Course Title:
Linear Algebra from Elementary to Advanced Specialization
Course Description:
This comprehensive course on Linear Algebra is designed to guide students from foundational concepts all the way to advanced techniques, providing a deep understanding of both theoretical and computational aspects of linear algebra. The course is structured into three key modules that build upon each other progressively, from elementary principles to advanced applications.
Course instructional level:
Advance
Course Duration:
6 Month
Hours: 45 Hrs
Course coordinator:
Dr. Pratik Lepse
Course coordinator's profile(s):
Course Contents:
| Module/Topic name | Sub-topic | Duration |
| 1. Linear Algebra: Linear Systems and Matrix Equations | 1. Introduction to Matrices | |
| 2. Vector and Matrix | ||
| 3. Linear Transformations | ||
| 4. Final Assessment | ||
| 2. Linear Algebra: Matrix Algebra, Determinants, & Eigenvectors | 1. Matrix algebra | |
| 2. Subspaces | ||
| 3. Determinants | ||
| 4. Eigenvectors and Eigenvalues | ||
| 5. Diagonalizaion and linear Transformations | ||
| 6. Final Assessment | ||
| 3. Linear Algebra: Orthogonality and Diagonalization | 1. Orthogonality | |
| 2. Orthogonal projections and least Squares Problem | ||
| 3. Symmetric Matrices and Quadratic Forms | ||
| 4. Final Assessment |
Course Outcomes:
This specialization is a three course sequence that will cover the main topics of undergraduate linear algebra. Defined simply, linear algebra is a branch of mathematics that studies vectors, matrices, lines and the areas and spaces they create. These concepts are foundational to almost every industry and discipline, giving linear algebra the informal name "The Theory of Everything".
This specialization assumes no prior knowledge of linear algebra and requires no calculus or similar courses as a prerequisite. The first course starts with the study of linear equations and matrices. Matrices and their properties, such as the determinant and eigenvalues are covered. The specialization ends with the theory of symmetric matrices and quadratic forms. Theory, applications, and examples are presented throughout the course. Examples and pictures are provided in low dimensions before abstracting to higher dimensions. An equal emphasis is placed on both algebraic manipulation as well as geometric understanding of the concepts of linear algebra. Upon completion of this specialization, students will be prepared for advanced topics in data science, AI, machine learning, finance, mathematics, computer science, or economics.
Applied Learning Project Learners will have the opportunity to complete special projects in the course. Projects include exploration of advanced topics in mathematics and their relevant applications. Project topics include Markov Chains, the Google PageRank matrix, and recursion removal using eigenvalues.