Welcome to Math 300! As its name suggests, this course will introduce you to the fundamental mathematical concepts and skills that you will need to study mathematics at a higher level than a typical introductory calculus and linear algebra sequence. We will emphasise both problem-solving and proof-writing skills, including typesetting mathematics using LaTeX.

Most administrative aspects of the course will be handled using Canvas.

**Time and place.** Class meets Mo(Tu)WeFr 9:00–9:50am in Lunt Hall 103.

**Syllabus.** You can download the course syllabus here.

**Textbook.** Our textbook will be my book-in-progress, *An infinite descent into pure mathematics*, which can be downloaded for free here.

**Homework.** Homework assignments will be due at the beginning of class on Wednesdays—they can be downloaded from Canvas.

**Examinations.** There will be a midterm exam and a final exam.

**Midterm.**During class on Wednesday 13th February 2019.**Final.**9:00–11:00am on Monday 18th March 2019.

**Handouts.** What follows are the handouts from class and solutions to exercises.

- Propositions, sets and divisibility — handout — solutions
- Rational numbers, assumptions and goals — handout — solutions
- Logical operators — handout — solutions
- Variables and quantifiers — handout — solutions
- Truth tables and logical equivalence — handout — solutions
- LaTeX practical #1 — tex source — pdf output
- Negation and de Morgan's laws — handout — solutions
- Sets and set operations — handout — solutions
- Power sets, products and indexed intersections — handout — solutions
- Functions and sequences — handout — solutions
- Images and preimages — handout — solutions
- Injections, surjections and bijections I — handout — solutions
- Injections, surjections and bijections II — handout — solutions
- Definition by recursion and proof by weak induction — handout — solutions
- Proof by strong induction — handout — solutions
- LaTeX practical #2 — tex source — pdf output
- Finite sets — handout — solutions
- Counting principles I — handout — solutions
- Counting principles II — handout — solutions
- Countable sets I — handout — solutions
- Countable sets II — handout — solutions
- Relations — handout — solutions
- Equivalence relations — handout — solutions
- Discrete probability spaces — handout — solutions
- Conditional probability — handout — solutions
- Discrete random variables — handout — solutions

The following calendar contains important dates related to Math 300, as well as the times and locations of my classes, discussions and office hours.