Linear Algebra

Is this course completely free, including all materials?

Yes, absolutely everything is free through MIT OpenCourseWare. You get complete access to all 35 video lectures by Professor Strang, problem sets with detailed solutions, exams with solutions, lecture summary notes, and links to MATLAB resources. The only material that isn’t free is Professor Strang’s textbook “Introduction to Linear Algebra,” which you can purchase separately, though many students successfully complete the course using just the free online materials and the lecture notes. MIT OpenCourseWare’s mission is to freely share knowledge with learners worldwide, so there are no hidden costs or paywalls.

What mathematical background do I need before starting?

You should have a solid foundation in high school algebra and be comfortable with basic mathematical concepts. The course is designed for MIT undergraduates, so it assumes mathematical maturity but doesn’t require prior linear algebra knowledge. Some familiarity with calculus is helpful, particularly for later lectures that touch on differential equations, though it’s not strictly necessary for understanding the core linear algebra concepts. If you’ve taken high school math through pre-calculus and are willing to work through challenging material, you can succeed in this course.

What topics are covered in the course?

The course provides comprehensive coverage starting with the geometry of linear equations and matrix operations, then progressing to vector spaces, the four fundamental subspaces, orthogonality, determinants, eigenvalues and eigenvectors, and positive definite matrices. You’ll learn practical applications including solving systems of equations, least-squares approximations, the Gram-Schmidt process, singular value decomposition, linear transformations, and connections to differential equations, Fourier transforms, and Markov processes. The course balances rigorous mathematical theory with real-world applications across science, engineering, economics, and computer science, including foundations for machine learning and data science.

How long does it take to complete this course?

The 35 video lectures range from 40-50 minutes each, totaling approximately 30 hours of video content. However, your actual completion time depends on how thoroughly you engage with the material. If you watch lectures, work through problem sets, and study the solutions, expect to invest 6-12 weeks at 10 hours per week for a comprehensive understanding. Many learners spread this over several months, revisiting challenging concepts and practicing problems extensively. The self-paced format allows you to adjust the timeline to your schedule and learning needs.

What makes Professor Strang’s teaching style special?

Professor Gilbert Strang is renowned for making complex mathematical concepts accessible and even beautiful. His teaching approach involves thinking out loud, working through problems step-by-step from a student’s perspective, and showing genuine enthusiasm for mathematical discoveries. He uses clear examples, geometric intuition, and practical applications to illuminate abstract concepts, making linear algebra feel natural rather than intimidating. His humble demeanor, sense of humor, and obvious love for mathematics are infectious, transforming what could be dry theory into engaging learning. After 63 years of teaching at MIT, his final lecture in May 2023 received a standing ovation and has nearly 2 million views.

Will I receive a certificate for completing this course?

No, MIT OpenCourseWare does not issue certificates of completion. OCW is designed as a free educational resource for self-learners worldwide, not as a credentialing program. However, the knowledge and skills you gain are equivalent to what MIT students learn in this course, which is highly respected in academic and professional circles. You can build a portfolio of solved problem sets and projects to demonstrate your linear algebra proficiency. If you want formal credentials, you’d need to enroll as a paying student at MIT or another institution offering the course for credit.

How does this course prepare me for machine learning and data science?

Linear algebra is the mathematical foundation underlying most machine learning and data science techniques. This course teaches you the essential concepts that power modern AI, including vector spaces for representing data, matrix operations for transformations, eigenvalues and eigenvectors for dimensionality reduction techniques like PCA, singular value decomposition for recommendation systems, and least-squares methods for regression. Professor Strang explicitly connects theoretical concepts to practical applications, helping you understand not just how algorithms work but why they work. Numerous data scientists and machine learning engineers credit this course with providing the mathematical intuition necessary for advanced work in the field, making it an invaluable preparation for anyone pursuing careers in AI, data science, or quantitative fields.