Why Traditional Linear Algebra Textbooks Fail and How MIT’s Strang Course Helps

Why Traditional Linear Algebra Textbooks Fail Students

Linear algebra appears in everything from structural mechanics to facial‑recognition algorithms, and a weak grasp of the subject can be disastrous for engineering and AI professionals. The standard Chinese textbook, the Tongji edition, is notorious for its confusing structure, abstract explanations, and scarce visual aids, leaving many students disinterested and fearful of the subject.

Student Complaints About the Tongji Edition

Common criticisms include:

Unreasonable chapter order – the book starts with determinants before introducing basic linear concepts.

Early introduction of inverse‑order numbers.

Matrix theory is taught before vectors.

Linear spaces are relegated to optional sections.

Overall abstract content with very few diagrams (only three vector illustrations in the entire book).

Students also note that many concepts are introduced without concrete examples, making it hard to see their practical relevance.

Alternative Approaches and MIT’s Strang Course

Some argue that every textbook serves a specific audience, but many students seek a more intuitive learning path. Tsinghua University recently switched its linear‑algebra curriculum to MIT professor Gilbert Strang’s English textbook, "Introduction to Linear Algebra," which has gained popularity for several reasons:

Practical focus with moderate difficulty, emphasizing real‑world applications.

Concrete examples that turn abstract concepts into understandable material, often linking to high‑school knowledge.

Step‑by‑step logical progression that guides students to discover why methods work rather than merely presenting formulas.

Strang’s 27‑hour video series (MIT 18.06) on Bilibili has amassed over 730,000 views, and the course has attracted millions of visitors worldwide since its launch in 2002.

Strang, born in 1934, earned his Ph.D. at UCLA and has taught at MIT since 1962. He recently published "Linear Algebra and Learning from Data" and, during the COVID‑19 pandemic, updated his video lectures for remote learners.

For those who prefer Chinese resources, alternatives such as the "High‑Level Algebra Concise Tutorial" and "Brief Linear Algebra" are also recommended.