1.1 How to use these notes

These notes are colour coded to help you identify the important bits.

Definition 1.1:

Definitions and Notations will be with this background colour. It is important to understand and know them to understand the course.

Theorem 1.2:

Results from the course, which will either be theorems, lemmas, propositions or corollaries, will have this background colour. It is important to know them so to be able to apply them to different situations.

Proof.

After most results, there will be a proof with this background colour. It is important to understand each proof as similar techniques can be applied in different mathematical situations. Note that many proofs are left as exercises so that one can practice coming up and writing proofs.

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Remark:

Remarks and proof techniques will have this background colour. They are statements that are note-worthy.

Example:

Examples will not have a background colour, however there is a line so that one can tell when an example starts and when it finishes. When possible, lectures and problem classes will have different examples from the notes. This is so that students can be showcased different examples.

Interest:

Interest, History and Etymological (origin of words) notes will not have a background colour, however there is a line to show the start and the end of the note. These notes are there for general interest and is not examinable content.

Most of the Etymology notes comes from the book “The words of Mathematics” by Steven Schwartzman (The Mathematical Association of America, 1994)

Most of the history of the development of Group Theory comes from the article “The Evolution of Group Theory: A Brief Survey” by Israel Kleiner (Mathematics Magazine, Vol 59, No 4, 192-215, 1986).