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In this video, Gilbert Strang discusses linear algebra, its importance, and how it is superior to calculus in terms of teaching and understanding. He also shares advice on how to be a successful teacher, emphasizing the importance of having a passion for learning and connecting with students.

**00:00:00**Gilbert Strang is a famous and impactful mathematics teacher at MIT who has taught linear algebra through his MIT OpenCourseWare lectures. He discusses how his videos on linear algebra have impacted students and how important linear algebra has become in recent years. He also discusses how his experience as a teacher has helped him organize and teach the subject effectively.**00:05:00**This lecture introduces the student to the four fundamental subspaces of linear algebra: the matrix, vector space, subspace, and span. Gilbert Strang outlines the various properties of these spaces and explains how they can be used in linear algebra.**00:10:00**Gilbert Strang discusses linear algebra, its origins, and its importance in mathematics. He also compares and contrasts it with calculus, which he feels is easier to understand. He finishes the video by encouraging students to learn linear algebra early in their education so they can understand complex concepts in two dimensions.**00:15:00**In this video, Gilbert Strang discusses linear algebra and its beauty. He goes on to say that, as a mathematician, he is constantly pushing his colleagues to learn this subject. He also mentions that singular values are a way to break down a matrix into its important pieces. Finally, he talks about how viewers can connect with mathematics by consuming a few videos on the topic.**00:20:00**Gilbert Strang discusses the usefulness of math in both the real world and in teaching. He talks about how math reveals truths that are often hidden in the real world, and how it can be a tool for both artists and engineers. He also discusses the importance of examples in teaching.**00:25:00**Gilbert Strang talks about his experiences as President of the Society for Industrial Applied Mathematics, and how it was important for math to get some attention in Washington during the early 2000s. He also talks about his experience with deep learning, and how it can be used to understand data.**00:30:00**Gilbert Strang, a professor at MIT, discusses the importance of linear algebra and neural networks in his teaching. He explains that linear algebra is a big part of defining a rule that will take training inputs to known outputs, and that neural networks are a powerful tool for doing this. He also notes that neural networks are limited in terms of their passivity, and that they have a lot of expressive power.**00:35:00**Gilbert Strang discusses how data is simply tensor vectors and matrices, how learning from data is useful, and how the linear algebra field sits within the larger scope of mathematics. He also mentions that there are different subfields within linear algebra, and that his own view is that math is best thought of as a spectrum of different fields.**00:40:00**Gilbert Strang discusses the importance of linear algebra and its superiority over calculus in terms of teaching and understanding. He also says that he is not a good teacher, as he does not enjoy grading exams. However, he does believe in the importance of teaching and does enjoy the teaching process.**00:45:00**Gilbert Strang shares advice on how to be a successful teacher, emphasizing the importance of having a passion for learning and connecting with students. He also discusses the importance of studying material thoroughly, and of having fun while learning.

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