Linear Algebra

Overview

Learn the beautiful mathematical language that underpins all modern computing including data science and artificial intelligence, as well as applied sciences, engineering and economics.

Course Details

This course provides an in-depth introduction to Linear Algebra - the fundamental mathematical language that underpins all data science and artificial intelligence, as well as wider sciences, engineering and economics. Complimented by examples written using the Python NumPy library, this course explores in detail the major topics in Linear Algebra including systems of linear equations, vectors, matrices, vector spaces, determinants, eigenvectors and eigenvalues, linear transformations and the application of Linear Algebra to statistics and statistical learning. This course is a fundamental pre-requisite in order to understand how data science and applied statistical learning, machine learning and deep learning models work beyond simple deployment and implementation of black box models, and enables entry-level and junior-grade data scientists to make the significant leap to becoming a senior-grade data scientist. The curriculum of this course is equivalent to the syllabus of a typical 1st year mathematics undergraduate course in Linear Algebra, and includes critical techniques for mathematically proving mathematical statements in order to understand why things work as opposed to only how.

Course Modules

• 1. Introduction to Linear Algebra
• 2. Vectors and Matrices
• 3. Solving Linear Equations
• 4. Vector Spaces and Subspaces
• 5. Mathematical Proofs
• 6. Linear Algebra Proofs
• 7. General Vector Spaces
• 8. Inner Product Spaces
• 9. Determinants
• 10. Eigenvectors and Eigenvalues
• 11. Linear Transformations
• 12. Singular Value Decomposition
• 13. Applications of Linear Algebra

Requirements

• Introduction to Python or equivalent.
• GCSE-level Mathematics or equivalent.

Outcomes

• Knowledge of the major topics in Linear Algebra equivalent to a 1st year mathematics undergraduate.
• Applied experience of using Python 3 and NumPy for Linear Algebra operations.
• Applied experience of proving mathematical statements, thus gaining the critical ability to think logically and gain a much deeper understanding of mathematical concepts as opposed to just learning by rote and following rules.
• Knowledge of how Linear Algebra is applied to probability and statistics, and thus how it underpins all data science models that utilise statistical learning and machine learning techniques.
• Foundational mathematical knowledge required to understand how statistical learning, machine learning and deep learning models work beyond simple deployment and implementation of black box models.