人工智能-必备数学基础 from Udemy

What's inside

Syllabus

高等数学基础

课程简介

函数

极限

无穷小与无穷大

连续性与导数

偏导数

方向导数

梯度

课程PPT数据代码下载（谷歌网盘）

微积分

微积分基本想法

微积分的解释

定积分

定积分性质

牛顿-莱布尼茨公式

泰勒公式与拉格朗日

泰勒公式出发点

一点一世界

阶数的作用

阶乘的作用

拉格朗日乘子法

求解拉格朗日乘子法

线性代数基础

行列式概述

矩阵与数据的关系

矩阵基本操作

矩阵的几种变换

矩阵的秩

内积与正交

特征值与矩阵分解

特征值与特征向量

特征空间与应用

SVD要解决的问题

特征值分解

SVD矩阵分解

随机变量与概率估计

离散型随机变量

连续型随机变量

简单随机抽样

似然函数

极大似然估计

概率论基础

概率与频率

古典概型

条件概率

条件概率小例子

独立性

二维离散型随机变量

二维连续型随机变量

边缘分布

期望

期望求解

马尔科夫不等式

切比雪夫不等式

后验概率估计

贝叶斯拼写纠错实例

垃圾邮件过滤实例

数据科学你得知道的几种分布

正太分布

二项式分布

泊松分布

均匀分布

卡方分布

beta分布

核函数变换

核函数的目的

线性核函数

多项式核函数

核函数实例

高斯核函数

参数的影响

熵与激活函数

熵的概念

熵的大小意味着什么

激活函数

激活函数的问题

回归分析

回归分析概述

回归方程定义

误差项的定义

最小二乘法推导与求解

回归方程求解小例子

回归直线拟合优度

多元与曲线回归问题

Python工具包介绍

statsmodels回归分析

高阶与分类变量实例

案例：汽车价格预测任务概述

缺失值填充

特征相关性

预处理问题

回归求解

假设检验

假设检验基本思想

左右侧检验与双侧检验

Z检验基本原理

Z检验实例

T检验基本原理

T检验实例

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Covers core topics and offers a strong introduction to this subject

Provides lessons on foundational high-level math concepts

Useful for understanding basic high-level math

This course's material may be suitable for beginners

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in 人工智能-必备数学基础 with these activities:

探索 Python 库

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探索 Python 库可以帮助学生了解用于数据科学和人工智能的工具，为后续课程内容做好准备。

Browse courses on Python

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选择一个与课程相关的 Python 库，如 NumPy、Pandas 或 Scikit-learn。
查找在线教程或文档来学习库的基本功能。
练习使用库进行简单的数据操作或建模任务。

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Career center

Learners who complete 人工智能-必备数学基础 will develop knowledge and skills that may be useful to these careers:

Statistician

Statisticians collect, analyze, interpret, and present data for various purposes, including research, quality control, and public policy. This course can be useful for aspiring Statisticians, as it provides a strong foundation in probability, statistics, and regression analysis. These concepts are essential for understanding statistical methods, designing and conducting studies, and interpreting statistical results.

See salaries and explore the career path for Statistician

Machine Learning Engineer

Machine Learning Engineers design, build, and maintain machine learning algorithms and models to solve complex problems in various domains. This course can be helpful as it provides a solid foundation in mathematical concepts such as linear algebra, which is commonly used in machine learning applications. Additionally, the coverage of probability and statistics is essential for understanding and developing machine learning models.

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Data Analyst

Data Analysts clean, analyze, and visualize data to identify trends and patterns, providing insights to inform decision-making. This course can be helpful as it covers fundamental mathematical concepts such as probability, statistics, and regression analysis. These concepts are essential for understanding data, performing statistical analysis, and presenting data-driven insights.

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Data Scientist

Data Scientists create mathematical models to identify trends and patterns in data to advance scientific research and innovation. This course may be useful for aspiring Data Scientists as it covers essential mathematical principles, including statistics, probability, and linear algebra, which serve as foundational building blocks for data science and machine learning.

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Operations Research Analyst

Operations Research Analysts use mathematical and statistical models to optimize decision-making processes within organizations. This course may be useful for aspiring Operations Research Analysts as it covers fundamental concepts such as probability, statistics, and regression analysis. These concepts are essential for understanding optimization techniques, modeling uncertainty, and analyzing data to improve operational efficiency.

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Actuary

Actuaries analyze the financial implications of risk and uncertainty, advising companies on financial planning. This course can be particularly helpful as it provides a strong foundation in probability and statistics, which are essential concepts in actuarial work. Furthermore, the course's coverage of regression analysis may be beneficial for understanding insurance pricing models.

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Economist

Economists analyze economic data and trends to understand economic behavior and develop policies. This course may be useful for aspiring Economists as it covers essential mathematical concepts such as probability, statistics, and regression analysis. These concepts are used in economic modeling, forecasting, and data analysis to understand economic phenomena and make informed policy decisions.

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Biostatistician

Biostatisticians use statistical methods to analyze and interpret health-related data, contributing to medical research and public health. This course may be useful for aspiring Biostatisticians as it covers fundamental concepts of probability, statistics, and regression analysis. Understanding these topics is crucial for designing and conducting biomedical studies and interpreting the results.

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Financial Risk Manager

Financial Risk Managers assess and manage financial risks within organizations. This course may be valuable for aspiring Financial Risk Managers as it provides a strong foundation in probability, statistics, and regression analysis. These concepts are essential for understanding and managing financial risks, developing risk models, and making informed decisions in financial risk management.

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Research Analyst

Research Analysts provide insights and recommendations based on data analysis and research. This course can be helpful for aspiring Research Analysts as it covers essential mathematical concepts such as probability, statistics, and regression analysis. These concepts are used in data analysis and modeling to extract meaningful insights and draw data-driven conclusions.

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Business Analyst

Business Analysts use data analysis and statistical techniques to help organizations make informed business decisions. This course can be useful as it covers essential mathematical foundations such as probability, statistics, and regression analysis. These concepts are crucial for understanding data, identifying trends, and making data-driven recommendations in a business context.

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Software Engineer

Software Engineers design, develop, and maintain software applications. This course may be helpful for aspiring Software Engineers who wish to specialize in data-driven software development or machine learning applications. The coverage of mathematical concepts such as probability, statistics, and linear algebra can provide a solid foundation for understanding data structures, algorithms, and modeling techniques used in software engineering.

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Financial Analyst

Financial Analysts use mathematical modeling and statistical analysis to evaluate and recommend investments. This course may be beneficial for aspiring Financial Analysts as it builds a foundation in topics such as probability, statistics, and regression analysis. These skills are essential for understanding financial data, building financial models, and making sound investment decisions.

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Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data for investment strategies. This course may be valuable for aspiring Quantitative Analysts, as it provides a strong foundation in probability, statistics, and regression analysis. These concepts are essential for understanding and developing financial models used in quantitative finance.

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Risk Manager

Risk Managers identify, assess, and mitigate risks within organizations. This course may be helpful as it covers fundamental concepts of probability and statistics, which are essential for understanding and managing risk. Additionally, the course's coverage of regression analysis can be beneficial for analyzing risk data and developing risk models.

See salaries and explore the career path for Risk Manager