radical exponent被开方数：radicand二次根式：quadratic surd最简二次根式：simplest quadratic surd同类二次根式：similar quadratic surds分母有理化：rationalize a denominator有理化因式：rationalizing factor根：root增根：extraneous root已知数：given number未知数：unknown number方程：equation列方程：form an equation等量关系：equality检验：check根：root解方程：solving equation解法、解：solution一元一次方程：linear equation in one variable方程的解：solution of equation移项：transposition of terms去括号：remove brackes去分母：remove denominator化简：simplify不成立：false不等式：inequality一元一次不等式：linear inequality in one unknown一元一次不等式组：system of linear inequalities in one variable不等号：non-equal sign含绝对值的不等式：inequality with absolute value大于：greater than小于：less than大于等于：greater than or equal to小于等于：less than or equal to不等式性质：property of inequality解集：solution set解不等式：solve inequality公共部分：common part无解：no solution二元一次方程：linear equation in two unknowns二元一次方程组：system of linear equations in two unknowns 代入（消元）法：elimination by substitution加减（消元）法：elimination by addition and subtraction三元一次方程：linear equation in three unknowns三元一次方程组：system of linear equations in three unknowns一元二次方程：quadratic equation in one unknown一般式：general form二次项：quadratic term一次项：linear term常数项：constant term开平方法：radication因式分解法：factorization配方法：complete a perfect squae求根公式法： formula method一元二次方程根的判别式：discriminant of quadratic equation in one variable整式方程：integral equation一元整式方程：linear integral eqution一元高次方程：linear high-order equation二项方程：binomial equation双二次方程：biquadratic equation分式方程：fractional equation无理方程：irrational equation二元二次方程：quadratic equation in two variables一元二次不等式：quadratic inequality in one variable。

高中英语学术论文研究方法练习题40题

高中英语学术论文研究方法练习题40题1.Which of the following topics is most suitable for a high school English academic paper?A.The history of video games.B.The influence of social media on teenagers' language learning.C.The development of artificial intelligence in the medical field.D.The architecture of ancient Rome.答案：B。

解析：选项 A 视频游戏历史与高中英语学术论文关联不大。

选项C 人工智能在医疗领域的发展与英语学科不相关。

选项D 古罗马建筑也与英语学科没有直接关系。

而选项B 社交媒体对青少年语言学习的影响既与英语语言相关，也适合高中学生进行研究。

2.In choosing a topic for an English academic paper, what should be considered first?A.Personal interest.B.Availability of resources.C.Relevance to the curriculum.D.Popularity of the topic.答案：C。

解析：选项 A 个人兴趣虽然重要，但不是首先要考虑的。

选项 B 资源的可获得性在确定选题后再考虑。

选项 D 话题的流行度不是关键因素。

首先应考虑与课程的相关性，这样才能确保论文在学科范围内有意义。

3.Which of the following is NOT a good criterion for choosing anacademic paper topic?A.Being too broad.B.Having enough research materials available.C.Being relevant to current events.D.Being easy to research.答案：A。

机器学习专业词汇中英文对照

机器学习专业词汇中英⽂对照activation 激活值activation function 激活函数additive noise 加性噪声autoencoder ⾃编码器Autoencoders ⾃编码算法average firing rate 平均激活率average sum-of-squares error 均⽅差backpropagation 后向传播basis 基basis feature vectors 特征基向量batch gradient ascent 批量梯度上升法Bayesian regularization method 贝叶斯规则化⽅法Bernoulli random variable 伯努利随机变量bias term 偏置项binary classfication ⼆元分类class labels 类型标记concatenation 级联conjugate gradient 共轭梯度contiguous groups 联通区域convex optimization software 凸优化软件convolution 卷积cost function 代价函数covariance matrix 协⽅差矩阵DC component 直流分量decorrelation 去相关degeneracy 退化demensionality reduction 降维derivative 导函数diagonal 对⾓线diffusion of gradients 梯度的弥散eigenvalue 特征值eigenvector 特征向量error term 残差feature matrix 特征矩阵feature standardization 特征标准化feedforward architectures 前馈结构算法feedforward neural network 前馈神经⽹络feedforward pass 前馈传导fine-tuned 微调first-order feature ⼀阶特征forward pass 前向传导forward propagation 前向传播Gaussian prior ⾼斯先验概率generative model ⽣成模型gradient descent 梯度下降Greedy layer-wise training 逐层贪婪训练⽅法grouping matrix 分组矩阵Hadamard product 阿达马乘积Hessian matrix Hessian 矩阵hidden layer 隐含层hidden units 隐藏神经元Hierarchical grouping 层次型分组higher-order features 更⾼阶特征highly non-convex optimization problem ⾼度⾮凸的优化问题histogram 直⽅图hyperbolic tangent 双曲正切函数hypothesis 估值，假设identity activation function 恒等激励函数IID 独⽴同分布illumination 照明inactive 抑制independent component analysis 独⽴成份分析input domains 输⼊域input layer 输⼊层intensity 亮度/灰度intercept term 截距KL divergence 相对熵KL divergence KL分散度k-Means K-均值learning rate 学习速率least squares 最⼩⼆乘法linear correspondence 线性响应linear superposition 线性叠加line-search algorithm 线搜索算法local mean subtraction 局部均值消减local optima 局部最优解logistic regression 逻辑回归loss function 损失函数low-pass filtering 低通滤波magnitude 幅值MAP 极⼤后验估计maximum likelihood estimation 极⼤似然估计mean 平均值MFCC Mel 倒频系数multi-class classification 多元分类neural networks 神经⽹络neuron 神经元Newton’s method ⽜顿法non-convex function ⾮凸函数non-linear feature ⾮线性特征norm 范式norm bounded 有界范数norm constrained 范数约束normalization 归⼀化numerical roundoff errors 数值舍⼊误差numerically checking 数值检验numerically reliable 数值计算上稳定object detection 物体检测objective function ⽬标函数off-by-one error 缺位错误orthogonalization 正交化output layer 输出层overall cost function 总体代价函数over-complete basis 超完备基over-fitting 过拟合parts of objects ⽬标的部件part-whole decompostion 部分-整体分解PCA 主元分析penalty term 惩罚因⼦per-example mean subtraction 逐样本均值消减pooling 池化pretrain 预训练principal components analysis 主成份分析quadratic constraints ⼆次约束RBMs 受限Boltzman机reconstruction based models 基于重构的模型reconstruction cost 重建代价reconstruction term 重构项redundant 冗余reflection matrix 反射矩阵regularization 正则化regularization term 正则化项rescaling 缩放robust 鲁棒性run ⾏程second-order feature ⼆阶特征sigmoid activation function S型激励函数significant digits 有效数字singular value 奇异值singular vector 奇异向量smoothed L1 penalty 平滑的L1范数惩罚Smoothed topographic L1 sparsity penalty 平滑地形L1稀疏惩罚函数smoothing 平滑Softmax Regresson Softmax回归sorted in decreasing order 降序排列source features 源特征sparse autoencoder 消减归⼀化Sparsity 稀疏性sparsity parameter 稀疏性参数sparsity penalty 稀疏惩罚square function 平⽅函数squared-error ⽅差stationary 平稳性（不变性）stationary stochastic process 平稳随机过程step-size 步长值supervised learning 监督学习symmetric positive semi-definite matrix 对称半正定矩阵symmetry breaking 对称失效tanh function 双曲正切函数the average activation 平均活跃度the derivative checking method 梯度验证⽅法the empirical distribution 经验分布函数the energy function 能量函数the Lagrange dual 拉格朗⽇对偶函数the log likelihood 对数似然函数the pixel intensity value 像素灰度值the rate of convergence 收敛速度topographic cost term 拓扑代价项topographic ordered 拓扑秩序transformation 变换translation invariant 平移不变性trivial answer 平凡解under-complete basis 不完备基unrolling 组合扩展unsupervised learning ⽆监督学习variance ⽅差vecotrized implementation 向量化实现vectorization ⽮量化visual cortex 视觉⽪层weight decay 权重衰减weighted average 加权平均值whitening ⽩化zero-mean 均值为零Letter AAccumulated error backpropagation 累积误差逆传播Activation Function 激活函数Adaptive Resonance Theory/ART ⾃适应谐振理论Addictive model 加性学习Adversarial Networks 对抗⽹络Affine Layer 仿射层Affinity matrix 亲和矩阵Agent 代理 / 智能体Algorithm 算法Alpha-beta pruning α-β剪枝Anomaly detection 异常检测Approximation 近似Area Under ROC Curve／AUC Roc 曲线下⾯积Artificial General Intelligence/AGI 通⽤⼈⼯智能Artificial Intelligence/AI ⼈⼯智能Association analysis 关联分析Attention mechanism 注意⼒机制Attribute conditional independence assumption 属性条件独⽴性假设Attribute space 属性空间Attribute value 属性值Autoencoder ⾃编码器Automatic speech recognition ⾃动语⾳识别Automatic summarization ⾃动摘要Average gradient 平均梯度Average-Pooling 平均池化Letter BBackpropagation Through Time 通过时间的反向传播Backpropagation/BP 反向传播Base learner 基学习器Base learning algorithm 基学习算法Batch Normalization/BN 批量归⼀化Bayes decision rule 贝叶斯判定准则Bayes Model Averaging／BMA 贝叶斯模型平均Bayes optimal classifier 贝叶斯最优分类器Bayesian decision theory 贝叶斯决策论Bayesian network 贝叶斯⽹络Between-class scatter matrix 类间散度矩阵Bias 偏置 / 偏差Bias-variance decomposition 偏差-⽅差分解Bias-Variance Dilemma 偏差 – ⽅差困境Bi-directional Long-Short Term Memory/Bi-LSTM 双向长短期记忆Binary classification ⼆分类Binomial test ⼆项检验Bi-partition ⼆分法Boltzmann machine 玻尔兹曼机Bootstrap sampling ⾃助采样法／可重复采样／有放回采样Bootstrapping ⾃助法Break-Event Point／BEP 平衡点Letter CCalibration 校准Cascade-Correlation 级联相关Categorical attribute 离散属性Class-conditional probability 类条件概率Classification and regression tree/CART 分类与回归树Classifier 分类器Class-imbalance 类别不平衡Closed -form 闭式Cluster 簇/类/集群Cluster analysis 聚类分析Clustering 聚类Clustering ensemble 聚类集成Co-adapting 共适应Coding matrix 编码矩阵COLT 国际学习理论会议Committee-based learning 基于委员会的学习Competitive learning 竞争型学习Component learner 组件学习器Comprehensibility 可解释性Computation Cost 计算成本Computational Linguistics 计算语⾔学Computer vision 计算机视觉Concept drift 概念漂移Concept Learning System /CLS 概念学习系统Conditional entropy 条件熵Conditional mutual information 条件互信息Conditional Probability Table／CPT 条件概率表Conditional random field/CRF 条件随机场Conditional risk 条件风险Confidence 置信度Confusion matrix 混淆矩阵Connection weight 连接权Connectionism 连结主义Consistency ⼀致性／相合性Contingency table 列联表Continuous attribute 连续属性Convergence 收敛Conversational agent 会话智能体Convex quadratic programming 凸⼆次规划Convexity 凸性Convolutional neural network/CNN 卷积神经⽹络Co-occurrence 同现Correlation coefficient 相关系数Cosine similarity 余弦相似度Cost curve 成本曲线Cost Function 成本函数Cost matrix 成本矩阵Cost-sensitive 成本敏感Cross entropy 交叉熵Cross validation 交叉验证Crowdsourcing 众包Curse of dimensionality 维数灾难Cut point 截断点Cutting plane algorithm 割平⾯法Letter DData mining 数据挖掘Data set 数据集Decision Boundary 决策边界Decision stump 决策树桩Decision tree 决策树／判定树Deduction 演绎Deep Belief Network 深度信念⽹络Deep Convolutional Generative Adversarial Network/DCGAN 深度卷积⽣成对抗⽹络Deep learning 深度学习Deep neural network/DNN 深度神经⽹络Deep Q-Learning 深度 Q 学习Deep Q-Network 深度 Q ⽹络Density estimation 密度估计Density-based clustering 密度聚类Differentiable neural computer 可微分神经计算机Dimensionality reduction algorithm 降维算法Directed edge 有向边Disagreement measure 不合度量Discriminative model 判别模型Discriminator 判别器Distance measure 距离度量Distance metric learning 距离度量学习Distribution 分布Divergence 散度Diversity measure 多样性度量／差异性度量Domain adaption 领域⾃适应Downsampling 下采样D-separation （Directed separation）有向分离Dual problem 对偶问题Dummy node 哑结点Dynamic Fusion 动态融合Dynamic programming 动态规划Letter EEigenvalue decomposition 特征值分解Embedding 嵌⼊Emotional analysis 情绪分析Empirical conditional entropy 经验条件熵Empirical entropy 经验熵Empirical error 经验误差Empirical risk 经验风险End-to-End 端到端Energy-based model 基于能量的模型Ensemble learning 集成学习Ensemble pruning 集成修剪Error Correcting Output Codes／ECOC 纠错输出码Error rate 错误率Error-ambiguity decomposition 误差-分歧分解Euclidean distance 欧⽒距离Evolutionary computation 演化计算Expectation-Maximization 期望最⼤化Expected loss 期望损失Exploding Gradient Problem 梯度爆炸问题Exponential loss function 指数损失函数Extreme Learning Machine/ELM 超限学习机Letter FFactorization 因⼦分解False negative 假负类False positive 假正类False Positive Rate/FPR 假正例率Feature engineering 特征⼯程Feature selection 特征选择Feature vector 特征向量Featured Learning 特征学习Feedforward Neural Networks/FNN 前馈神经⽹络Fine-tuning 微调Flipping output 翻转法Fluctuation 震荡Forward stagewise algorithm 前向分步算法Frequentist 频率主义学派Full-rank matrix 满秩矩阵Functional neuron 功能神经元Letter GGain ratio 增益率Game theory 博弈论Gaussian kernel function ⾼斯核函数Gaussian Mixture Model ⾼斯混合模型General Problem Solving 通⽤问题求解Generalization 泛化Generalization error 泛化误差Generalization error bound 泛化误差上界Generalized Lagrange function ⼴义拉格朗⽇函数Generalized linear model ⼴义线性模型Generalized Rayleigh quotient ⼴义瑞利商Generative Adversarial Networks/GAN ⽣成对抗⽹络Generative Model ⽣成模型Generator ⽣成器Genetic Algorithm/GA 遗传算法Gibbs sampling 吉布斯采样Gini index 基尼指数Global minimum 全局最⼩Global Optimization 全局优化Gradient boosting 梯度提升Gradient Descent 梯度下降Graph theory 图论Ground-truth 真相／真实Letter HHard margin 硬间隔Hard voting 硬投票Harmonic mean 调和平均Hesse matrix 海塞矩阵Hidden dynamic model 隐动态模型Hidden layer 隐藏层Hidden Markov Model/HMM 隐马尔可夫模型Hierarchical clustering 层次聚类Hilbert space 希尔伯特空间Hinge loss function 合页损失函数Hold-out 留出法Homogeneous 同质Hybrid computing 混合计算Hyperparameter 超参数Hypothesis 假设Hypothesis test 假设验证Letter IICML 国际机器学习会议Improved iterative scaling/IIS 改进的迭代尺度法Incremental learning 增量学习Independent and identically distributed/i.i.d. 独⽴同分布Independent Component Analysis/ICA 独⽴成分分析Indicator function 指⽰函数Individual learner 个体学习器Induction 归纳Inductive bias 归纳偏好Inductive learning 归纳学习Inductive Logic Programming／ILP 归纳逻辑程序设计Information entropy 信息熵Information gain 信息增益Input layer 输⼊层Insensitive loss 不敏感损失Inter-cluster similarity 簇间相似度International Conference for Machine Learning/ICML 国际机器学习⼤会Intra-cluster similarity 簇内相似度Intrinsic value 固有值Isometric Mapping/Isomap 等度量映射Isotonic regression 等分回归Iterative Dichotomiser 迭代⼆分器Letter KKernel method 核⽅法Kernel trick 核技巧Kernelized Linear Discriminant Analysis／KLDA 核线性判别分析K-fold cross validation k 折交叉验证／k 倍交叉验证K-Means Clustering K – 均值聚类K-Nearest Neighbours Algorithm/KNN K近邻算法Knowledge base 知识库Knowledge Representation 知识表征Letter LLabel space 标记空间Lagrange duality 拉格朗⽇对偶性Lagrange multiplier 拉格朗⽇乘⼦Laplace smoothing 拉普拉斯平滑Laplacian correction 拉普拉斯修正Latent Dirichlet Allocation 隐狄利克雷分布Latent semantic analysis 潜在语义分析Latent variable 隐变量Lazy learning 懒惰学习Learner 学习器Learning by analogy 类⽐学习Learning rate 学习率Learning Vector Quantization/LVQ 学习向量量化Least squares regression tree 最⼩⼆乘回归树Leave-One-Out/LOO 留⼀法linear chain conditional random field 线性链条件随机场Linear Discriminant Analysis／LDA 线性判别分析Linear model 线性模型Linear Regression 线性回归Link function 联系函数Local Markov property 局部马尔可夫性Local minimum 局部最⼩Log likelihood 对数似然Log odds／logit 对数⼏率Logistic Regression Logistic 回归Log-likelihood 对数似然Log-linear regression 对数线性回归Long-Short Term Memory/LSTM 长短期记忆Loss function 损失函数Letter MMachine translation/MT 机器翻译Macron-P 宏查准率Macron-R 宏查全率Majority voting 绝对多数投票法Manifold assumption 流形假设Manifold learning 流形学习Margin theory 间隔理论Marginal distribution 边际分布Marginal independence 边际独⽴性Marginalization 边际化Markov Chain Monte Carlo/MCMC 马尔可夫链蒙特卡罗⽅法Markov Random Field 马尔可夫随机场Maximal clique 最⼤团Maximum Likelihood Estimation/MLE 极⼤似然估计／极⼤似然法Maximum margin 最⼤间隔Maximum weighted spanning tree 最⼤带权⽣成树Max-Pooling 最⼤池化Mean squared error 均⽅误差Meta-learner 元学习器Metric learning 度量学习Micro-P 微查准率Micro-R 微查全率Minimal Description Length/MDL 最⼩描述长度Minimax game 极⼩极⼤博弈Misclassification cost 误分类成本Mixture of experts 混合专家Momentum 动量Moral graph 道德图／端正图Multi-class classification 多分类Multi-document summarization 多⽂档摘要Multi-layer feedforward neural networks 多层前馈神经⽹络Multilayer Perceptron/MLP 多层感知器Multimodal learning 多模态学习Multiple Dimensional Scaling 多维缩放Multiple linear regression 多元线性回归Multi-response Linear Regression ／MLR 多响应线性回归Mutual information 互信息Letter NNaive bayes 朴素贝叶斯Naive Bayes Classifier 朴素贝叶斯分类器Named entity recognition 命名实体识别Nash equilibrium 纳什均衡Natural language generation/NLG ⾃然语⾔⽣成Natural language processing ⾃然语⾔处理Negative class 负类Negative correlation 负相关法Negative Log Likelihood 负对数似然Neighbourhood Component Analysis/NCA 近邻成分分析Neural Machine Translation 神经机器翻译Neural Turing Machine 神经图灵机Newton method ⽜顿法NIPS 国际神经信息处理系统会议No Free Lunch Theorem／NFL 没有免费的午餐定理Noise-contrastive estimation 噪⾳对⽐估计Nominal attribute 列名属性Non-convex optimization ⾮凸优化Nonlinear model ⾮线性模型Non-metric distance ⾮度量距离Non-negative matrix factorization ⾮负矩阵分解Non-ordinal attribute ⽆序属性Non-Saturating Game ⾮饱和博弈Norm 范数Normalization 归⼀化Nuclear norm 核范数Numerical attribute 数值属性Letter OObjective function ⽬标函数Oblique decision tree 斜决策树Occam’s razor 奥卡姆剃⼑Odds ⼏率Off-Policy 离策略One shot learning ⼀次性学习One-Dependent Estimator／ODE 独依赖估计On-Policy 在策略Ordinal attribute 有序属性Out-of-bag estimate 包外估计Output layer 输出层Output smearing 输出调制法Overfitting 过拟合／过配Oversampling 过采样Letter PPaired t-test 成对 t 检验Pairwise 成对型Pairwise Markov property 成对马尔可夫性Parameter 参数Parameter estimation 参数估计Parameter tuning 调参Parse tree 解析树Particle Swarm Optimization/PSO 粒⼦群优化算法Part-of-speech tagging 词性标注Perceptron 感知机Performance measure 性能度量Plug and Play Generative Network 即插即⽤⽣成⽹络Plurality voting 相对多数投票法Polarity detection 极性检测Polynomial kernel function 多项式核函数Pooling 池化Positive class 正类Positive definite matrix 正定矩阵Post-hoc test 后续检验Post-pruning 后剪枝potential function 势函数Precision 查准率／准确率Prepruning 预剪枝Principal component analysis/PCA 主成分分析Principle of multiple explanations 多释原则Prior 先验Probability Graphical Model 概率图模型Proximal Gradient Descent/PGD 近端梯度下降Pruning 剪枝Pseudo-label 伪标记Letter QQuantized Neural Network 量⼦化神经⽹络Quantum computer 量⼦计算机Quantum Computing 量⼦计算Quasi Newton method 拟⽜顿法Letter RRadial Basis Function／RBF 径向基函数Random Forest Algorithm 随机森林算法Random walk 随机漫步Recall 查全率／召回率Receiver Operating Characteristic/ROC 受试者⼯作特征Rectified Linear Unit/ReLU 线性修正单元Recurrent Neural Network 循环神经⽹络Recursive neural network 递归神经⽹络Reference model 参考模型Regression 回归Regularization 正则化Reinforcement learning/RL 强化学习Representation learning 表征学习Representer theorem 表⽰定理reproducing kernel Hilbert space/RKHS 再⽣核希尔伯特空间Re-sampling 重采样法Rescaling 再缩放Residual Mapping 残差映射Residual Network 残差⽹络Restricted Boltzmann Machine/RBM 受限玻尔兹曼机Restricted Isometry Property/RIP 限定等距性Re-weighting 重赋权法Robustness 稳健性/鲁棒性Root node 根结点Rule Engine 规则引擎Rule learning 规则学习Letter SSaddle point 鞍点Sample space 样本空间Sampling 采样Score function 评分函数Self-Driving ⾃动驾驶Self-Organizing Map／SOM ⾃组织映射Semi-naive Bayes classifiers 半朴素贝叶斯分类器Semi-Supervised Learning 半监督学习semi-Supervised Support Vector Machine 半监督⽀持向量机Sentiment analysis 情感分析Separating hyperplane 分离超平⾯Sigmoid function Sigmoid 函数Similarity measure 相似度度量Simulated annealing 模拟退⽕Simultaneous localization and mapping 同步定位与地图构建Singular Value Decomposition 奇异值分解Slack variables 松弛变量Smoothing 平滑Soft margin 软间隔Soft margin maximization 软间隔最⼤化Soft voting 软投票Sparse representation 稀疏表征Sparsity 稀疏性Specialization 特化Spectral Clustering 谱聚类Speech Recognition 语⾳识别Splitting variable 切分变量Squashing function 挤压函数Stability-plasticity dilemma 可塑性-稳定性困境Statistical learning 统计学习Status feature function 状态特征函Stochastic gradient descent 随机梯度下降Stratified sampling 分层采样Structural risk 结构风险Structural risk minimization/SRM 结构风险最⼩化Subspace ⼦空间Supervised learning 监督学习／有导师学习support vector expansion ⽀持向量展式Support Vector Machine/SVM ⽀持向量机Surrogat loss 替代损失Surrogate function 替代函数Symbolic learning 符号学习Symbolism 符号主义Synset 同义词集Letter TT-Distribution Stochastic Neighbour Embedding/t-SNE T – 分布随机近邻嵌⼊Tensor 张量Tensor Processing Units/TPU 张量处理单元The least square method 最⼩⼆乘法Threshold 阈值Threshold logic unit 阈值逻辑单元Threshold-moving 阈值移动Time Step 时间步骤Tokenization 标记化Training error 训练误差Training instance 训练⽰例／训练例Transductive learning 直推学习Transfer learning 迁移学习Treebank 树库Tria-by-error 试错法True negative 真负类True positive 真正类True Positive Rate/TPR 真正例率Turing Machine 图灵机Twice-learning ⼆次学习Letter UUnderfitting ⽋拟合／⽋配Undersampling ⽋采样Understandability 可理解性Unequal cost ⾮均等代价Unit-step function 单位阶跃函数Univariate decision tree 单变量决策树Unsupervised learning ⽆监督学习／⽆导师学习Unsupervised layer-wise training ⽆监督逐层训练Upsampling 上采样Letter VVanishing Gradient Problem 梯度消失问题Variational inference 变分推断VC Theory VC维理论Version space 版本空间Viterbi algorithm 维特⽐算法Von Neumann architecture 冯 · 诺伊曼架构Letter WWasserstein GAN/WGAN Wasserstein⽣成对抗⽹络Weak learner 弱学习器Weight 权重Weight sharing 权共享Weighted voting 加权投票法Within-class scatter matrix 类内散度矩阵Word embedding 词嵌⼊Word sense disambiguation 词义消歧Letter ZZero-data learning 零数据学习Zero-shot learning 零次学习Aapproximations近似值arbitrary随意的affine仿射的arbitrary任意的amino acid氨基酸amenable经得起检验的axiom公理，原则abstract提取architecture架构，体系结构；建造业absolute绝对的arsenal军⽕库assignment分配algebra线性代数asymptotically⽆症状的appropriate恰当的Bbias偏差brevity简短，简洁；短暂broader⼴泛briefly简短的batch批量Cconvergence 收敛，集中到⼀点convex凸的contours轮廓constraint约束constant常理commercial商务的complementarity补充coordinate ascent同等级上升clipping剪下物；剪报；修剪component分量；部件continuous连续的covariance协⽅差canonical正规的，正则的concave⾮凸的corresponds相符合；相当；通信corollary推论concrete具体的事物，实在的东西cross validation交叉验证correlation相互关系convention约定cluster⼀簇centroids 质⼼，形⼼converge收敛computationally计算(机)的calculus计算Dderive获得，取得dual⼆元的duality⼆元性；⼆象性；对偶性derivation求导；得到；起源denote预⽰，表⽰，是…的标志；意味着，[逻]指称divergence 散度；发散性dimension尺度，规格；维数dot⼩圆点distortion变形density概率密度函数discrete离散的discriminative有识别能⼒的diagonal对⾓dispersion分散，散开determinant决定因素disjoint不相交的Eencounter遇到ellipses椭圆equality等式extra额外的empirical经验；观察ennmerate例举，计数exceed超过，越出expectation期望efficient⽣效的endow赋予explicitly清楚的exponential family指数家族equivalently等价的Ffeasible可⾏的forary初次尝试finite有限的，限定的forgo摒弃，放弃fliter过滤frequentist最常发⽣的forward search前向式搜索formalize使定形Ggeneralized归纳的generalization概括，归纳；普遍化；判断（根据不⾜）guarantee保证；抵押品generate形成，产⽣geometric margins⼏何边界gap裂⼝generative⽣产的；有⽣产⼒的Hheuristic启发式的；启发法；启发程序hone怀恋；磨hyperplane超平⾯Linitial最初的implement执⾏intuitive凭直觉获知的incremental增加的intercept截距intuitious直觉instantiation例⼦indicator指⽰物，指⽰器interative重复的，迭代的integral积分identical相等的；完全相同的indicate表⽰，指出invariance不变性，恒定性impose把…强加于intermediate中间的interpretation解释，翻译Jjoint distribution联合概率Llieu替代logarithmic对数的，⽤对数表⽰的latent潜在的Leave-one-out cross validation留⼀法交叉验证Mmagnitude巨⼤mapping绘图，制图；映射matrix矩阵mutual相互的，共同的monotonically单调的minor较⼩的，次要的multinomial多项的multi-class classification⼆分类问题Nnasty讨厌的notation标志，注释naïve朴素的Oobtain得到oscillate摆动optimization problem最优化问题objective function⽬标函数optimal最理想的orthogonal(⽮量，矩阵等)正交的orientation⽅向ordinary普通的occasionally偶然的Ppartial derivative偏导数property性质proportional成⽐例的primal原始的，最初的permit允许pseudocode伪代码permissible可允许的polynomial多项式preliminary预备precision精度perturbation 不安，扰乱poist假定，设想positive semi-definite半正定的parentheses圆括号posterior probability后验概率plementarity补充pictorially图像的parameterize确定…的参数poisson distribution柏松分布pertinent相关的Qquadratic⼆次的quantity量，数量；分量query疑问的Rregularization使系统化；调整reoptimize重新优化restrict限制；限定；约束reminiscent回忆往事的；提醒的；使⼈联想…的（of）remark注意random variable随机变量respect考虑respectively各⾃的；分别的redundant过多的；冗余的Ssusceptible敏感的stochastic可能的；随机的symmetric对称的sophisticated复杂的spurious假的；伪造的subtract减去；减法器simultaneously同时发⽣地；同步地suffice满⾜scarce稀有的，难得的split分解，分离subset⼦集statistic统计量successive iteratious连续的迭代scale标度sort of有⼏分的squares平⽅Ttrajectory轨迹temporarily暂时的terminology专⽤名词tolerance容忍；公差thumb翻阅threshold阈，临界theorem定理tangent正弦Uunit-length vector单位向量Vvalid有效的，正确的variance⽅差variable变量；变元vocabulary词汇valued经估价的；宝贵的Wwrapper包装分类:。

数学名词中英文对照表

Aabbreviation 简写符号；简写absolute error 绝对误差absolute value 绝对值accuracy 准确度acute angle 锐角acute-angled triangle 锐角三角形add 加addition 加法addition formula 加法公式addition law 加法定律addition law(of probability)（概率）加法定律additive property 可加性adjacent angle 邻角adjacent side 邻边algebra 代数algebraic 代数的algebraic equation 代数方程algebraic expression 代数式algebraic fraction 代数分式；代数分数式algebraic inequality 代数不等式algebraic operation 代数运算alternate angle （交）错角alternate segment 交错弓形altitude 高；高度；顶垂线；高线ambiguous case 两义情况；二义情况amount 本利和；总数analysis 分析；解析analytic geometry 解析几何angle 角angle at the centre 圆心角angle at the circumference 圆周角angle between a line and a plane 直与平面的交角angle between two planes 两平面的交角angle bisection 角平分angle bisector 角平分线；分角线angle in the alternate segment 交错弓形的圆周角angle in the same segment 同弓形内的圆周角angle of depression 俯角angle of elevation 仰角angle of greatest slope 最大斜率的角angle of inclination 倾斜角angle of intersection 相交角；交角angle of rotation 旋转角angle of the sector 扇形角angle sum of a triangle 三角形内角和angles at a point 同顶角annum(X% per annum) 年（年利率X%）anti-clockwise direction 逆时针方向；返时针方向anti-logarithm 逆对数；反对数anti-symmetric 反对称apex 顶点approach 接近；趋近approximate value 近似值approximation 近似；略计；逼近Arabic system 阿刺伯数字系统arbitrary 任意arbitrary constant 任意常数arc 弧arc length 弧长arc-cosine function 反余弦函数arc-sin function 反正弦函数arc-tangent function 反正切函数area 面积arithmetic 算术arithmetic mean 算术平均；等差中顶；算术中顶arithmetic progression 算术级数；等差级数arithmetic sequence 等差序列arithmetic series 等差级数arm 边arrow 前号ascending order 递升序ascending powers of X X 的升幂associative law 结合律assumed mean 假定平均数assumption 假定；假设average 平均；平均数；平均值average speed 平均速率axiom 公理axis 轴axis of parabola 拋物线的轴axis of symmetry 对称轴Bback substitution 回代bar chart 棒形图；条线图；条形图；线条图base （1）底；（2）基；基数base angle 底角base area 底面base line 底线base number 底数；基数base of logarithm 对数的底bearing 方位（角）；角方向（角）bell-shaped curve 钟形图bias 偏差；偏倚billion 十亿binary number 二进数binary operation 二元运算binary scale 二进法binary system 二进制binomial 二项式binomial expression 二项式bisect 平分；等分bisection method 分半法；分半方法bisector 等分线；平分线boundary condition 边界条件boundary line 界（线）；边界bounded 有界的bounded above 有上界的；上有界的bounded below 有下界的；下有界的bounded function 有界函数brace 大括号bracket 括号breadth 阔度broken line graph 折线图Ccalculation 计算calculator 计算器；计算器cancel 消法；相消canellation law 消去律capacity 容量Cartesian coordinates 笛卡儿坐标Cartesian plane 笛卡儿平面category 类型；范畴central line 中线central tendency 集中趋centre 中心；心centre of a circle 圆心centroid 形心；距心certain event 必然事件chance 机会change of base 基的变换change of subject 主项变换change of variable 换元；变量的换chart 图；图表checking 验算chord 弦chord of contact 切点弦circle 圆circular 圆形；圆的circular function 圆函数；三角函数circular measure 弧度法circumcentre 外心；外接圆心circumcircle 外接圆circumference 圆周circumradius 外接圆半径circumscribed circle 外接圆class 区；组；类class boundary 组界class interval 组区间；组距class limit 组限；区限class mark 组中点；区中点classification 分类clnometer 测斜仪clockwise dirction 顺时针方向closed convex region 闭凸区域closed interval 闭区间coefficient 系数coincide 迭合；重合collection of terms 并项collinear 共线collinear planes 共线面column (1)列；纵行；(2) 柱combination 组合common chord 公弦common denominator 同分母；公分母common difference 公差common divisor 公约数；公约common factor 公因子；公因子common logarithm 常用对数common multiple 公位数；公倍common ratio 公比common tangetn 公切commutative law 交换律comparable 可比较的compass 罗盘compass bearing 罗盘方位角compasses 圆规compasses construction 圆规作图complement 余；补余complementary angle 余角complementary event 互补事件complementary probability 互补概率completing the square 配方complex number 复数complex root 复数根composite number 复合数；合成数compound bar chart 综合棒形图compound discount 复折扣compound interest 复利；复利息computation 计算computer 计算机；电子计算器concave 凹concave downward 凹向下的Ddata 数据decagon 十边形decay 衰变decay factor 衰变因子decimal 小数decimal place 小数位decimal point 小数点decimal system 十进制decrease 递减decreasing function 递减函数；下降函数decreasing sequence 递减序列；下降序列decreasing series 递减级数；下降级数decrement 减量deduce 演绎deduction 推论deductive reasoning 演绎推理definite 确定的；定的distance 距离distance formula 距离公式distinct roots 相异根distincr solution 相异解distribution 公布distrivutive law 分配律divide 除dividend (1)被除数；(2)股息divisible 可整除division 除法division algorithm 除法算式divisor 除数；除式；因子divisor of zero 零因子dodecagon 十二边形dot 点double root 二重根due east/ south/ west /north 向东/ 南/ 西/ 北definiton 定义degree (1)度；(2)次degree of a polynomial 多项式的次数degree of accuracy 准确度degree of precision 精确度delete 删除；删去denary number 十进数denary scale 十进法denary system 十进制denominator 分母dependence (1)相关；(2)应变dependent event(s) 相关事件；相依事件；从属事件dependent variable 应变量；应变数depreciation 折旧descending order 递降序descending powers of X X的降序detached coefficients 分离系数(法) deviation 偏差；变差deviation from the mean 离均差diagonal 对角diagram 图；图表diameter 直径difference 差digit 数字dimension 量；量网；维(数)direct proportion 正比例direct tax, direct taxation 直接税direct variation 正变（分）directed angle 有向角directed number 有向数direction 方向；方位discontinuous 间断(的)；非连续(的)；不连续(的)discount 折扣discount per cent 折扣百分率discrete 分立；离散discrete data 离散数据；间断数据discriminant 判别式dispersion 离差displacement 位移disprove 反证Eedge 棱；边elimination 消法elimination method 消去法；消元法elongation 伸张；展empirical data 实验数据empirical formula 实验公式empirical probability 实验概率；经验概率enclosure 界限end point 端点entire surd 整方根equal 相等equal ratios theorem 等比定理equal roots 等根equality 等(式)equality sign 等号equation 方程equation in one unknown 一元方程equation in two unknowns (variables) 二元方程equation of a straight line 直线方程equation of locus 轨迹方程equiangular 等角(的)extreme value 极值equidistant 等距(的)equilaeral 等边(的) equilateral polygon 等边多边形equilateral triangle 等边三角形equivalent 等价(的)error 误差escribed circle 旁切圆estimate 估计；估计量Euler's formula 尤拉公式；欧拉公式evaluate 计值even function 偶函数even number 偶数evenly distributed 均匀分布的event 事件exact 真确exact solution 准确解；精确解；真确解exact value 法确解；精确解；真确解example 例excentre 外心exception 例外excess 起exclusive 不包含exclusive events 互斥事件exercise 练习expand 展开expand form 展开式expansion 展式expectation 期望expectation value, expected value 期望值；预期值experiment 实验；试验experimental 试验的experimental probability 实验概率exponent 指数express…in terms of….. 以………表达expression 式；数式extension 外延；延长；扩张；扩充exterior angle 外角external angle bisector 外分角external point of division 外分点extreme point 极值点Fface 面factor 因子；因式；商factor method 因式分解法factor theorem 因子定理；因式定理factorial 阶乘factorization 因子分解；因式分解factorization of polynomial 多项式因式分解FALSE 假(的)feasible solution 可行解；容许解Fermat’s last theorem 费尔马最后定理Fibonacci number 斐波那契数；黄金分割数Fibonacci sequence 斐波那契序列fictitious mean 假定平均数figure (1)图(形)；(2)数字finite 有限finite population 有限总体finite sequence 有限序列finite series 有限级数first quartile 第一四分位数first term 首项fixed deposit 定期存款fixed point 定点flow chart 流程图foot of perpendicular 垂足for all X 对所有Xfor each /every X 对每一X form 形式；型formal proof 形式化的证明format 格式；规格formula(formulae) 公式four rules 四则four-figure table 四位数表fourth root 四次方根fraction 分数；分式fraction in lowest term 最简分数fractional equation 分式方程fractional index 分数指数fractional inequality 分式不等式free fall 自由下坠frequency 频数；频率frequency distribution 频数分布；频率分布frequency distribution table 频数分布表frequency polygon 频数多边形；频率多边形frustum 平截头体function 函数function of function 复合函数；迭函数functional notation 函数记号Ggain 增益；赚；盈利gain per cent 赚率；增益率；盈利百分率game （1）对策；（2）博奕general form 一般式；通式general solution 通解；一般解general term 通项geoborad 几何板geometric mean 几何平均数；等比中项geometric progression 几何级数；等比级数geometric sequence 等比序列geometric series 等比级数geometry 几何；几何学given 给定；已知golden section 黄金分割grade 等级gradient (1)斜率；倾斜率；(2)梯度grand total 总计graph 图像；图形；图表graph paper 图表纸graphical method 图解法graphical representation 图示；以图样表达graphical solution 图解greatest term 最大项greatest value 最大值grid lines 网网格线group 组；grouped data 分组数据；分类数据grouping terms 并项；集项growth 增长growth factor 增长因子Hhalf closed interval 半闭区间half open interval 半开区间head 正面（钱币）height 高（度）hemisphere 半球体；半球heptagon 七边形Heron's formula 希罗公式hexagon 六边形higher order derivative 高阶导数highest common factor(H.C.F) 最大公因子；最高公因式；最高公因子Hindu-Arabic numeral 阿刺伯数字histogram 组织图；直方图；矩形图horizontal 水平的；水平horizontal line 横线；水平线hyperbola 双曲线hypotenuse 斜边Iidentical 全等；恒等identity 等（式）identity relation 恒等关系式if and only if/iff 当且仅当；若且仅若if…., then 若….则；如果…..则illustration 例证；说明image 像点；像imaginary circle 虚圆imaginary number 虚数imaginary root 虚根implication 蕴涵式；蕴含式imply 蕴涵；蕴含impossible event 不可能事件improper fraction 假分数inclination 倾角；斜角inclined plane 斜面included angle 夹角included side 夹边inclusive 包含的；可兼的inconsistent 不相的(的)；不一致(的) increase 递增；增加increasing function 递增函数interior angles on the same side of the transversal 同旁内角interior opposite angle 内对角internal bisector 内分角internal division 内分割internal point of division 内分点inter-quartile range 四分位数间距intersect 相交intersection (1)交集；(2)相交；(3)交点interval 区间intuition 直观invariance 不变性invariant (1)不变的；(2)不变量；不变式inverse 反的；逆的inverse circular function 反三角函数inverse cosine function 反余弦函数inverse function 反函数；逆函数inverse problem 逆算问题inverse proportion 反比例；逆比例inverse sine function 反正弦函数inverse tangent function 反正切函数inverse variation 反变(分)；逆变(分) irrational equation 无理方程irrational number 无理数irreducibility 不可约性irregular 不规则isosceles triangle 等腰三角形increasing sequence 递增序列increasing series 递增级数increment 增量independence 独立；自变independent event 独立事件independent variable 自变量；独立变量indeterminate (1)不定的；(2)不定元；未定元indeterminate coefficient 不定系数；未定系数indeterminate form 待定型；不定型index,indices 指数；指index notation 指数记数法inequality 不等式；不等inequality sign 不等号infinite 无限；无穷infinite population 无限总体infinite sequence 无限序列；无穷序列infinite series 无限级数；无穷级数infinitely many 无穷多infinitesimal 无限小；无穷小infinity 无限(大)；无穷(大)initial point 始点；起点initial side 始边initial value 初值；始值input 输入input box 输入inscribed circle 内切圆insertion 插入insertion of brackets 加括号instantaneous 瞬时的integer 整数integral index 整数指数integral solution 整数解integral value 整数值intercept 截距；截段intercept form 截距式intercept theorem 截线定理interchange 互换interest 利息interest rate 利率interest tax 利息税interior angle 内角Jjoint variation 联变(分)；连变(分) Kknown 己知LL.H.S. 末项law 律；定律law of indices 指数律；指数定律law of trichotomy 三分律leading coefficient 首项系数least common multiple, lowest common multiple (L.C.M) 最小公倍数；最低公倍式least value 最小值lemma 引理length 长(度)letter 文字；字母like surd 同类根式like terms 同类项limit 极限line 线；行line of best-fit 最佳拟合line of greatest slope 最大斜率的直；最大斜率line of intersection 交线line segment 线段linear 线性；一次linear equation 线性方程；一次方程linear equation in two unknowns 二元一次方程；二元线性方程linear inequality 一次不等式；线性不等式linear programming 线性规划literal coefficient 文字系数literal equation 文字方程load 负荷loaded coin 不公正钱币loaded die 不公正骰子locus, loci 轨迹logarithm 对数logarithmic equation 对数方程logarithmic function 对数函数logic 逻辑logical deduction 逻辑推论；逻辑推理logical step 逻辑步骤long division method 长除法loss 赔本；亏蚀loss per cent 赔率；亏蚀百分率lower bound 下界lower limit 下限lower quartile 下四分位数lowest common multiple(L.C.M) 最小公倍数Mmagnitude 量；数量；长度；大小major arc 优弧；大弧major axis 长轴major sector 优扇形；大扇形major segment 优弓形；大弓形mantissa 尾数mantissa of logarithm 对数的尾数；对数的定值部many-sided figure 多边形marked price 标价mathematical induction 数学归纳法mathematical sentence 数句mathematics 数学maximize 极大maximum absolute error 最大绝对误差maximum point 极大点maximum value 极大值mean 平均(值)；平均数；中数mean deviation 中均差；平均偏差measure of dispersion 离差的量度measurement 量度median (1)中位数；(2)中线meet 相交；相遇mensuration 计量；求积法method 方法method of completing square 配方法method of substitution 代换法；换元法metric unit 十进制单位mid-point 中点mid-point formula 中点公式mid-point theorem 中点定理million 百万minimize 极小minimum point 极小点minimum value 极小值minor (1)子行列式；(2)劣；较小的minor arc 劣弧；小弧minor axis 短轴minor sector 劣扇形；小扇形minor segment 劣弓形；小弓形minus 减minute 分mixed number(fraction) 带分数modal class 众数组mode 众数model 模型monomial 单项式multinomial 多项式multiple 倍数multiple root 多重根multiplicand 被乘数multiplication 乘法multiplication law (of probability) (概率)乘法定律multiplicative property 可乘性multiplier 乘数；乘式multiply 乘mutually exclusive events 互斥事件mutually independent 独立; 互相独立mutually perpendicular lines 互相垂直Nn factorial n阶乘n th root n次根；n次方根natural number 自然数negative 负negative angle 负角negative index 负指数negative integer 负整数negative number 负数neighborhood 邻域net 净(值)n-gon n边形nonagon 九边形non-collinear 不共线non-linear 非线性non-linear equation 非线性方程non-negative 非负的non-trivial 非平凡的non-zero 非零normal (1)垂直的；正交的；法线的(2)正态的(3)正常的；正规的normal curve 正态分记伲怀１分记伲徽媲伲徽忧?normal distribution 正态分布，常态分布normal form 法线式notation 记法；记号number 数number line 数线number pair 数偶number pattern 数型number plane 数平面number system 数系numeral 数字；数码numeral system 记数系统numerator 分子numerical 数值的；数字的numerical expression 数字式numerical method 计算方法；数值法Ooblique 斜的oblique cone 斜圆锥oblique triangle 斜三角形obtuse angle 钝角obtuse-angled triangle 钝角三角形octagon 八边形octahedron 八面体odd function 奇函数odd number 奇数one-one correspondence 一一对应open interval 开区间open sentence 开句operation 运算opposite angle 对角opposite interior angle 内对角opposite side 对边optimal solution 最优解order (1)序；次序；(2)阶；级ordered pair 序偶origin 原点outcome 结果output 输出overlap 交迭；相交Pparabola 拋物线parallel 平行(的)parallel lines 平行(直线) parallelogram 平行四边形parameter 参数；参变量partial fraction 部分分数；分项分式polar coordinate system 极坐标系统polar coordinates 极坐标pole 极polygon 多边形polyhedron 多面体polynomial 多项式polynomial equation 多项式方程positive 正positive index 正指数positive integer 正整数positive number 正数power (1)幂；乘方；(2)功率；(3)检定力precise 精密precision 精确度prime 素prime factor 质因子；质因素prime number 素数；质数primitive (1)本原的；原始的；(2)原函数principal (1)主要的；(2)本金prism 梭柱(体)；角柱(体)prismoid 平截防庾短?probability 概率problem 应用题produce 延长product 乘积；积product rule 积法则profit 盈利profit per cent 盈利百分率profits tax 利得税progression 级数proof 证(题)；证明proper fraction 真分数property 性质property tax 物业税proportion 比例proportional 成比例protractor 量角器pyramid 棱锥(体)；角锥(体) Pythagoras’Theorem 勾股定理Pythagorean triplet 毕氏三元数组partial sum 部分和partial variation 部分变(分) particular solution 特解Pascal’s triangle 帕斯卡斯三角形pattern 模型；规律pegboard 有孔版pentadecagon 十五边形pentagon 五边形per cent 百分率percentage 百分法；百分数percentage decrease 百分减少percentage error 百分误差percentage increase 百分增加percentile 百分位数perfect number 完全数perfecr square 完全平方perimeter 周长；周界period 周期periodic function 周期函数permutation 排列perpendicular 垂线；垂直(于) perpendicular bisector 垂直平分线；中垂线perpendicular line 垂直线pictogram 象形图pie chart 饼图；圆瓣图pinboard 钉板place holder 补位数字place value 位值plan (1)平面图；(2)计划plane 平面plane figure 平面图形plot 绘图plus 加point 点point circle 点圆point of contact 切点point of division 分点point of intersection 交点point-slope form 点斜式polar axis 极轴polar coordinate plane 极坐标平面polar coordinate 极坐标系统Qquadrant 象限quadratic equation 二次方程(式) quadratic formula 二次公式quardratic function 二次函数quadratic inequality 二次不等式quadratic polynomial 四边形quantity 数量quartile 四分位数quotient 商；商式RR.H.S 右radian 弧度radian measure 弧度法radical 根式；根号；根数radius, radii 半径random 随机random experiment 随机试验random number 随机数range 值域；区域；范围；极差；分布域rate 率；利率ratio 比; 比率rational expression 有理式；有理数式rational function 有理函数rational index 有理数指数rational number 有理数rationalization 有理化raw data 原始数据raw score 原始分（数）real axis 实轴real number 实数real root 实根reason 理由reciprocal 倒数rectangle 长方形；矩形rectangular block 长方体rectangular coordinate plane 直角坐标平面rectangular coordinates 直角坐rectilinear figure 直线图形recurrent 循环的recurring decimal 循环小数reduce 简化reducible 可约的；可化简的reference angle 参考角reflex angle 优角；反角region 区域regular 正；规则regular polygon 正多边形reject 舍去；否定relation 关系；关系式relative error 相对误差remainder 余数；余式；剩余remainder term 余项remainder theorem 余式定理removal of brackets 撤括号；去括号repeated trials 重复试验resolve 分解revolution 旋转；周转rhombus 菱形right angle 直角right circular cone 直立圆锥（体）right circular cylinder 直立圆柱（体）right prism 直立棱柱；直立角柱(体) right pyramid 直立棱锥；直立角锥(体) right-angled triangle 直角二角形root 根rotation 旋转round angle 周角rounded number 舍数rounding(off) 舍入；四舍五入row 行；棋行rule 规则；法(则)ruler 直尺Ssalaries tax 俸税sample 抽样；样本sample space 样本空间satisfy 满足；适合scale 比例尺；标度；图尺scalene triangle 不等边三角形；不规则三角形scientific notation 科学记数法solution of triangle 三角形解法solve 解special angle 特殊角；特别角speed 速率sphere 球形；球面square (1)平方；(2)正方形square bracket 方括号square number 正方形数；平方数square root 平方根；二次根standard deviation 标准差；标准偏离secant 割second 秒second quartile 第二四分位数(1)截面；截线；(2)截点section (1)截面；截线；(2)截点section formula 截点公式sector 扇式segment 段；节segment of a circle 弓形selling price 售价semi-circle 半圆semi-vertical angle 半顶角sentence 句；语句sequence 序列series 级数set square 三角尺；三角板shaded portion 有阴影部分shape 形状side 边；侧sign 符号；记号signed number 有符号数significant figure 有效数字similar 相似similar figures 相似图形similar triangles 相似三角形similarity 相似(性)simple equation 简易方程simple interest 单利；单利息simplify 简化simultaneous equations 联立方程simultaneous inequalities 联立不等式simultaneous linear equations in two unknowns 联合二次线性方程式sine 正弦sine formula 正弦公式slant edge 斜棱slant height 斜高slope 斜率；斜度；倾斜；坡度slope-intercept form 斜率截距式；斜截式solid 立体；固体soild with uniform corss-section 有均匀横切面的立体solution 解；解法solution of equation 方程解Uuniform 一致(的)；均匀(的)uniform cross-section 均匀横切面uniform speed 匀速率uniformly distributed 均匀分布unique solution 唯一解uniqueness 唯一性unit 单位unit area 单位面积unit circle 单位圆unit volume 单位体积unknown 未知数；未知量unlike 异类项upper bound 上界upper limit 上限upper quartile 上四分位数Vvalue 值variable 变项；变量；元；变元；变数variable speed 可变速率variance 方差variation 变数；变分verify 证明；验证vertex, vertices 顶(点)；极点vertical 铅垂；垂直vertical angle 顶角vertical line 纵线；铅垂vertically opposite angles 对顶角volume 体积Wweight (1)重量；(2)权weighted average, weighted mean 加权平均数whole number 整数；完整数width 阔度without loss of generality 不失一般性Xx-axis x轴x-coordinate x坐标x-intercept x轴截距Yy-axis y轴y-coordinate y坐标y-intercept y轴截距Zzero 零zero factor 零因子00——串串（象形+谐音，圈圈-“串串”）页脚内容zeros of a function 函数零值统计学population 母体 sample 样本 census 普查 sampling 抽样 quantitative 量的qualitative/categorical 质的 discrete 离散的 continuous 连续的population parameters 母体参数 sample statistics 样本统计量 descriptive statistics 叙述统计学inferential/inductive statistics 推论/归纳统计学levels of measurement 衡量尺度 nominal scale 名目尺度 ordinal scale 顺序尺度 interval scale 区间尺度 ratio scale 比例尺度frequency distribution 次数分配 relative frequency 相对次数 range 全距class midpoint 组中点 class limits 组限 class boundaries 组界 class width 组距cumulative frequency (以下) 累加次数 decumulative frequency 以上累加次数 histogram 直方图 pie chart 饼图 ogive 肩形图frequency polygon 多边形图cumulative frequency polygon 累加次数多边形图box plot 盒须图stem and leaf plot 枝叶图measures of central tendency 中央趋势量数 mean 平均数median 中位数 mode 众数location measures 位置量数 percentile 百分位数 quartile 四分位数 decile 十分位数dispersion measures 分散量数 range 全距interquartile-range IQR 四分位距mean absolute deviation 平均绝对离差 variance 变异数standard deviation 标准差coefficient of variation 变异系数 left-skewed 左偏negative-skewed 负偏 right-skewed 右偏 positive-skewed 正偏 contingency table 列联表sampling distribution (of a statistic)(某个统计量的) 抽样分布point estimate 点估计值 point estimator 点估计式unbiased estimator 不偏点估计式 efficient estimator 有效点估计式 consistent estimator 一致点估计式 confidence level 信赖水准 confidence interval 信赖区间 null hypothesis 虚无假设alternative hypothesis 对立假设 left-tailed test 左尾检定 right-tailed test 右尾检定 two-tailed test 双尾检定 test statistic 检定统计量critical value 临界值。

2024年教师资格考试高级中学学科知识与教学能力英语模拟试卷与参考答案

2024年教师资格考试高级中学英语学科知识与教学能力模拟试卷与参考答案一、单项选择题（本大题有30小题，每小题2分，共60分）1、题干：The teacher’s ability to foster critical thinking in students is particularly important in the discipline of ________.A. MathematicsB. HistoryC. EnglishD. Science答案：C解析：The correct answer is C. English. The question emphasizes the importance of fostering critical thinking, which is a key aspect of language arts education. English as a discipline often emphasizes critical thinking skills, such as analyzing texts and interpreting literature, which makes it the most relevant option among the choices provided.2、题干：Which of the following is NOT a common instructional strategy used to promote student engagement in an English class?A. Group discussionsB. Project-based learningC. Teacher-centered lecturesD. Socratic seminars答案：C解析：The correct answer is C. Teacher-centered lectures. The question asks for the instructional strategy that is NOT common for promoting student engagement. Group discussions (A), project-based learning (B), and Socratic seminars (D) are all known to increase student participation and engagement.Teacher-centered lectures (C), on the other hand, are more traditional and may not encourage active student involvement as much as the other strategies.3、The se ntence “She has a bright smile” can be paraphrased as:A. She has a cheerful expression.B. She has a dim smile.C. She has a bright thought.D. She has a dark smile.Answer: AExplanation: The phrase “a bright smile” implies a pleasant and friendly expres sion, which can be accurately paraphrased as “a cheerful expression.” The other options either change the meaning or are not close synonyms of the original phrase.4、Which of the following sentences is an example of a declarative sentence?A. “Where is my pen?”B. “I will be there tomorrow.”C. “Don’t you think she’s talented?”D. “Can you help me with this?”Answer: BExplanation: A declarative sentence makes a statement or declares a fact. “I will be there tomorrow” is a clear statement of future intentio n, making it a declarative sentence. The other options are questions (A and D) or a tag question (C), which are not declarative sentences.5、The teacher’s role in the classroom is crucial for student learning. Which of the following statements best describes the role of a teacher in fostering student engagement?A)The teacher should act as a passive facilitator, allowing students to guide their ownlearning.B)The teacher should dominate the class, ensuring that all students follow the samecurriculum.C)The teacher should create a supportive and interactive environment that encouragesstudent participation.D)The teacher should primarily focus on correcting student mistakes to improve theirperformance.Answer: C) The teacher should create a supportive and interactive environment that encourages student participation.Explanation: A supportive and interactive classroom environment is essential for student engagement. This approach allows students to actively participate in their learning, which can lead to better understanding and retention of the material.6、When designing a lesson plan for a unit on environmental conservation, which of the following teaching strategies would be most effective in promoting critical thinking and understanding among students?A)Presenting a lecture and providing a list of facts about different environmental issues.B)Using multimedia presentations to showcase images and videos related toenvironmental conservation.C)Facilitating a debate or discussion on the causes and solutions to environmentalproblems.D)Assigning a research project where students investigate a specific environmentalissue.Answer: C) Facilitating a debate or discussion on the causes and solutions to environmental problems.Explanation: A debate or discussion encourages students to think critically about the topic, analyze different perspectives, and develop arguments. This interactive approach can enhance their understanding and appreciation of the complexities involved in environmental conservation.7、The following sentence is a fragment. Which of the following words can be added to make it a complete sentence?A. The students enjoyed the movie, but they _______.B. The students were enjoying the movie _______.C. The students enjoyed the movie _______.D. The students were enjoying the movie, and they _______.Answer: BExplanation: The sentence “The students were enjoying the movie” is a complete sentence on its own. The word “but” can be added to show contrast with the following clause, making it a compound sentence. The other options do not make the sentence grammatically correct or complete.8、Which of the following sentence structures is most appropriate for describing a sequence of events?A. It is important that we should do this, because it will help us learn.B. The first step is to collect the necessary information, the second step is to analyze it, and the final step is to make a decision.C. Although we tried, we were unable to reach the destination on time.D. If we do not act now, the situation will become worse.Answer: BExplanation: The structure “The first step is to collect the necessary information, the second step is to analyze it, and the final step is to make a decision” effectively describes a sequence of events, with each step clearly identified. The other options do not present a clear sequence of events.9、The sentence “The students were all engaged in their activities when the bell rang.” is an example of which tense structure?A. Simple PresentB. Simple PastC. Present ContinuousD. Past ContinuousAnswer: C. Present ContinuousExplanation: The sentence describes an action that was ongoing at the moment the bell rang. The present continuous tense is used to talk about actions happening at the moment of speaking, which fits the context of the sentence.10、In the following sentence, “She has finished her homework and is now preparing for the exam,” which part of speech is underlined?A. has finishedB. herC. nowD. preparingAnswer: D. preparingExplanation: The underlined word “preparing” is a gerund, which is a verb form that functions as a noun. Gerunds are often used as subjects, objects, or complements in sentences. In this case, “preparing” is the gerund that functions as the subject of the second clause.11.The teacher, who has been teaching for five years, is highly respected by his students for his_______teaching style.A. creativeB. strictC. humorousD. traditionalAnswer: AExplanation: The question is asking about the teacher’s teaching style that is highly respected by his students. “Creative” is the most appropriate choice to describe a style that is likely to be respected, as it implies innovation and engagement in the teaching process.12.In order to enhance the students’ reading comprehension, the teacher uses a variety of_______techniques in her English class.A. readingB. questioningC. listeningD. writingAnswer: BExplanation: The question is inquiring about the techniques used to improve reading comprehension in an English class. “Questioning” techniques, such as Socratic questioning or guided inquiry, are specifically designed to enhance comprehension and critical thinking skills, making it the most suitable answer among the options provided.13、What is the most appropriate tense to use when describing a routine activity that occurs on a daily basis?A. Present simpleB. Present perfectC. Past simpleD. Future simpleAnswer: A. Present simpleExplanation: The present simple tense is used to describe habits, regular routines, and general truths. It is the correct tense to use when referring to daily activities that are habits or routines.14、Which of the following sentences uses the correct form of the passive voice?A. The students are given by the teacher.B. The teacher gives the students.C. The students are given to by the teacher.D. The students are given from the teacher.Answer: C. The students are given to by the teacher.Explanation: The passive voice is formed by using the past participle of the verb after “be” followed by the subject. In this case, “given” is the past participle of “give.” The correct construction uses “given to by” to indicate that the students are the recipients of the action.15.The teacher is discussing the importance of reading aloud with the students. Which of the following statements is the most appropriate to use in this context?A)“Reading silently is better because it helps you concentrate better.”B)“Reading aloud is unnecessary; it only slows down the reading process.”C)“Reading aloud is beneficial because it enhances comprehension and pronunciation.”D)“We should only read aloud in class when we have time.”Answer: CExplanation: The correct answer is C because it highlights the positive aspects of reading aloud, such as improving comprehension and pronunciation. The other options either dismiss the importance of reading aloud or suggest it is unnecessary, which are not appropriate responses in the context of discussing its benefits.16.In a lesson on Shakespeare’s “Romeo and Juliet,” the teacher wants to engage students in a debate about the theme of fate versus free will. Which activity would best facilitate this discussion?A)Assigning students to write a short essay on the theme.B)Organizing a group discussion with prepared questions.C)Playing a scene from the movie adaptation of the play.D)Giving students a multiple-choice quiz about the characters.Answer: BExplanation: The correct answer is B because it encourages active participation and discussion among the students, which is ideal for exploring complex themes like fate versus free will. The other options either focus on individual writing or passive consumption, which may not foster the kind of interactive and critical thinking required for this type of discussion.17.The sentence “She is as tall as her father” is an example of which sentence structure?A. ComparisonB. ConditionalC. FutureD. PastAnswer: AExplanation: The sentence “She is as tall as her father” is using the comparison structure to show that two things (her height and her father’s height) are equal.18.Which of the following sentence is correct in terms of verb tense and subject-verb agreement?A. The dog run in the park every morning.B. The dogs are runs in the park every morning.C. The dog runs in the park every morning.D. The dogs is runs in the park every morning.Answer: CExplanation: The correct sentence is “The dog runs in the park every morning.” It uses the present simple tense correctly with the subject “dog,” which is singular, and agrees with the singular verb “runs.” The other options have incorrect verb tenses or subject-verb agreement errors.19.The teacher is using a teaching strategy to encourage student participation. Which of the following is the most appropriate strategy for discussing a complex historical event?A)Presenting a detailed timeline of the event.B)Asking students to write a brief summary of the event.C)Pairing students to debate the causes and effects of the event.D)Showing a documentary about the event.Answer: C) Pairing students to debate the causes and effects of the event.Explanation: Pairing students to debate a complex historical event encourages critical thinking and collaborative learning. It allows students to engage with the material from different perspectives, fostering a deeper understanding of the event.20.In the context of English language teaching, which of the following activities is most effective for improving students’ listening skills?A)Reading aloud a passage of text and asking students to retell it.B)Listening to a short story and then summarizing the main points.C)Watching a video clip and discussing the characters’ motivations.D)Listening to a dialogue and then analyzing the pronunciation of the speakers.Answer: B) Listening to a short story and then summarizing the main points.Explanation: Listening to a short story and summarizing the main points helps students practice active listening skills, identify key information, and improve their ability to process and recall spoken language. It also encourages them to engage with the content on a deeper level.21.The sentence “He has lived here for ten years, but he doesn’t feel at home yet.” demonstrates which of the following sentence structures?A)SimpleB)ComplexC)CompoundD)Complex-complexAnswer: B) ComplexExplanation: This sentence is a complex sentence because it has one mainclause (“He doesn’t feel at home yet”) and one or more dependent clauses that provide additional information. The dependent clause “He has lived here for ten years” adds extra informa tion about the main clause.22.Which of the following phrases is an example of a gerund phrase?A)To eating ice creamB)Eating ice creamC)Eat ice creamD)Eating ice-creamAnswer: B) Eating ice creamExplanation: A gerund phrase is a phrase that functions as a noun and consists of a gerund (a verb form that ends in -ing and functions as a noun). In this case, “Eating ice cream” is a gerund phrase that can act as a subject, object, or complement in a sentence. The other options do not fit the definition of a gerund phrase.23.What is the main purpose of using cooperative learning in the English classroom?A)To ensure that all students have the same level of English proficiency.B)To encourage students to work independently and develop their own learningstrategies.C)To promote interaction and collaboration among students.D)To test students’ ability to work under time pressure.Answer: CExplanation: The main purpose of using cooperative learning in the English classroom is topromote interaction and collaboration among students. This approach helps students develop their communication skills, critical thinking, and teamwork abilities.24.Which of the following activities is most suitable for assessing students’ understanding of a literary text in an English class?A) A written test that covers all the details of the text.B) A group discussion where students present their own interpretations of the text.C)An individual project that requires students to create a visual representation of thetext.D) A multiple-choice quiz that tests students’ recall of the main events.Answer: BExplanation: A group discussion where students present their own interpretations of the textis the most suitable activity for assessing students’ understanding of a literary text. This method encourages critical thinking, creativity, and the ability to articulate thoughts and ideas. It also promotes peer learning and collaboration.25.The following sentence is a direct quote. Which one of the following punctuation marks is correctly used at the end of the quote?A)Period (.)B)Question mark (?)C)Exclamation mark (!)D)Semicolon (;)Answer: A) Period (.)Explanation: When a direct quote is used within a sentence, it is always followed by a period. The period signifies the end of the quote.26.In the following sentence, “They had been working on the project for months, and it was finally completed,” the comma after “months” is used to:A)Separate a list of itemsB)Introduce a non-restrictive relative clauseC)Indicate a pause in the sentenceD)Separate independent clausesAnswer: B) Introduce a non-restrictive relative clause.Explanation: The comma after “months” i s used to introduce anon-restrictive relative clause, which provides additional information about the subject but is not essential to the main idea of the sentence. The clause “and it was finally completed” adds detail to the time frame of the project.27.The following sentence contains an error in verb tense usage. Which one is it?A. The students will be working on their projects until the end of the month.B. The students worked on their projects last week.C. The students are working on their projects at the moment.D. The students will have worked on their projects by the end of the month.Answer: BExplanation: The sentence that contains an error in verb tense usage is B. The correct tense should be present continuous for the ongoing action, but “worked” is in the past simple tense, which does not fit with the present continuous tense of “are working” in the other parts of the sentence.28.Choose the word that best fits the blank in the following sentence:The teacher_______to the students that the exam would be postponed due to bad weather.A. mentionedB. suggestedC. notifiedD. impliedAnswer: CExplanation: The correct word to fill in the blank is “notified.” The teacher is informing the students of an important change, which is best described by “notified,” meaning to inform formally. “Mentioned” could also be correct, but “notified” is more formal and appropriate for official announcements. “Suggested” and “implied” do not fit the context of formally informing students of a change.29、Which of the following is NOT a component of communicative language teaching (CLT)?A) Focus on accuracyB) Emphasis on using the language for real communicationC) Grammar translation as the main activityD) Task-based learning activitiesAnswer: C) Grammar translation as the main activityExplanation: Communicative Language Teaching (CLT) emphasizes the use of language for real communication and often incorporates task-based learningactivities. While focus on accuracy is also important, CLT moves away from the traditional grammar-translation method, which focuses more on the analysis and translation of written texts rather than the ability to communicate effectively in the target language.30、In the context of second language acquisition, what does the term “comprehensible input” refer to?A) Input that is slightly above the learner’s current level of competenceB) Input that is slightly below the learner’s current level of competenceC) Input that matches exactly the learner’s current level of competenceD) Any form of input regardless of the learner’s level of competenceAnswer: A) Input that is slightly above the learner’s current level of competenceExplanation: The concept of “comprehensible input,” developed by Stephen Krashen, suggests that learners acquire language best when they receive input that is just beyond their current linguistic capabilities, known as i+1, where “i” represents the learner’s current language level and “+1” is the next level of language complexity. This type of input challenges learners without overwhelming them, facilitating language acquisition effectively.二、简答题（20分）Question:In your opinion, what are the key factors that contribute to successful language learning inhigh school students? Explain how you would incorporate these factors into your teaching practice.Answer:The key factors that contribute to successful language learning in high school students include:1.Motivation: Motivation plays a crucial role in language learning. High school students need to be intrinsically motivated to learn the language, as well as extrinsically motivated by the goals and expectations set by their teachers and parents. As a teacher, I would create a positive learning environment by using engaging materials, encouraging students to set personal goals, and recognizing their achievements.2.Interaction: Interaction among students and with the teacher is essential for language learning. By incorporating activities such as group discussions, role-playing, and pair work, I would encourage students to communicate in English and practice their speaking and listening skills.3.Authentic materials: Using authentic materials such as newspapers, films, and songs can help students connect the language they learn in the classroom to real-life situations. I would integrate these materials into my lessons to provide students with practical language use.4.Effective assessment: Regular and varied assessment methods can help students monitor their progress and identify areas for improvement. As a teacher, I would use formative and summative assessments to track student performance and adapt my teaching strategies accordingly.5.Collaborative learning: Encouraging students to collaborate and worktogether can enhance their language skills and foster a sense of community in the classroom. I would incorporate group projects, peer tutoring, and cooperative learning activities to promote collaboration among students.6.Individual differences: Recognizing and addressing individual differences among students is crucial for successful language learning. I would differentiate my instruction by using varied teaching methods, providing additional support for struggling students, and challenging advanced learners.Incorporating these factors into my teaching practice would involve: •Creating a motivating and supportive learning environment•Incorporating interactive and collaborative activities•Utilizing authentic materials•Employing various assessment methods•Differentiating instruction to meet individual student needs•Continuously reflecting on and improving my teaching strategiesBy focusing on these key factors, I believe that high school students can achieve successful language learning and develop their English language skills.三、教学情境分析题（30分）III.Teaching Situation Analysis (30 points)Question 1:You are a high school English teacher preparing to teach a unit on American literature. Your students come from diverse backgrounds and have varying levelsof English proficiency. You notice that some students are particularly interested in contemporary issues, while others prefer classic literature. Considering these factors, design a lesson plan for a 45-minute class session that incorporates both traditional and modern elements of American literature. The lesson should aim to engage all students and foster critical thinking about the relevance of literature today. Include:•Objectives•Materials needed•Activities and procedures•Assessment methodsAnswer:Lesson Plan: Bridging Past and Present Through American LiteratureObjectives:1.Students will explore themes common to both classical and contemporary American literature.2.Students will analyze how different literary works reflect societal changes over time.3.Students will engage in a group discussion to compare and contrast two texts: one classical and one contemporary.Materials Needed:1.Excerpts from “The Great Gatsby” by F. Scott Fitzgerald (classical text).2.A short story or poem from a contemporary author such as “Interpreter of Maladies” by Jhumpa Lahiri.3.Handouts with guiding questions for each text.4.Access to online resources for additional research if available.Activities and Procedures:1.Introduction (5 minutes): Briefly introduce the authors and provide historical context for their works.2.Reading and Individual Analysis (20 minutes): Distribute the excerpts and handouts. Instruct students to read the texts silently and answer the guiding questions individually.3.Group Discussion (15 minutes): Organize students into small groups to share their insights and discuss the similarities and differences between the texts. Encourage them to consider how each work reflects its respective era.4.Whole-Class Sharing (5 minutes): Invite each group to present key points from their discussion to the class.Assessment Methods:1.Participation in group discussions will be observed and noted.2.Students’ written response s to the guiding questions will be collected and evaluated for comprehension and critical analysis.3.Group presentations will be assessed based on clarity, engagement, and depth of analysis.Analysis:This lesson plan addresses the diverse interests and English proficiency levels of the students by combining classical and contemporary literature. It allows for differentiated instruction, as students can choose which text theyfeel more comfortable with initially, yet still exposes them to both. The guiding questions facilitate deeper understanding and encourage students to make connections between the texts and the world around them, thereby enhancing their critical thinking skills. The combination of individual work, group discussion, and whole-class sharing ensures multiple opportunities for engagement and learning, catering to different learning styles and preferences within the classroom.四、教学设计题（40分）Question:Design a 45-minute lesson plan for an Advanced High School English class on the topic of “Global Warming and Its Impact on the Environment”. The lesson should include activities that encourage critical thinking, group discussion, and a creative project. Students are expected to be able to identify the causes of global warming, discuss its effects, and propose potential solutions.Answer:Lesson Title: “The Perils of Climate Change: Causes, Effects, and Solutions”Objective:By the end of this lesson, students will be able to:1.Identify the main causes of global warming.2.Discuss the effects of global warming on the environment.3.Propose potential solutions to mitigate the impact of global warming.Materials:1.Projector and screen2.Handouts with facts about global warming3.Whiteboard and markers4.Chart paper5.Pencils and colored markersLesson Outline:I. Introduction (10 minutes)1.Begin with a short video clip on global warming to spark students’ interest.2.Ask students to write down three things they learned from the video.3.Facilitate a class discussion on what global warming is and its importance.II.Group Work - Causes of Global Warming (15 minutes)1.Divide the class into small groups of four.2.Distribute handouts with facts about the causes of global warming.3.Instruct each group to identify at least three causes and explain their impact.4.Each group will create a poster highlighting their findings.5.Allow groups to present their posters to the class.III.Class Discussion - Effects of Global Warming (15 minutes)1.Discuss the effects of global warming on the environment, such as rising sea levels, extreme weather events, and loss of biodiversity.2.Facilitate a class discussion, encouraging students to share their opinions and experiences.3.Summarize the key points on the whiteboard.IV.Creative Project - Potential Solutions (5 minutes)1.Instruct students to work in pairs to brainstorm potential solutions to mitigate the impact of global warming.2.Give each pair 5 minutes to present their ideas to the class.V. Conclusion (5 minutes)1.Summarize the main points discussed in the lesson.2.Encourage students to continue exploring the topic outside the classroom.Explanation:The lesson plan is designed to engage students in an interactive and thought-provoking way. By using a combination of videos, group work, and class discussions, students will be able to gain a deeper understanding of the causes, effects, and potential solutions to global warming. The creative project allows students to apply their knowledge and come up with innovative ideas to tackle this pressing issue.。

关于b+a+ab的作文

关于b+a+ab的作文英文回答：In the realm of mathematical equations, the expression `b+a+ab` invites exploration and elucidation. This trinomial, a composition of three terms, presents a unique opportunity to delve into the intricacies of algebra and discover its hidden patterns.One method to approach this expression is to employ the distributive property, which states that `a(b+c) = ab+ac`. Applying this property, we can rewrite `b+a+ab` as`a(1+b)+b`. Further simplification reveals that `a(1+b)+b = a+ab+b`, which implies that `b+a+ab = a(1+b)+b`.Another approach involves rearranging the terms to form a factorable expression. By grouping `b+a` and `ab`, we obtain `b(1+a)+a(1+b)`. Factorizing the common factor`(1+b)`, we arrive at `(1+b)(a+b)`.The expression `b+a+ab` can also be analyzed in terms of its degree and leading coefficient. The degree of a polynomial is the highest exponent of its variables. Inthis case, both `a` and `b` have an exponent of 1, indicating that the degree of `b+a+ab` is 1. The leading coefficient is the coefficient of the term with the highest degree. Since the coefficient of `ab` is 1, it follows that the leading coefficient of `b+a+ab` is also 1.Furthermore, by examining the expression's factors, we can deduce that it has two real roots, which are `-1` and `0`. These roots represent the values of `b` for which the expression evaluates to zero.In conclusion, the expression `b+a+ab` can be dissected in various ways to reveal its underlying properties. By employing algebraic techniques such as the distributive property and factorization, we can uncover its structure and deduce its characteristics.中文回答：关于b+a+ab的探讨。

初中二年级数学知识点总结

初中二年级数学知识点总结初中二年级数学是学生数学学习的关键阶段，这个阶段的知识点不仅为后续的数学学习打下基础，也在很大程度上影响着学生的逻辑思维和问题解决能力。

以下是初中二年级数学的主要知识点总结：# 1. 数与代数- 整数 and Rational Numbers- 整数 operations (addition, subtraction, multiplication, division)- Properties of rational numbers (including absolute value and divisibility rules)- Scientific notation and estimation- Algebraic Expressions- Simplification of algebraic expressions- Combining like terms- Factoring expressions (including common factors and factoring by grouping)- Expanding expressions (distributive property)- Linear Equations- Solving linear equations in one variable- Solving systems of linear equations (substitution and elimination methods)- Applications of linear equations (word problems)- Inequalities- Writing and solving inequalities- Graphing inequalities on a number line- Solving systems of inequalities# 2. Geometry- Angles- Types of angles (acute, obtuse, right, straight, and reflex)- Angle properties and theorems (vertical angles, adjacent supplementary angles)- Angle bisectors and their properties- Parallel and Perpendicular Lines- Properties and theorems related to parallel and perpendicular lines- Criteria for parallel lines- The perpendicular bisector and its properties- Triangles- Classification of triangles (by sides and by angles)- Properties of triangles (sum of angles, base and height, median, altitude)- Special triangles (right triangles, isosceles triangles, equilateral triangles)- Pythagorean theorem and its applications- Quadrilaterals- Classification and properties of quadrilaterals (parallelograms, rectangles, squares, trapezoids, rhombuses) - Diagonals and angles in quadrilaterals- Area formulas for different types of quadrilaterals- Circles- Basic concepts (center, radius, diameter, circumference) - Properties of a circle- Inscribed angles, central angles, and their relationships - Area and circumference formulas for a circle- Symmetry- Line symmetry (reflection)- Point symmetry (rotation)- Translation and its effects on shapes# 3. Statistics and Probability- Data Collection and Representation- Organizing data (tables, charts, graphs)- Measures of central tendency (mean, median, mode)- Measures of variability (range, interquartile range, standard deviation)- Probability- Basic concepts of probability- Calculating the probability of simple events- Complementary events and probability# 4. Coordinate Geometry- Coordinates and Graphing- Cartesian coordinate system- Plotting points and lines- Equations of lines (slope-intercept form, point-slope form)# 5. Number Theory- Prime and Composite Numbers- Understanding and identifying prime and composite numbers - Prime factorization- Divisibility Rules- Special divisibility rules (e.g., multiples of 3, 5, 10)- Greatest Common Divisor (GCD) and Least Common Multiple (LCM)- Finding the GCD and LCM of numbers- Using the prime factorization method# 6. Additional Topics- Percentages- Calculating percentages- Solving percentage problems (e.g., discounts, interest, profit, loss)- Ratios and Proportions- Understanding and setting up ratios and proportions- Solving problems involving ratios and proportions- Exponents and Powers- Introduction to exponents and powers- Basic rules of exponents (product rule, quotient rule, power rule)以上总结了初中二年级数学的核心知识点。

JBI评价——病例对照研究

JBI评价——病例对照研究The Joanna Briggs InstituteIntroductionThe Joanna Briggs Institute (JBI) is an international, membership based research and development organization within the Faculty of Health Sciences at the University of Adelaide. The Institute specializes in promoting and supporting evidence-based healthcare by providing access to resources for professionals in nursing, midwifery, medicine, and allied health. With over 80 collaborating centres and entities, servicing over 90 countries, the Institute is a recognized global leader in evidence-based healthcare.JBI Systematic ReviewsThe core of evidence synthesis is the systematic review of literature of a particular intervention, condition or issue. The systematic review is essentially an analysis of the available literature (that is, evidence) and a judgment of the effectiveness or otherwise of a practice, involving a series of complex steps. The JBI takes a particular view on what counts as evidence and the methods utilized to synthesize those different types of evidence. In line with this broader view of evidence, the Institute has developed theories, methodologies and rigorous processesfor the critical appraisal and synthesis of these diverse forms of evidence in order to aid in clinical decision-making in health care. There now exists JBI guidance for conducting reviews of effectiveness research, qualitative research, prevalence/incidence, etiology/risk, economic evaluations, text/opinion, diagnostic test accuracy, mixed-methods, umbrella reviews and scoping reviews. Further information regarding JBI systematic reviews can be found in the JBI Reviewer’s Manual on our website.JBI Critical Appraisal ToolsAll systematic reviews incorporate a process of critique or appraisal of the research evidence. The purpose of this appraisal is to assess the methodological quality of a study and to determine the extent to which a study has addressed the possibility of bias in its design, conduct and analysis. All papers selected for inclusion in the systematic review (that is –those that meet the inclusion criteria described in the protocol) need to be subjected to rigorous appraisal by two critical appraisers. The results of this appraisal can then be used to inform synthesis and interpretation of the results of the study. JBI Critical appraisal tools have been developed by the JBI and collaborators and approved by the JBI Scientific Committee following extensive peer review. Although designed for use in systematic reviews, JBI critical appraisal tools can also be used when creating Critically Appraised Topics (CAT), in journal clubs and as an educational tool.JBI Critical Appraisal Checklist for Case Control StudiesReviewer DateAuthor Year Record NumberYes No Unclear Not applicable1.Were the groups comparable other than thepresence of disease in cases or the absence ofdisease in controls?□□□□2.Were cases and controls matched appropriately? □□□□3.Were the same criteria used for identification ofcases and controls?□□□□4.Was exposure measured in a standard, valid andreliable way?□□□□5.Was exposure measured in the same way forcases and controls?□□□□6.Were confounding factors identified? □□□□7.Were strategies to deal with confounding factorsstated?□□□□8.Were outcomes assessed in a standard, valid andreliable way for cases?□□□□9.Was the exposure period of interest long enoughto be meaningful?□□□□10.Was appropriate statistical analysis used? □□□□Overall appraisal: Inc lude □Exclude □Seek further info □Comments (Including reason for exclusion)Explanation of case control studies critical appraisalHow to cite: The Joanna Briggs Institute. Joanna Briggs Institute Reviewers' Manual: 2016 edition. Australia: The Joanna Briggs Institute; 2016.Case Control Studies Critical Appraisal ToolAnswers: Yes, No, Unclear or Not/Applicable1.Were the groups comparable other than presence of disease in cases or absence of diseasein controls?The control group should be representative of the source population that produced the cases. This is usually done by individual matching; wherein controls are selected for each case on the basis of similarity with respect to certain characteristics other than the exposure of interest. Frequency or group matching is alternative method. Selection bias may result if the groups are not comparable.2.Were cases and controls matched appropriately?As in item 1, the study should include clear definitions of the source population. Sources from which cases and controls were recruited should be carefully looked at. For example, cancer registries may be used to recruit participants in a study examining risk factors for lung cancer, which typify population-based case-control studies. Study participants may be selected from the target population, the source population, or from a pool of eligible participants (such as in hospital-based case-control studies).3.Were the same criteria used for identification of cases and controls?It is useful to determine if patients were included in the study based on either a specified diagnosis or definition. This is more likely to decrease the risk of bias. Characteristics are another useful approach to matching groups, and studies that did not use specified diagnostic methods or definitions should provide evidence on matching by key characteristics. A case should be defined clearly. It is also important that controls must fulfil all the eligibility criteria defined for the cases except for those relating to diagnosis of the disease.4.Was exposure measured in a standard, valid and reliable way?The study should clearly describe the method of measurement of exposure. Assessing validity requires that a 'gold standard' is available to which the measure can be compared. The validity of exposure measurement usually relates to whether a current measure is appropriate or whether a measure of past exposure is needed.Case-control studies may investigate many different ‘exposures’ that may or may not be associated with the condition. In these cases, reviewers should use the main exposure of interest for their review to answer this question when using this tool at the study level. Reliability refers to the processes included in an epidemiological study to check repeatability of measurements of the exposures. These usually include intra-observer reliability and inter-observer reliability.5.Was exposure measured in the same way for cases and controls?As in item 4, the study should clearly describe the method of measurement of exposure. The exposure measures should be clearly defined and described in detail. Assessment of exposure or risk factors should have been carried out according to same procedures or protocols for both cases and controls.6.Were confounding factors identified?Confounding has occurred where the estimated intervention exposure effect is biased by the presence of some difference between the comparison groups (apart from the exposure investigated/of interest). Typical confounders include baseline characteristics, prognostic factors, or concomitant exposures (e.g. smoking). A confounder is a difference between the comparison groups and it influences the direction of the study results. A high quality study at the level of case control design will identify the potential confounders and measure them (where possible). This is difficult for studies where behavioral, attitudinal or lifestyle factors may impact on the results.7.Were strategies to deal with confounding factors stated?Strategies to deal with effects of confounding factors may be dealt within the study design or in data analysis. By matching or stratifying sampling of participants, effects of confounding factors can be adjusted for. When dealing adjustment in data analysis, assess the statistics used in the study. Most will be some form of multivariate regression analysis to account for the confounding factors measured. Look out for description of statistical methods as regression methods such as logistic regression are usually employed to deal with confounding factorsvariables of interest.8.Were outcomes assessed in a standard, valid and reliable way for cases and controls?Read the methods section of the paper. If for e.g. lung cancer is assessed based on existing definitions or diagnostic criteria, then the answer to this question is likely to be yes. If lung cancer is assessed using observer reported, or self-reported scales, the risk of over- or under-reporting is increased, and objectivity is compromised. Importantly, determine if the measurement tools used were validated instruments as this has a significant impact on outcome assessment validity.Having established the objectivity of the outcome measurement (e.g. lung cancer) instrument, it’s important to establish how the measurement was conducted. Were those involved in collecting data trained or educated in the use of the instrument/s? (e.g. radiographers). If there was more than one data collector, were they similar in terms of level of education, clinical or research experience, or level of responsibility in the piece of research being appraised?9.Was the exposure period of interest long enough to be meaningful?It is particularly important in a case-control study that the exposure time was sufficient enough to show an association between the exposure and the outcome. It may be that the exposure period may be too short or too long to influence the outcome.10.Was appropriate statistical analysis used?As with any consideration of statistical analysis, consideration should be given to whether there was a more appropriate alternate statistical method that could have been used. Additionally, it is also important to assess the appropriateness of the analytical strategy in terms of the assumptions associated with the approach as differing methods of analysis are based on differing assumptions about the data and how it will respond.。

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Appeared in Proceedings, European Conference on Computer Vision, 1998
This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonpro t educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Information Technology Center America; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Information Technology Center America. All rights reserved. Copyright c Mitsubishi Electric Information Technology Center America, 1999 201 Broadway, Cambridge, Massachusetts 02139
1 Introduction
Fig. 1 shows a distribution of points in the plane. Taken one by one the points are identical to each other. However, it is quite apparent that their mutual positions in the plane contain some `global' information. While it is somewhat unclear how to de ne this global information, it is natural to consider a local property: the `pairwise similarity' of these points: two points that are close by are `similar' and two points that are far apart are `di erent'. This is a common situation in vision: we extract tokens from an image using some early visual process, and the notion of `closeness' between pairs of tokens is natural and well de ned. The tokens may be anything: from pixels to points, to edgels, to textured patches. While it is unclear how to extract, and even how to de ne, the global high-level properties of the scene, it is easy and natural to de ne the pairwise a nity of any two tokens. This idea comes to us from the work by Shi and Malik on grouping using normalized-cuts see 8 and references therein. In this paper we explore a weaker approach than that of Shi and Malik: rather than formulating a grouping problem explicitly, we notice that a useful global property of the scene, the foreground set, may be both `discovered' and estimated starting from the notion of pairwise closeness, or pairwise a nity, of individual elements. We develop a simple algorithm which factorizes the matrix of pairwise element a nities, and compare it with the algorithm of Shi and Malik.
2 The a nity function
Given two elements i; j in the scene S , let's suppose that it is possible to assign a number Ai;j that tells us how `similar' the two objects are. When the two objects are very similar then Ai;j has a high value and when they are not similar at all then Ai;j 0. We will suppose that this a nity function has the following properties:
Abstract. The foreground group in a scene may be `discovered' and
computed as a factorized approximation to the pairwise a nity of the elements in the scene. A pointwise approximation of the pairwise a nity information may in fact be interpreted as a `saliency' index, and the foreground of the scene may be obtained by thresholding it. An algorithm called `a nity factorization' is thus obtained which may be used for grouping. The a nity factorization algorithm is demonstrated on displays composed of points, of lines and of brightness values. Its relationship to the Shi-Malik normalized cuts algorithms is explored both analytically and experimentally. The a nity factorization algorithm is shown to be computationally e cient On oating-point operations for a scene composed of n elements and to perform well on displays where the background is unstructured. Generalizations to solve more complex problems are also discussed.
W. T. Freeman Mitsubishi Electric Research Labs 201 Broadway Cambridge, MA 02139 TR-99-03 May 1999 The foreground group in a scene may be `discovered' and computed as a factorized approximation to the pairwise a nity of the elements in the scene. A pointwise approximation of the pairwise a nity information may in fact be interpreted as a `saliency' index, and the foreground of the scene may be obtained by thresholding it. An algorithm called `a nity factorization' is thus obtained which may be used for grouping. The a nity factorization algorithm is demonstrated on displays com- posed of points, of lines and of brightness values. Its relationship to the Shi-Malik normalized cuts algorithms is explored both analytically and experimentally. The a nity factorization algorithm is shown to be com- putationally e cient On oating-point operations for a scene com- posed of n elements and to perform well on displays where the back- ground is unstructured. Generalizations to solve more complex problems are also discussed.