Linear Algebra for Applications
Master the fundamental concepts of linear algebra with our advanced 50-hour course. Perfect for computer science, engineering, and data science students who need a solid understanding of vectors, matrices, and linear transformations.
What You'll Learn:
- Vector spaces and subspaces
- Matrix operations and properties
- Linear transformations
- Eigenvalues and eigenvectors
- Orthogonality and projections
- Singular value decomposition
- Applications in machine learning
- Computational techniques
Course Overview
Linear algebra is the foundation of modern applied mathematics. From computer graphics to machine learning, from quantum mechanics to economics, linear algebra provides the mathematical framework for understanding and solving complex problems.
This 50-hour advanced course is specifically designed for students and professionals in technical fields. We focus not just on the theoretical foundations but also on practical applications and computational methods. You'll learn how linear algebra is used in data science, machine learning algorithms, computer graphics, and engineering systems.
The course includes extensive computational exercises using real-world datasets, visualization tools to help understand abstract concepts, and projects that demonstrate practical applications of linear algebra in various fields.
Course Curriculum
Module 1: Vectors and Spaces
- Vector operations
- Linear combinations
- Vector spaces and subspaces
- Basis and dimension
Module 2: Matrices
- Matrix operations
- Matrix algebra
- Inverse matrices
- Determinants
Module 3: Linear Transformations
- Definition and properties
- Matrix representations
- Change of basis
- Kernel and range
Module 4: Advanced Topics
- Eigenvalues and eigenvectors
- Diagonalization
- Orthogonality
- SVD and applications
Your Instructor
Professor Jennifer Wang is a leading expert in applied mathematics with a Ph.D. from Stanford University. She has over 12 years of experience teaching linear algebra to engineering and computer science students and has published numerous papers on computational methods in linear algebra.
Professor Wang's research focuses on the applications of linear algebra in machine learning and data science. Her teaching approach emphasizes both theoretical understanding and practical implementation, preparing students for real-world applications in technology and research.