CIP 27. - 数学和统计 Mathematics and statistics

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27. - 数学和统计 Mathematics and statistics

该系列包括专注于系统研究逻辑符号语言及其应用的教学计划。 This series comprises instructional programs that focus on the systematic study of logical symbolic language and its applications.

27.01 - 数学 Mathematics

该子系列包括教学课程类别 27.0101 至 27.0199。 This subseries comprises instructional program classes 27.0101 to 27.0199.

27.0101 - 数学，一般 Mathematics, general

该教学课程包括任何使用符号逻辑和语言专注于分析数量、大小、形式及其关系的通用课程。这些课程包括代数、微积分、泛函分析、几何、数论、逻辑、拓扑和其他数学专业课程。 This instructional program class comprises any general program that focuses on the analysis of quantities, magnitudes, forms, and their relationships, using symbolic logic and language. These programs include courses in algebra, calculus, functional analysis, geometry, number theory, logic, topology and other mathematical specializations.

说明性示例 Illustrative example(s)
数学 mathematics
纯数学 pure mathematics
排除项 Exclusion(s)
应用数学(27.0301) applied mathematics(27.0301)
逻辑（38.0102） logic(38.0102)
数学物理（40.0810） mathematical physics(40.0810)
数学与统计学(27.0503) mathematics and statistics(27.0503)
数学教师教育(13.1311) mathematics teacher education(13.1311)
计算能力和计算能力（不计学分）(32.0104) numeracy and computational skills (not for credit)(32.0104)

27.0102 - 代数和数论 Algebra and number theory

该教学课程包括任何专注于通过符号、向量、矩阵和方程以及整数的属性来表达数量及其关系的课程。这些课程包括代数结构、二次和自守形式、组合数学、线性代数和代数几何方面的课程。 This instructional program class comprises any program that focuses on the expression of quantities and their relationships by means of symbols, vectors, matrices, and equations, and the properties of integers. These programs include courses in algebraic structures, quadratic and automorphic forms, combinatorics, linear algebra, and algebraic geometry.

说明性示例 Illustrative example(s)
代数 algebra
代数和数论 algebra and number theory

27.0103 - 分析和功能分析 Analysis and functional analysis

此教学程序类包括任何专注于方程、多元解、函数和动态系统的属性和行为的程序。这些课程包括微分方程、变分、近似、复变量、积分、谐波分析和小波理论、动态系统以及数学物理应用等课程。 This instructional program class comprises any program that focuses on the properties and behaviour of equations, multivariate solutions, functions, and dynamic systems. These programs include courses in differential equations, variation, approximations, complex variables, integrals, harmonic analysis and wavelet theory, dynamic systems, and applications to mathematical physics.

说明性示例 Illustrative example(s)
分析和功能分析 analysis and functional analysis

27.0104 - 几何/几何分析 Geometry/geometric analysis

此教学程序类包括任何专注于与点、线、角度、曲面和实体有关的属性、测量和关系的程序。这些课程包括全局分析、微分几何、欧几里得和非欧几里得几何、集合论、流形、积分几何以及代数和其他主题的应用课程。 This instructional program class comprises any program that focuses on the properties, measurements, and relationships pertaining to points, lines, angles, surfaces, and solids. These programs include courses in global analysis, differential geometry, Euclidian and non-Euclidian geometry, set theory, manifolds, integral geometry, and applications to algebra and other topics.

说明性示例 Illustrative example(s)
几何分析 geometric analysis
几何学 geometry

27.0105 - 拓扑和基础 Topology and foundations

该教学课程包括任何专注于连续多向变换条件下未改变几何配置特性的课程。这些课程包括数理逻辑、证明论、模型论、集合论、组合学、连续体、同伦、同源、链接和变换操作方面的课程。 This instructional program class comprises any program that focuses on the properties of unaltered geometric configurations under conditions of continuous, multi-directional transformations. These programs include courses in mathematical logic, proof theory, model theory, set theory, combinatorics, continua, homotopy, homology, links, and transformation actions.

说明性示例 Illustrative example(s)
拓扑 topology
拓扑和基础 topology and foundations
排除项 Exclusion(s)
地质工程(14.3901) geological engineering(14.3901)
地理信息工程(14.3801) geomatics engineering(14.3801)
逻辑（38.0102） logic(38.0102)

27.0199 - 数学，其他 Mathematics, other

该教学课程包括上面未列出的任何与数学相关的课程。 This instructional program class comprises any program not listed above that relates to Mathematics.

说明性示例 Illustrative example(s)
其他数学 other mathematics
排除项 Exclusion(s)
精算数学（52.1304） actuarial mathematics(52.1304)

27.03 - 应用数学 Applied mathematics

该子系列包括教学程序类别 27.0301 至 27.0399。 This subseries comprises instructional program classes 27.0301 to 27.0399.

27.0301 - 应用数学，普通 Applied mathematics, general

该教学课程包括任何专注于数学应用以解决工程和应用科学等领域的功能性问题的课程。这些课程包括自然现象建模连续介质力学、反应扩散、波传播、动态系统、数值分析、控制理论、渐近方法、变分、优化理论、反问题以及特定科学和工业主题的应用等课程。 This instructional program class comprises any program that focuses on the application of mathematics to the solution of functional problems in fields such as engineering and the applied sciences. These programs include courses in natural phenomena modelling continuum mechanics, reaction-diffusion, wave propagation, dynamic systems, numerical analysis, controlled theory, asymptotic methods, variation, optimization theory, inverse problems, and applications to specific scientific and industrial topics.

说明性示例 Illustrative example(s)
应用数学 applied mathematics
数学科学 mathematical sciences
数学科学 mathematics science
排除项 Exclusion(s)
应用统计（27.0601） applied statistics(27.0601)
计算与应用数学(27.0304) computational and applied mathematics(27.0304)
金融数学(27.0305) financial mathematics(27.0305)
数学生物学(27.0306) mathematical biology(27.0306)
数理经济学（30.4901） mathematical economics(30.4901)
数学物理（40.0810） mathematical physics(40.0810)
运筹学(14.3701) operations research(14.3701)

27.0303 - 计算数学 Computational mathematics

该教学课程包括任何专注于数学在计算机、计算技术和算法的理论、体系结构和设计中的应用的课程。这些课程包括计算机理论、控制论、数值分析、算法开发、二进制结构、组合学、高级统计和相关主题的课程。 This instructional program class comprises any program that focuses on the application of mathematics to the theory, architecture, and design of computers, computational techniques, and algorithms. These programs include courses in computer theory, cybernetics, numerical analysis, algorithm development, binary structures, combinatorics, advanced statistics, and related topics.

说明性示例 Illustrative example(s)
计算数学 computational mathematics
排除项 Exclusion(s)
精算数学（52.1304） actuarial mathematics(52.1304)
计算与应用数学(27.0304) computational and applied mathematics(27.0304)
计算机科学(11.0701) computer science(11.0701)
数学与计算机科学(30.0801) mathematics and computer science(30.0801)
科学计算（30.3001） scientific computing(30.3001)

27.0304 - 计算与应用数学 Computational and applied mathematics

该教学课程包括任何专注于将广泛的数学和计算方法应用于建模、分析、算法开发和模拟以解决复杂科学和工程问题的课程。这些课程包括数值分析、离散数学、运筹学、优化、微分方程、统计学、科学计算以及特定科学和工业主题的应用课程。 This instructional program class comprises any program that focuses on the application of a broad range of mathematical and computational methods to modelling, analysis, algorithm development, and simulation for the solution of complex scientific and engineering problems. These programs include courses in numerical analysis, discrete mathematics, operations research, optimization, differential equations, statistics, scientific computation, and applications to specific scientific and industrial topics.

说明性示例 Illustrative example(s)
应用和计算数学 applied and computational mathematics
结合计算和应用数学 combined computational and applied mathematics
计算和应用数学 computational and applied mathematics
排除项 Exclusion(s)
应用数学(27.0301) applied mathematics(27.0301)
计算数学（27.0303） computational mathematics(27.0303)
科学计算（30.3001） scientific computing(30.3001)

27.0305 - 金融数学 Financial mathematics

该教学课程包括任何专注于将数学和统计学应用于金融业的课程，包括各种金融模型的开发、批判和使用。这些课程包括概率论、统计分析、数值方法、计算和模拟方法、随机过程、经济学以及金融市场和应用等课程。 This instructional program class comprises any program that focuses on the application of mathematics and statistics to the finance industry, including the development, critique, and use of various financial models. These programs include courses in probability theory, statistical analysis, numerical methods, computation and simulation methods, stochastic processes, economics, and financial markets and applications.

说明性示例 Illustrative example(s)
数学金融 mathematical finance
定量和计算金融 quantitative and computational finance
量化金融 quantitative finance
排除项 Exclusion(s)
应用数学(27.0301) applied mathematics(27.0301)

27.0306 - 数学生物学 Mathematical biology

该教学课程包括任何专注于将数学应用于基因组学、分子建模、结构生物学、生态学、进化生物学以及神经生物学、生理学和新陈代谢分析系统的课程。这些课程包括计算数学、混沌和非线性系统、微扰方法、进化生物学、分子生物学、生物信息学和神经生物学等课程。 This instructional program class comprises any program that focuses on the application of mathematics to genomics, molecular modelling, structural biology, ecology, evolutionary biology and systems of analysis of neurobiology, physiology, and metabolism. These programs include courses in computational mathematics, chaos and nonlinear systems, perturbation methods, evolutionary biology, molecular biology, bioinformatics, and neurobiology.

说明性示例 Illustrative example(s)
数学生物学 mathematical biology
排除项 Exclusion(s)
应用数学(27.0301) applied mathematics(27.0301)
生物信息学(26.1103) bioinformatics(26.1103)
生物识别（26.1101） biometrics(26.1101)
生物统计学（26.1102） biostatistics(26.1102)
计算生物学（26.1104） computational biology(26.1104)

27.0399 - 应用数学，其他 Applied mathematics, other

该教学课程包括上面未列出的任何与应用数学相关的课程。 This instructional program class comprises any program not listed above that relates to Applied mathematics.

说明性示例 Illustrative example(s)
组合学和优化 combinatorics and optimization
金融保险 financial insurance
其他应用数学 other applied mathematics

27.05 - 统计数据 Statistics

该子系列包括教学程序类别 27.0501 至 27.0599。 This subseries comprises instructional program classes 27.0501 to 27.0599.

27.0501 - 统计，一般 Statistics, general

该教学计划类包括任何一般计划，这些计划使用概率论和从中派生的技术来关注测量组之间的关系以及异同。这些课程包括概率论、二项式分布、回归分析、标准差、随机过程、蒙特卡罗方法、贝叶斯统计、非参数统计、抽样理论和统计技术的原理课程。 This instructional program class comprises any general program that focuses on the relationships between groups of measurements, and similarities and differences, using probability theory and techniques derived from it. These programs include courses in the principles in probability theory, binomial distribution, regression analysis, standard deviation, stochastic processes, Monte Carlo method, Bayesian statistics, non-parametric statistics, sampling theory, and statistical techniques.

说明性示例 Illustrative example(s)
统计数据 statistics
排除项 Exclusion(s)
精算数学（52.1304） actuarial mathematics(52.1304)
应用统计（27.0601） applied statistics(27.0601)
生物统计学（26.1102） biostatistics(26.1102)
业务统计(52.1302) business statistics(52.1302)
教育统计与研究方法(13.0603) educational statistics and research methods(13.0603)
数学与统计学(27.0503) mathematics and statistics(27.0503)
社会研究方法(45.0102) social research methods(45.0102)

27.0502 - 数理统计与概率 Mathematical statistics and probability

该教学课程包括任何专注于统计方法及其使用的数学理论的课程。这些课程包括概率论、参数和非参数推理、顺序分析、多变量分析、贝叶斯分析、实验设计、时间序列分析、重采样、稳健统计、极限理论、无限粒子系统、随机过程、鞅、马尔可夫过程和巴拿赫空间。 This instructional program class comprises any program that focuses on the mathematical theory underlying statistical methods and their use. These programs include courses in probability theory, parametric and nonparametric inference, sequential analysis, multivariate analysis, Bayesian analysis, experimental design, time series analysis, resampling, robust statistics, limit theory, infinite particle systems, stochastic processes, martingales, Markov processes, and Banach spaces.

说明性示例 Illustrative example(s)
数理统计 mathematical statistics
概率 probability
概率与统计 probability and statistics
理论统计 theoretical statistics
排除项 Exclusion(s)
精算数学（52.1304） actuarial mathematics(52.1304)
生物统计学（26.1102） biostatistics(26.1102)
业务统计(52.1302) business statistics(52.1302)
教育统计与研究方法(13.0603) educational statistics and research methods(13.0603)

27.0503 - 数学和统计 Mathematics and statistics

该教学课程包括任何具有数学和统计学综合综合或从数学和统计学中汲取专业知识的课程。这些课程包括微积分、线性代数、数值分析和偏微分方程、离散数学、概率论、统计学、计算和其他相关主题的课程。 This instructional program class comprises any program with a general synthesis of mathematics and statistics or a specialization which draws from mathematics and statistics. These programs include courses in calculus, linear algebra, numerical analysis and partial differential equations, discrete mathematics, probability theory, statistics, computing, and other related topics.

说明性示例 Illustrative example(s)
结合数学和统计学 combined mathematics and statistics
数学和统计学 mathematics and statistics
排除项 Exclusion(s)
数学（27.0101） mathematics(27.0101)
统计数据（27.0501） statistics(27.0501)

27.0599 - 统计，其他 Statistics, other

该教学课程包括上面未列出的任何与统计相关的课程。 This instructional program class comprises any program not listed above that relates to Statistics.

说明性示例 Illustrative example(s)
其他统计数据 other statistics

27.06 - 应用统计 Applied statistics

该子系列包括教学程序类 27.0601。 This subseries comprises instructional program class 27.0601.

27.0601 - 应用统计，一般 Applied statistics, general

该教学课程包括任何侧重于应用统计学来解决商业、工程、医学和应用科学等领域的功能性问题的课程。这些课程包括推理原理、概率论、回归分析、描述性统计、随机过程、蒙特卡罗方法、贝叶斯统计、非参数统计、抽样理论、统计计算和统计技术等课程。 This instructional program class comprises any program that focuses on the application of statistics to the solution of functional problems in fields such as business, engineering, medicine, and the applied sciences. These programs include courses in the principles in inference, probability theory, regression analysis, descriptive statistics, stochastic processes, Monte Carlo method, Bayesian statistics, non-parametric statistics, sampling theory, statistical computing, and statistical techniques.

说明性示例 Illustrative example(s)
应用统计 applied statistics
排除项 Exclusion(s)
应用数学(27.0301) applied mathematics(27.0301)
运筹学(14.3701) operations research(14.3701)
统计数据（27.0501） statistics(27.0501)

27.99 - 数学和统计，其他 Mathematics and statistics, other

该子系列包括教学程序类 27.9999。 This subseries comprises instructional program class 27.9999.

27.9999 - 数学和统计，其他 Mathematics and statistics, other

该教学课程包括上面未列出的任何与数学和统计学相关的课程。 This instructional program class comprises any program not listed above that relates to Mathematics and statistics.

说明性示例 Illustrative example(s)
其他数学和统计学 other mathematics and statistics