Part I: Applied Math and Machine Learning Basics Part I. Applied Math and Machine. Learning Basics. 27. This part of the book intro

duces the basic mathematical concepts needed to. understand deep learning.Part I Applied Math and Machine Learning Basics.pdf 《Deep Learning》《深度学习》 by Ian Goodfellow, Yoshua Bengio and Aaron

mathematics of machine learning

Mathematics and statistics are the foundation of data science and machine learning. As far as I know, most successful data scientists come from these fields — computer science, applied mathematics and statistics, economics. If you want to master data science, you have to have a good understanding of basic algebra and statistics.

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However, for those without a mathematical background, the starting path may be difficult. First, you have to figure out what must be learned and what is not necessary — which may include many topics such as linear algebra, calculus, probability, statistics, discrete mathematics, regression, optimization, and so on. How much do you need to go deep into these topics? Self-study is difficult to grasp all of this by yourself.

If you are facing such a problem, don’t panic, now I have done this hard work for you. This list recommends the most popular open courses in data science mathematics from Coursera, edX, Udemy, and Udacity. This list has been carefully orchestrated so that you can self-learn the mathematical concepts required for data science.

Table of Contents

# Start learning now!

**What kind of course is right for you?**

To help you navigate through these courses, I have divided the courses into primary, intermediate, and advanced categories for different learners. Before you study in depth, please choose your level of mathematics. I added the homework that I had to do before I took each course for reference.

After completing the preparatory courses, you can better understand the follow-up courses. There are very few such courses.Therefore, you must be sure to understand the subject of these courses or have taken these courses.

Then read and find the course that suits you!

**Content directory:**

- Primary mathematics level / statistics
- Data science math skills
- Introduction to statistics
- Introduction to inferential statistics
- Getting started with probability and data
- Ubiquitous Mathematics: Finite Math Applications
- Probability: Basic Concepts & Discrete Random Variables
- Mathematical Biostatistics Training Camp 1
- Linear Algebra Application Part 1
- Introduction to Mathematical Thinking
- Intermediate mathematics level / statistics
- Bayesian statistics: from concept to data analysis
- Game theory 1
- Game Theory 2: Advanced Applications
- Advanced Linear Model of Data Science 1: Least Squares
- Advanced Linear Model of Data Science 2: Statistical Linear Model
- Introduction to linear models and matrix algebra
- Mathematics in motion
- Advanced mathematics level / statistics
- Discrete optimization
- Genomic data science statistics
- Biostatistics for big data applications

mathematics of machine learning

**Primary level mathematics and statistics**

**1. Data Science Maths Skills**

Address: https://www.coursera.org/learn/datasciencemathskills

Course period: 4 weeks

Class: Duke University (Coursera)

If you are a beginner and have a limited amount of math, then this course is for you. In the course, you will learn about many algebra concepts, such as set theory, inequalities, functions, coordinate geometry, logarithms, and probabilities.

This course will take you through all the basic math skills required for mathematics and lay a solid foundation.

The course starts on January 9, 2017 and the instructor is from Duke University.

Pre-Knowledge: Basic Math Knowledge

**2. Introduction to Statistics (Intro to Descriptive Statistics)**

Address: https://www.udacity.com/course/intro-to-descriptive-statistics–ud827

Course period: 8 weeks

Class: Udacity (Coursera)

For beginners who want to learn statistics, this course at Udacity is a great guide to getting started. The content is interesting, practical, and has many examples. Descriptive statistics will first familiarize you with the various statistics and definitions. Then teach statistical concepts such as central tendency, variability, standard normal distribution, and sampling distribution. This course does not require you to master some statistical knowledge in advance, and is now open for registration.

Prerequisite knowledge: none

**3. Intro to Inferential Statistics**

Address: https://www.udacity.com/course/intro-to-inferential-statistics–ud201

Course period: 8 weeks

Class: Udacity (Coursera)

After learning to describe the statistics, it is time to learn the inference statistics. This course continues the practical way of teaching.

In the course, you will learn statistical concepts such as estimation, hypothesis testing, t-test, chi-square test, one-way ANOVA, two-way ANOVA, and correlation and regression.

Each topic is followed by a problem set and a small test. After the course, you can also test the learning on the real data set.The course is open for registration.

Prerequisite knowledge: Full understanding of Descriptive Statistics (the second recommendation above)

Alternative course: “Statistics: Unlocking the World of Data”, a six-week course at the University of Pittsburgh (edX). Address: https://www.edx.org/course/statistics-unlocking-world-data-edinburghx-statsx#!

**4. Introduction to Probability and Data**

Address: https://www.coursera.org/learn/probability-intro

Course period: 5 weeks

Class: Duke University (Coursera)

This lesson will take you through R and RStudio contact data visualization and numerical statistics.

First, take you through the basic concepts of probability and data mining and begin to have a basic understanding of the course.Then, explain the different concepts under different topics. Finally, you will use a real data set to test your learning through a data analysis project.

The instructor is a professor of statistics from Duke University, and you need to have a special knowledge of R statistics. If you want to learn R in order to study mathematics, then this course should not be missed. The course is open for registration.

Prerequisite knowledge: basic statistics and R knowledge.

**5. Mathematical Everywhere: Applications of Finite Math**

Address: https://www.udemy.com/math-is-everywhere-applications-of-finite-math/

Course duration: 1 week

Class: Davidson (Udemy)

As the name suggests, teach ubiquitous mathematics, from angry birds to Google. Teaching mathematical concepts in your application in an interesting way.

In the course, you will learn how to use the equation of lines to create computer fonts, how graph theory plays an important role in angry birds, how linear systems model the performance of a sports team, and how Google uses it. Probability and simulation to maintain a leading edge in search engines.

The instructor is a mathematics professor at Davis, open for registration.

Prerequisite knowledge: To understand linear algebra and programming.

**6. Probability Theory: Basic Concepts and Discrete Random Variables (Probability: Basic Concepts & Discrete Random Variables)**

Address: https://www.edx.org/course/probability-basic-concepts-discrete-purduex-416-1x

Course period: 6 weeks

Class: Purdue University

This course is designed for professionals who are interested in data science and information science. It covers the basic elements of mathematical probability theory.

In this course, you will learn the basic concepts of probability theory, random variables, distribution, Bayesian theorem probability mass function and CDF, joint distribution law and expectation.

Once you are familiar with these basics, you can study more in-depth concepts such as Bogey and Binomial distribution, geometric distribution, negative binomial distribution, Poisson distribution, hypergeometric distribution, and discrete uniform distribution.

After studying this course, you will have an in-depth understanding of the probabilistic application of everyday life. This course is open for registration.

Prerequisite knowledge: basic statistical knowledge.

**7. Math Biostatistics Boot Camp 1**

Address: https://www.coursera.org/learn/biostatistics

Course period: 4 weeks

Class: Johns Hopkins University

In fact, the “biological” in “biometrics” is misleading. This course is all about the probabilistic and statistical technical basis for data analysis.

The course includes probability, expectation, conditional probability, distribution, confidence interval, bootstrapping, binomial proportions, and logarithmic distribution (logs).

The background of linear algebra and programming is helpful for this course, but it is not a prerequisite for mandatory use. The course begins on January 16, 2017 and is taught by Professor of Biostatistics at Johns Hopkins University.

The course is reasonable and will provide a complete analysis of mathematical statistics.

Prerequisite knowledge: basic linear algebra, calculus, and practical programming (not mandatory).

**8. Application of Linear Algebra (Part 1) (Applications of Linear Algebra Part 1)**

Address: https://www.edx.org/course/applications-linear-algebra-part-1-davidsonx-d003x-1

Course period: 5 weeks

Lecture: Davidson College (edX)

This is an interesting lesson about the application of linear algebra in data science.

This course will first introduce the basics of linear algebra. You will then be introduced to linear algebra applications such as online code for handwritten digit recognition and team ranking.

This course is open for registration.

Prerequisite knowledge: basic linear algebra knowledge

**9. Introduction to Mathematical Thinking**

Address: https://www.coursera.org/learn/mathematical-thinking#

Course period: 8 weeks

Teaching: Stanford University (Coursera)

This course from Stanford University will teach you analytical thinking skills. You can learn interesting out-of-the-box thinking ways to help you stay ahead of the competition.

In this class, you will learn a simple introduction to language, quantifier analysis, number theory, and real analysis. Mastering this course requires familiarity with algebra, number system, and primary set theory.

The course will begin on January 9, 2017 and the instructor will be from Stanford University. Registration is currently open.

Pre-knowledge: basic algebra, number system, and elementary set theory.

**Medium mathematics and statistics**

At this time, you should already know all the basic concepts that a data scientist needs to know. It’s time to take your math knowledge to the next level.

**1. Bayesian Statistics: From Concept to Data Analysis (Bayesian Statistics: From Concept to Data Analysis)**

Address: https://www.coursera.org/learn/bayesian-statistics

Course period: 4 weeks

Lecture: University of California (Coursera)

Bayesian statistician is an important topic in data science. For some reason, it did not receive enough attention.

In this course, the first section covers basic probabilistic topics such as conditional probability, probability distribution, and Bayes’ theorem. Then, you will learn the statistical inference of the Frequentist and Bayesian methods, the method of selecting the optimal distribution, the model of the discrete data, and the Bayesian analysis of the continuous data.

This course requires prior knowledge of statistical concepts and the course begins on January 16, 2017.

Prerequisite knowledge: basic and advanced statistics

**2. Game Theory 1**

Address: https://www.coursera.org/learn/game-theory-1

Course period: 8 weeks

Classes: Stanford University and the University of British Columbia (Coursera)

Game theory is a very important part of data science. In this lesson, you will learn the basics of game theory and its applications.If you plan to master intensive study this year, this course is perfect for you.

The course will give you a basic understanding of the following things: characterization of games and strategies, extended forms (computer scientists call the game tree), Bayesian games (for modeling things like auctions), repetition and random games.Each concept is complemented by examples and applications. The instructors are from Stanford University and the University of British Columbia and are open for registration.

Pre-Knowledge: Basic Probability and Mathematical Thinking

**3. Game Theory II: Advanced Application (Game Theory II: Advanced Applications)**

Address: https://www.coursera.org/learn/game-theory-2

Course period: 5 weeks

Classes: Stanford University and the University of British Columbia (Coursera)

After the game theory foundation in the previous course, the course is an explanation of the advanced application of game theory.

In this course, you will learn how to design interactions between agents to achieve good social outcomes. The three main topics covered by the course are: social choice theory, mechanism design and bidding.

The course began on January 30, 2017 and was taught by professors from Stanford University and the University of British Columbia.

The course is open for registration.

Prerequisite knowledge: the basis of game theory

**4. Introduction to Linear Models and Matrix Algebra**

Address: https://www.edx.org/course/introduction-linear-models-matrix-harvardx-ph525-2x-0

Course period: 4 weeks

Class: Harvard University (edX)

Matrix algebra has been used in various tools for experimental design and high-dimensional data analysis.

For ease of understanding, this course is divided into 7 parts in a step-by-step manner. You will learn about the symbols of matrix algebra and its operations, matrix algebra applications in data analysis, linear models and QR decomposition.

The programming language used in this course is the R language. You are free to choose the part of the course content that caters to your point of interest and learn the content.

This course is taught by Harvard University’s Professor of Biostatistics and is currently only open to students enrolled in the course.

Prerequisite knowledge: linear algebra basics and R language knowledge

**5. High-order linear model of data science 1: Advanced Linear Models for Data Science 1: Least Squares**

Address: https://www.coursera.org/learn/linear-models

Course period: 6 weeks

Lecture: Johns Hopkins University (Source: Coursera)

This course is the first part of a two-part series of high-order linear statistical learning models. Those who already know about the regression model and want to seek further study on it must learn this course.

In this course, you will learn one and two parameters of regression analysis, linear regression analysis, general least squares, least squares examples, foundations, and residuals. Before you start the next step, I need to clarify that you need to have a linear algebra basis, a multivariate calculus foundation, an understanding of statistics and regression models, familiarity with argument-based mathematics, and operational knowledge of the R language. This course will begin on January 23, 2017.

Prerequisite knowledge: linear algebra, calculus, statistics, and R language knowledge

**6. High-order linear model of data science 2: Statistical Linear Models (Advanced Linear Models for Data Science 2: Statistical Linear Models)**

Address: https://www.coursera.org/learn/linear-models-2

Course period: 6 weeks

Lecture: Johns Hopkins University

This is the second part of the high-order linear statistical learning model course. Those who already know about the regression model and want to seek further study on it must learn this course.

In this course, you will learn the basics of statistical modeling foundations, distribution results, and residual options for multivariate normal distribution. Before you start the next step, I need to clarify that you need to have a linear algebra basis, a multivariate calculus foundation, an understanding of statistics and regression models, familiarity with argument-based mathematics, and operational knowledge of the R language. This course will begin on January 23, 2017.

Prerequisite knowledge: linear algebra, calculus, statistics, and R language knowledge

**7. Math in sports**

Address: https://www.edx.org/course/math-sports-notredamex-mat150x

Course period: 8 weeks

Class: Notre Dame University (source edX)

I am a very curious person about how mathematics is used to trigger more insight into sports and everyday life.

I found this course, which shows how to use mathematics to analyze data and predict the trends and future performance of athletes and their teams in your favorite sports.

In this course, you will learn how inductive reasoning is used for mathematical analysis; how probability theory is used for data evaluation and assessment of risk and any event outcome.

All major team sports, athletics, and even extreme sports such as rock climbing are included in the course. This course is taught by a professor at the University of Notre Dame and is currently only open to students enrolled in the course.

Prerequisite knowledge: statistics and linear algebra

**Advanced mathematics and statistics**

Great, so far, you will be able to learn completely. You should have mastered some math and statistical skills, and you will have confidence in the next step of learning. Come on!

**1. Discrete Optimization (Discrete Optimization)**

Address: https://www.coursera.org/learn/discrete-optimization

Course period: 8 weeks

Class: University of Melbourne (source Coursera)

All industries and companies use optimization. Airlines use optimization to ensure a fixed turnaround time; e-commerce companies such as Amazon use optimization to achieve on-time delivery of goods. The application of optimization at the macro level includes the deployment of power for thousands of people, the development of new drugs, and so on.

This course gives you an opportunity to fully understand discrete optimization, and discrete optimization has been used in our daily lives. This course will first take you through the basics of discrete optimization and its different techniques. You will learn about constraints, linear and mixed integer programming. The final part of this course includes the most advanced high-level topics.

The prerequisite for learning this course is that you need to have good programming skills, an understanding of the underlying algorithms, and knowledge of linear algebra. This course will begin on January 16, 2017 and will be taught by a professor at the University of Melbourne.

Prerequisite knowledge: programming, algorithms, and linear algebra

**2. Statistics for Genomic Data Science**

Address: https://www.coursera.org/learn/statistical-genomics

Course period: 4 weeks

Lecture: Johns Hopkins University

If you are eager to be the next generation of data sequencing scientists, then you must study this course.

In this course, you will learn exploratory analysis; linear modeling; hypothesis testing and multiple hypothesis tracking testing; different types of data processing such as transcriptome sequencing (RNA-seq), genome-wide association studies (GWAS), staining Mass immunoprecipitation sequencing (ChIP-Seq) and DNA methylation (DNA Methylation) studies. This course is part of a special topic for genomic data scientists at Johns Hopkins University. The course will begin on January 16, 2017.

Prerequisite knowledge: high-order statistics and algorithms

**3. Biostatistics for Big Data Applications**

Address: https://www.edx.org/course/biostatistics-big-data-applications-utmbx-stat101x

Course period: 8 weeks

Class: University of Texas Medical School (source edX)

This course is an introduction to data analysis using biomedical big data.

In this course, you will learn the basic components of biometric methods. People unfamiliar with statistics can encounter different types of challenges when dealing with biomedical big data.

Learn how basic statistics are used in biomedical data types. You will learn the basics of R language programming in the course; how to create and interpret graphical summaries of data; and parametric and nonparametric inference statistics methods. You will gain experience in dealing with biomedical issues in the R language.

This course is open to students enrolled in the course.

Prerequisite knowledge: high-level statistics and R language knowledge

**to sum up**

I hope you find this article useful. So far, you have figured out the self-study field of study. If you have a mathematical background, you can take an advanced course. If not, start from the beginning and move forward step by step.

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