# 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

### 6 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:

Dear Professor Cameron,

I’m trying to learn mathematics on my own and this material is great.
Thank you very much!

4. ENOCH SULEIMAN says:

It was really helpful to me. Thank you Prof Peter Cameron, God bless you abundantly.

5. pgeerkens says:

Dear Professor Cameron,

Thank you for posting this material; in particular the Number Theory link above. I’ve been looking for a while for a good intro to Algebraic Number Theory and this material fits the bill exactly.

I have a question on the proof at the end of Section 3.1, on the uniqueness of the continued fraction representation. At the bottom of page 20, the observation that the fraction
1 / [b1;b2,…,bm]
is less than 1 because the denominator is greater than 1 is certainly correct; however it seems to me that the pertinent observation, to generate the contradiction, is that the fraction is greater than 0 because the denominator is finite. Have I missed something here?

Looking forward to the rest of the material.

Sincerely,

P. Geerkens

This site uses Akismet to reduce spam. Learn how your comment data is processed.