'Use Python' Series

In this series, I will try to teach the basic knowledge in Calculus, Linear Algebra, Advanced statistics and etc. by using python, which are required courses in UIC.

*In these articles, most of the time, I will use numpy, sumpy and matplotlib. We can use numpy and sympy to deal with the high dimensional array or the matrix operation easily. With matplotlib, we can visualize the data and this is more intuitionistic. *

Calculus

1. What is Function
2. Composition
3. Euler's Formula
4. Limits
5. Derivative
6. Newton's Method
7. Optimization
8. Integration and Differentiation
9. Ordinary Differential Equations,ODE)

Linear Algebra

1. Chapter Zero multiplication in LA and the lib we use
2. Chapter One Matrix
3. Chapter Two Determinant
4. Chapter Three Vector
5. Chapter Four Vector Space
6. Chapter Five Linear Algebra Advanced Text

Advanced Statistics（Probability and Statistics)

1. Chapter One Probability

• Random Experiment and Sample Space
• Law of Total Probability and Bayes Formula
• Random Variable
• Discrete Distribution and Python Code
• Contiuous Distribution and Python Code

2. Chapter Two Statistics

Bayesian Statistics

1. Chapter Zero Review

• Omission

2. Chapter One Introduction

• Conditional Probability
• Conjoint Probability
• Bayes's Theorem (in this semester, we has finished Bayesian Analysis course, but the course is to use R language as auxiliary material. I am now looking for Bayes theorem related python, Think Bayes too simple)

Regression Analysis

Although this course's recommanded language is R, and you can check the R code in Using-R-Series I will rewrite it in Python

1. Chapter One Introduction
2. Chapter Two Simple Linear Regression
3. Chapter Three Multiple Linear Regression
4. Chapter Four Model Adjusting
5. Chapter Five Model Diagnositc

Optimization (Convex Optimization)

Although this course's recommanded language is MATLAB, and you can check the MATLAB code in Using-R-Series I will rewrite it in Python

1. Chapter One Introduction

---

This repo is writen with jupyter notebook

Who is suitable for this lesson? Those who are interested in both statistics and python

I also put the .ipynb into the colab-google, you can try it if you want

Reference

用 python 学微积分

机器学习的数学基础：矩阵篇

机器学习的数学基础：向量篇

机器学习的数学基础：线性代数进阶篇

Python-for-Probability-Statistics-and-Machine-Learning

Think bayes

统计分布 [Statistical Distribution] Written by Prof.Kai Tai Fang, Prof.Jian Lun Xu

概率论与数理统计 [Probailities and Statistics] Written by Prof Xi Ru Chen

Linear Regression in Python with Scikit-Learn

Contributors

• Timothy Wu
• ECWU

Timothy Wu put forward a amendments： `

1. Higher order function应为 composite function复合函数;
   
2. Big O 那段写的不是很清楚，其实Big O主要是表示算法的计算复杂度，微积分里面用的不多;
   
3. 切线前面可以介绍割线，再用极限的概念引入切线；
   
4. 可加入包括原函数、一阶导和二阶导（或更高阶导）图像的图；
   
5. 常微分方程是比不定积分更“高级”的概念，最好使用微积分基本定理引入不定积分；
   
6. 可以加入曲线下（间）面积、黎曼和和定积分的关系；
   
7. 可以加入求旋转体的体积作为积分的应用
   

Wiki

• Wiki

中文版文檔請看： README_CN