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What is the right logical unit for a textbook?
Image generated by AI.
Most textbooks are divided into chapters, many of which can take several class periods to cover.
Other textbooks are divided into lectures, each of which can be covered in a single class period, anywhere from 50 to 110 minutes.
A textbook could also be divided into micro-lectures or a series of connected blog posts. This is an idea I’ve kicked around, but haven’t figured out yet.
Any way, chapters can be too imposing while micro-lectures may require too much prior knowledge of the subject. I believe lectures are the sweet spot for the logical units of a textbook.
An example of the lecture textbook format is Numerical Linear Algebra by Trefethen and Bau.
Trefethen and Bau, Numerical Linear Algebra, 1997.
This book is very good and to the point, covering many topics relevant to structural analysis, such as:
- Lecture 1 - Matrix-Vector Multiplication
- Lecture 2 - Orthogonal Vectors and Matrices
- Lecture 3 - Norms
- Lecture 12 - Conditioning and Condition Numbers
- Lecture 13 - Floating Point Arithmetic
- Lecture 20 - Gaussian Elimination
- Lecture 21 - Pivoting
- Lecture 22 - Stability of Gaussian Elimination
- Lecture 24 - Eigenvalue Problems
- Lecture 27 - Rayleigh Quotient
- Lecture 32 - Overview of Iterative Methods (for solving Ax=b)
A 25th anniversary edition of the book was published in 2022. Anniversary editions are usually reserved for great albums like OK Computer, so you know the book is worth reading!