2.2 Environments

Environments works the same as in LateX, the main difference being how you signal the start and end of an environment.

A key bit of these lectures notes is that most environments have a coloured box around them. This help students identify the start and end of the relevant environment. At Bristol (if you have copied across our template), we default to the following colour scheme

2.2.1 Results like environments

Theorems, Propositions, Corollaries etc are within a blue box:

Proposition 2.1: (Fundamental Theorem of Lecture Notes)

Let \(X\) be the set of all colourings possible for lecture notes and \(Y\) denote the set of all lecturers. Let \(f\colon Y \to X\) be the function that associates to each lecturer their preference within \(X\). Then \(f\) is surjective but not injective.

Proof.

The non-injectivity follows from the pigeonhole principle. The other claim is folklore and so is clearly known by the experts within the field

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Theorem 2.2:

All of these environments are numbered by default. You can label an environment to refer to it later, see the code for this theorem.

Corollary 2.3: (Corollary of Theorem 2.2)

This corollary follows from Theorem 2.2. Note the use of a double backslash when doing a reference as part of a name.

Lemma 2.4:

Bookdown has been set up to understand the standard environments such as lemma, proposition, theorem, proof, corollary, remark and definition…

Algorithm:

However, we have also created a couple more environments such as Algorithm. These have a slightly different syntax to use. You can also create your own environment by modifying the ’_bookdown.yml file’ and (for pdf output) the ‘colourfulv2ClavertonDown.sty’ file.

2.2.2 Remark like environment

So to not overwhelm the document with colour, these ‘remark’-ish environments have only a coloured line on the side. They have an orange side.

Remark:

This is a remark

Note we do not use the standard Bookdown remark environment as otherwise it uses the colours associated to the proof environment.

Proof techniques:

A little environment to help students understand proofs. Unfortunately, because the word proof is found in the environment title, a little proof box is added at the end.

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2.2.3 Examples and exercises

Examples and exercises are in a green box.

Example:

Notice that by default all the ‘extra’ environments are unnumbered. However, the environment Remark, Exercise, Example and Algorithm can have individual numbering. This is done by adding a label to it.

Exercise:

Normally exercises are unnumbered, but by labelling the following exercise, it has been numbered, see Exercise 2.5.

Exercise 2.5:

Other environments can not be numbered, but this can be changed by editing the ’_bookdown.yml’ file and the ‘colourfulv2ClavertonDown.sty’ file.

Let Florian know if you want support with this.

2.2.4 Definition like

Definitions, notations etc are in a pink box

Definition 2.6:

Definitions, which are always numbered

Notation:

Notations, which are never numbered

2.2.5 Non-examinable notes of interest

These three environments with a purple side have been added.

History:

History notes

Etymology:

Etymological notes

Interest:

General notes of interest