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### Foundations of Higher Mathematics (Math 300) — Winter 2019

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.

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.

1. Propositions, sets and divisibility — handoutsolutions
2. Rational numbers, assumptions and goals — handoutsolutions
3. Logical operators — handoutsolutions
4. Variables and quantifiers — handoutsolutions
5. Truth tables and logical equivalence — handoutsolutions
6. LaTeX practical #1 — tex sourcepdf output
7. Negation and de Morgan's laws — handoutsolutions
8. Sets and set operations — handoutsolutions
9. Power sets, products and indexed intersections — handoutsolutions
10. Functions and sequences — handoutsolutions
11. Images and preimages — handoutsolutions
12. Injections, surjections and bijections I — handoutsolutions
13. Injections, surjections and bijections II — handoutsolutions
14. Definition by recursion and proof by weak induction — handoutsolutions
15. Proof by strong induction — handoutsolutions
16. LaTeX practical #2 — tex sourcepdf output
17. Finite sets — handoutsolutions
18. Counting principles I — handoutsolutions
19. Counting principles II — handoutsolutions
20. Countable sets I — handoutsolutions
21. Countable sets II — handoutsolutions
22. Relations — handoutsolutions
23. Equivalence relations — handoutsolutions
24. Discrete probability spaces — handoutsolutions
25. Conditional probability — handoutsolutions
26. Discrete random variables — handoutsolutions

### Course calendar

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