# Lecture notes

I am moving my collection of lecture notes here. At present there is the following.

### St Andrews Notes on Advanced Combinatorics

• Part 1: The art of counting
• Part 2: Structure, symmetry and polynomials
• Part 3: Finite geometry and strongly regular graphs

### 4 Responses to Lecture notes

1. peterisdaugulis says:

Notes on linear algebra are very nice. Even notations, especially the coordinate vector notation [v]_B.

Here are some ideas and suggestions for linear algebra teaching. May not be original but I have not seen then widely used.

1) Promote the following computational technique for matrix multiplication: move the second matrix upwards so that its bottom left corner coincides with the top right corner of the first matrix, each entry of the product is a dot product which is easy to see and compute.

2) Define determinant using multiplicativity as the basic axiom. First define it for elementary matrices and 0 for noninvertible ones. The multiplicativity axiom seems well motivated.

3) Promote actively the functional graph analogue for linear mappings.

4) One should consider writing superscripts denoting operations to the left from the object e.g. ^{T}A not A^{T}

5) use indefinite integration k[X]->k[X]/ as an example of quotient space usage.

2. a.uzjthr says:

3. Ana Paula de Mello says: