Are you interested in Data Science but lack the math background for it? Has math always been a tough subject that you tend to avoid? This course will teach you the most fundamental Linear Algebra that you will need for a career in Data Science without a ton of unnecessary proofs and concepts that you may never use. Consider this an expressway to Data Science with approachable methods and friendly concepts that will guide you to truly understanding the most important ideas in Linear Algebra.
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This course is designed to prepare learners to successfully complete Statistical Modeling for Data Science Application, which is part of CU Boulder's Master of Science in Data Science (MS-DS) program.
What You Will Learn
- Solve real-world problems using the foundational concept of matrices and explain where those problems might arise.
- Recognize what a matrix represents in n-dimensional space and how transformations act in that space
- Identify key properties of any system of equations, such as independence, basis, rank, and more, and what they mean for the overall system.
- Demonstrate your understanding of projections in lower dimensions, while being able to carry out higher dimension projections for real-world problems
Syllabus
WEEK 1
Linear Systems and Gaussian Elimination
In this module we will learn what a matrix is and what it represents. We will explore how a system of linear equations can be expressed in a neat package via matrices. Lastly, we will delve into coordinate systems and provide visualizations to help you understand matrices in a more well-rounded way.
WEEK 2
Matrix Algebra
In this module we will learn how to solve a linear system of equations with matrix algebra.
WEEK 3
Properties of a Linear System
In this module we will explore concepts and properties of linear systems. This includes independence, basis, rank, row space, column space, and much more.
WEEK 4
Determinant and Eigens
In this module we will discuss projections and how they work. We will build on a foundation using 2-dimensional projections and explore the concept in higher dimensions over time.
WEEK 5
Projections and Least Squares
In this module we will learn how to compute the determinant of a matrix. Afterwards, Eigenvalues and Eigenvectors will be covered.
