Mathematics and Statistics Essentials for Data Science (5 credits)


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Mathematical and statistical foundations of machine learning and data science are essential to understand 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. This course will introduce the student 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 students understand the fundamental concepts using interesting examples.

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: Beginning with This Course

  • 1.1. Our Approach in This Course
  • 1.2. About TechClass AI Department
  • 1.3. Your Expectations, Goals, and Knowledge

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. Test Yourself

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. Test Yourself

Chapter 6: Analytic Geometry

  • 6.1. Introduction
  • 6.2. Norm
  • 6.3. Inner Product
  • 6.4. Distance Function
  • 6.5. Test Yourself

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. Test Yourself

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. Test Yourself

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. Test Yourself

Chapter 10: Final Tasks

  • 10.1. Project
  • 10.2. Self-study Essay
  • 10.3. Congrats! You did it!

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