Gilbert Strang, the professor who taught MIT’s classic linear algebra course, is 86 years old. His books have been selected as textbooks by Tsinghua University and his courses have attracted a large number of students from home and abroad. Now, with the outbreak of COVID-19, he has recorded a new course in front of a camera alone, with videos, PPT and transcripts uploaded.

Heart of Machine reporting, participating: Qian Zhang, Jamin, Raccon X.

Whether you’ve studied Linear Algebra in school, YouTube, YouTube, or elsewhere, you’re familiar with Gilbert Strang at MIT.




Last year, Tsinghua caused a stir when it moved its “Linear Algebra” textbook into English, using “Introduction to Linear Algebra” by Gilbert Strang.

Strang’s linear Algebra MIT 18.06 course has been viewed more than 600,000 times (just one source’s statistics) on B, making it the most popular English Linear Algebra course on B. It’s also one of the most popular courses at MIT. According to the OCW website, the course has received more than 10 million visits since it was first published in 2002.

Why are his textbooks and courses so popular? From the discussion on various platforms, we can summarize the following key words:




1, practical, moderate difficulty.Zhihu has a post devoted to Gilbert Strang’s Linear Algebra textbook, Introduction to Linear Algebra. “Strang’s materials are more practical, with moderate difficulty and focus on developing mathematical intuition from practical problems, which is suitable for engineering students,” said one.


This point is relative to the common faults of some teaching materials in China. The textbook that we are usually exposed to gives the definition first, then theorems and proofs, which can easily turn off non-mathematics students.


But a Strang professor teaching materials “to tell you some interesting mathematical facts first, then tell you how can we solve the problem of relatively simple, some methods and even rely on experiment, and mathematics intuition), to explore together with you so why to solve, if there is a theoretical foundation, have some problem so that you can try it for yourself is really about, And then you do some more digging, and you refine it into a theorem.” (Quoted from zhihu user @Li Jiafan)


2. Make the abstract concrete.“Linear algebra” is really a very abstract course for those who are not well versed in math. However, from the evaluation of Professor Strang’s linear Algebra, the consensus is that it is “not very abstract” and can even be “connected with high school”.


Professor Strang will insert a lot of examples into his linear algebra lectures to help students understand some abstract concepts. He is very friendly to students who are not math majors. Some students said, “I feel that many concepts are no longer memorized by rote.”

In addition, the logic of the course is instructive, “not telling you that this is the right thing to do, but guiding you step by step to understand that this is the way it should be.”




What is the origin of this professor who gives such a good lecture?


Professor Strang was born in Chicago in 1934, received his PhD from the University of California, Los Angeles, and has been a mathematics professor at THE Massachusetts Institute of Technology since 1962. He also published a new book, Linear Algebra and Learning from Data, early last year.


Professor Strang has been dedicated to mathematics education, and is constantly developing new insights into key mathematical subjects, such as the new textbook Calculus Equations and Linear Algebra, published in 2014. In 2016, this textbook was developed into a series of 55 lectures supported by MathWorks, including a video by MATLAB founder Professor Cleve Moler on numerical solutions, which is worth checking out. Resources can be found on the MathWorks website.


On the other hand, Professor Strang launched a new undergraduate course at MIT in 2017, Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, which was published on the OCW platform in 2019 and is currently available on SITE B. The course was very well received and focused on using linear algebra to understand and build machine learning algorithms, particularly for deep learning and neural networks. This course is also very friendly for beginners, with a systematic multi-dimensional introduction to deep learning through a review of linear algebra, probability, statistics, and optimization.




The 2020 syllabus


The original 2011 classic, designed for self-learners and posted on MIT’s OCW platform, contains 35 lecture videos and 36 ta videos. Interested readers can read it in combination.


Here’s a look at the syllabus for this new course:


Introduction: New ways to understand linear algebra


In his introduction, Strang stated that his goal of this course was to introduce you to the concept of singular values, which are particularly important in linear algebra. He decomposed the matrix into two or three parts so that we could understand its properties more deeply.

The column space of a matrix and the basis of a vector space




Professor Strang takes us into the world of linear algebra, starting with the column space of matrices.




We also looked at the basis for column space and row space:




Big Picture in linear algebra


In this section, Professor Strang explains the row space, column space, null space of A, the null space of A^T, and the relationship between these four subspaces.




Orthogonal vector


In this section, Professor Strang discusses orthogonal vectors, orthogonal matrices and their subspaces, which cover Gram-Schmidt orthogonalization and least squares.






Eigenvalues and eigenvectors


Eigenvalues and eigenvectors are one of the important ways to understand the properties of matrices and they have many important applications in engineering and research fields.




Singular values and singular vectors




In machine learning, data matrices are not square matrices, so they require a different approach than eigenvalues: singular value decomposition (SVD). Singular value decomposition represents each matrix with singular values and vectors.




Finally, it should be noted that in addition to videos and PPT, each class of this course has a corresponding transcript for reference, which can be said to be very friendly to students with poor English hearing.


Courses address: https://ocw.mit.edu/resources/res-18-010-a-2020-vision-of-linear-algebra-spring-2020/index.htm