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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.

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.

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.