| A | B | C | D | E | F | G | ||
|---|---|---|---|---|---|---|---|---|
1 | Date. Purple means past | Time | Lecture Number | Topic | Lecture Notes Sections | ICA | Assignment due dates | |
2 | Wed, Sep 7 | 9:30-10:20 | Lecture 1 | Intro to the course. Statements, compound statements, negation. | 1.1, 1.2, 1.3 | |||
3 | Fri, Sep 9 | 9:30-10:20 | Lecture 2 | Truth tables, tautologies, contradiction | 1.4, 1.5 | lCA 1, start of class | ||
4 | Tue, Sep 13 | 9:30-10:20 | Lecture 3 | Logical equivalence. Logical implication. Converse and contrapositive. Necessary and sufficient. | 1.6, 1.11, 1.7 | ICA 2, truth tables | ||
5 | Wed, Sep 14 | 9:30-10:20 | Lecture 4 | Laws of logic and other Known LEs. | 1.9 | |||
6 | Fri, Sep 16 | 9:30-10:20 | Lecture 5 | Every logical statement can be expressed with just ∧, ∨ and ¬. Valid arguments and inference rules. Proof by contradiction. | 1.10, 1.12 | |||
7 | Tue, Sep 20 | 9:30-10:20 | Lecture 6, Quiz 1 | More valid arguments, proof by cases. Quiz 1 at end of class. | 1.12, 1.13 | |||
8 | Tue, Sep 20 | Last day to drop courses and get a 100% fee refund | ||||||
9 | Wed, Sep 21 | 9:30-10:20 | Lecture 7 | Open statements, quantifiers. Negating statements involving quantifiers. | 2.1, 2.2, 2.3 | ICA 3 (valid arguments and counterexamples; they will find this hard) | ||
10 | Fri, Sep 23 | 9:30-10:20 | Lecture 8 | Math & Stats Assistance Centre Announcement. Examples of proofs. | 2.4 | |||
11 | Fri, Sep 23 | Last day to add courses | ||||||
12 | Tue, Sep 27 | 9:30-10:20 | Lecture 9 | Examples of proofs, continued. Introduction to sets. | 2.4, 3.1 | ICA 4, quantifiers | Assignment 1 | |
13 | Wed, Sep 28 | 9:30-10:20 | Lecture 10 | Set membership and set equality. The empty set, special sets. Subsets | 3.1, 3.2, 3.4, 3.5, 3.3, 3.6, 3.7 | ICA 5 (a proof) | ||
14 | Fri, Sep 30 | National Day for Truth and Reconciliation (no classes) | ||||||
15 | Tue, Oct 4 | 9:30-10:20 | Lecture 11, Quiz 2 | Set operations, complements and the laws of set theory. Quiz 2 at end of class. | 3.10, 3.11 | |||
16 | Wed, Oct 5 | 9:30-10:20 | Lecture 12 | Proofs involving sets. | 3.10, 3.11, 3.8 | |||
17 | Fri, Oct 7 | 9:30-10:20 | Lecture 13 | The power set. Set proofs involving subsets. | 3.11, 3.1 | ICA 6 (Jeopardy, end of class) | ||
18 | Tue, Oct 11 | Last day to drop classes and get a 50% refund | ||||||
19 | Tue, Oct 11 | 9:30-10:20 | Lecture 14 | Counting sets and subsets. Venn diagrams. | 3.13, 3.9, 3.12 | Assignment 2 | ||
20 | Wed, Oct 12 | 9:30-10:20 | Lecture 15 | Inclusion-exclusion. Inclusion-exclusion examples. | 3.12, 3.14, | ICA 7 (power set) | ||
21 | Fri, Oct 14 | 9:30-10:20 | Lecture 16 | More inclusion-exclusion examples. Introduction to Mathematical Induction. | 3.14, 4.6, 4.7 | ICA 8 (Set proof?) | ||
22 | Tue, Oct 18 | 9:30-10:20 | Lecture 17, Quiz 3 | Induction and recursion examples. Quiz 3 at end of class. | 4.1, 4.2, 4.3, 4.6, 4.7, 4.8 | |||
23 | Wed, Oct 19 | 9:30-10:20 | Lecture 18 | Recursive definitions. Strong induction. Induction examples continued. | 4.1, 4.4, 4.7, 4.8 | ICA 8, end of class | ||
24 | Fri, Oct 21 | 9:30-10:20 | Lecture 19 | Some special sums. Solving 1-term recurrences. | 4.9 | |||
25 | Tue, Oct 25 | 9:30-10:20 | Lecture 20 | Division algorithm. Floors and ceilings. Representing numbers in base b. | 5.1, 5.2, 5.3 | Assignment 3 | ||
26 | Wed, Oct 26 | 9:30-10:20 | Lecture 21 | More changing bases. Divisibility. Prime numbers. Fundamental Theorem of Arithmetic. | 5.5, 5.6, 5.8 | ICA 9, changing base | ||
27 | Fri, Oct 28 | 9:30-10:20 | Lecture 22 | More FTA, Irrationality proofs. Infinitude of primes. | 5.7, 5.9, | |||
28 | Mon, Oct 31 | Last day to withdraw from courses without penalty of failure | ||||||
29 | Tue, Nov 1 | 9:30-10:20 | Lecture 23, Quiz 4 | More divisibility and FTA, gcd, lcm. Quiz 4 at end of class. | 5.10, 5.11, 5.12 | |||
30 | Wed, Nov 2 | 9:30-10:20 | Lecture 24 | Euclidean Algorithm and Integer linear combinations. | 5.12, 5.13 | ICA 10 Euclidean | ||
31 | Fri, Nov 4 | 9:30-10:20 | Lecture 25 | More integer linear combinations. Relatively Prime. Modular arithmetic. | 5.14, 5.15 | |||
32 | Tue, Nov 8 | 9:30-10:20 | Lecture 26 | Cool Modular Arithmetic Tricks. Divisibility by 3 and 9. Cartesian product. Maybe a little intro to relations. | 5.16, 6.1, 6.2, 6.3 | ICA 11, ax+by and find last digit | Assignment 4 | |
33 | Wed, Nov 9 | Reading break (no classes) | ||||||
34 | Fri, Nov 11 | Reading break (no classes) | ||||||
35 | Tue, Nov 15 | 9:30-10:20 | Lecture 27 | More relations. Reflexive, symmetric, transitive and antisymmetric relations. | 6.4, 6.5, 6.6, 6.7 | ICA 14 | Check out UVic's 5 Days of Action (Not for Course Credit) | |
36 | Wed, Nov 16 | 9:30-10:20 | Lecture 28 | Equivalence relations, partitions | 6.9, 6.10 | ICA 15 | ||
37 | Fri, Nov 18 | 9:30-10:20 | Lecture 29, Quiz 5 | More about relations and partitions. A bit of functions. Quiz 5 at end of class. | 6.9, 6.10, 7.1 | |||
38 | Tue, Nov 22 | 9:30-10:20 | Lecture 30 | Introduction to functions | 7.1 | |||
39 | Wed, Nov 23 | 9:30-10:20 | Lecture 31 | Injectivity, surjectivity and bijectivity | 7.3, 7.4, 7.5 | |||
40 | Fri, Nov 25 | 9:30-10:20 | Lecture 32 | Function composition. The identity function and inverses. | 7.6, 7.6, 7.8 | Assignment 5 | ||
41 | Tue, Nov 29 | 9:30-10:20 | Lecture 33 | Introduction to cardinality, countability | 8.1, 8.2, 8.3 | |||
42 | Wed, Nov 30 | 9:30-10:20 | Lecture 34 | Uncountablility | 8.4, 8.5, 8.6 | |||
43 | Fri, Dec 2 | 9:30-10:20 | Lecture 35, Quiz 6 | More cardinality examples. Quiz 6 at end of class. | 8.7, 8.8 | |||
44 | Mon, Dec 5 | Currently, no lecture scheduled. This may change later, if more time is needed. | ||||||
45 | Dec 15 | 7:00 PM | Final Exam | Worth 40% |