Data science is an interdisciplinary field that uses techniques and theories drawn from many fields within the context of mathematics, statistics, and computer science. Mathematical and statistical foundations of machine learning and data analysis are essential to grasp fundamental principles applicable to data manipulation and model fitting. Understanding these principles can facilitate creating new data-driven solutions, understanding existing approaches, exploring data insights, and detecting statistical behaviors of data. Besides, it can aid in the development of novel machine learning solutions, the comprehension and debugging of existing systems, and learning about the basic assumptions and limitations of the procedures we employ. Mathematics and statistics can be found in almost all aspects of data science, including data collection, data cleaning, data relationship, data analysis, and modeling.

TechClass Essential Math and Statistics for Data Science online course will introduce you to the main pillars of mathematics and statistics essentials for data science, including linear algebra, calculus, descriptive statistics, distributions, and probability. Our approach in this course is to help you comprehend the core ideas through a large number of interesting examples. By the end of this course, you will be familiar with the mathematical and statistical foundation of data science as your very first steps on the journey to the data science world.

#### Learning outcomes

- Get familiar with the basics and the intuitions of calculus, especially the role of functions in mathematics and how they work and can be constructed
- Learn how to calculate a function’s derivative and find the extremum points
- Get familiar with the basics and the intuitions of linear algebra and the concepts of vector and matrix, and vector/matrix arithmetic operations
- Get familiar with the basics and the intuitions of analytic geometry
- Learn the concepts of inner product and norms, and how to compute the inner product and calculate the norm of a vector
- Get familiar with different types of data and measures
- Get familiar with descriptive statistics and how they can be extracted from data
- Understand the intuition behind non-linear relationships between variables
- Understand the intuitions of probability, probabilistic experiments, random variables, and distributions
- Get familiar with the general framework of probability distributions and some popular distributions

#### Table of contents

**Chapter 1: Intro to Course **

- 1.1. Welcome!

- 1.2. About TechClass Data Science Department

- 1.3. Learning Outcomes

- 1.4. Your Expectations, Goals, and Knowledge

- 1.5. Abbreviations

- 1.6. Copyright Notice

**Chapter 2: Introduction**

- 2.1. What is Data Science?
- 2.2. Essential Math for Data Science
- 2.3. Essential Statistics for Data Science

**Chapter 3: Calculus**

- 3.1. What is a Function?
- 3.2. Some Special Functions
- 3.3. Derivative
- 3.4. Find Derivative of Functions
- 3.5. Increasing and Decreasing Functions
- 3.6. Extermums
- 3.7. Multivariable Functions
- 3.8. Partial Derivatives and Extremums
- 3.9. Quiz

**Chapter 4: Linear Algebra**

- 4.1. Introduction
- 4.2. Vectors
- 4.3. Vectors: Notation
- 4.4. Vectors: Magnitude and Direction
- 4.5. Vectors: Multiply with Scalars
- 4.6. Vectors: Addition
- 4.7. Vectors: Higher Dimensional
- 4.8. Matrix
- 4.9. Matrix Dimension
- 4.10. Matrix and Vector Multiplication
- 4.11. Some Well-Known Matrices
- 4.12. Matrix by Scalar Multiplication4.13. Matrix Addition
- 4.14. Matrix by Matrix Multiplication

**Chapter 5: More Topics on Linear Algebra**

- 5.1. Linear Combination
- 5.2. Linear Dependency
- 5.3. Subspaces
- 5.4. Special Subspaces
- 5.5. Quiz

**Chapter 6: Analytic Geometry**

- 6.1. Introduction
- 6.2. Norm
- 6.3. Inner Product
- 6.4. Distance Function
- 6.5. Quiz

**Chapter 7: Descriptive Statistics**

- 7.1. Population and Sample
- 7.2. Types of Data
- 7.3. Measures of Central Tendency
- 7.4. Variance and Standard Deviation
- 7.5. Covariance
- 7.6. Correlation
- 7.7. Covariance Matrix
- 7.8. Quiz

**Chapter 8: Basics of Probability**

- 8.1. Introduction
- 8.2. Properties of Sets
- 8.3. Probabilistic Experiment
- 8.4. Probability of an Event
- 8.5. Properties of Probability Functions
- 8.6. Conditional Probability
- 8.7. Quiz

**Chapter 9: Probability Distributions**

- 9.1. Introduction
- 9.2. Random Variable
- 9.3. Discrete and Continuous Random Variables
- 9.4. Discrete Probability
- 9.5. Continuous Probability
- 9.6. Expected Values
- 9.7. Normal Distribution
- 9.8. Some other types of Distributions
- 9.9. Quiz

**Chapter 10: Final Tasks**

- 10.1. Project
- 10.2. Self-study Essay

**Chapter 11: Finishing the Course**

- 11.1. What We Have Learned
- 11.2. Where to Go Next?
- 11.3. Your Opinion Matters
- 11.4. Congrats! You did it!

#### Brochure