MTH299 Transitions
The official course website is on D2L. We keep references and the schedule here.
References
How to Think Like a Mathematician. Kevin Houston, Cambridge University Press (2009).
Schedule
(Sept 1, W) welcome. syllabus. #1 sets
(Sept 2, R) #2 set operations, functions
(Sept 9, R) #6 statement, negation, truth tables, and/or
(Sept 14, T) #7-#8 implications
(Sept 16, R) #8-#9 converse and equivalence
(Sept 21, T) #10 quantifiers: for all and there exists
(Sept 23, R) #17 #18 #12 proofs, examples, counter-examples
(Sept 28, T) #20 proof I: direct method
(Sept 30, R) #22 proof II: proof by cases
(Oct 5, T) #23 proof III: contradiction
(Oct 7, R) #24 proof IV: induction
(Oct 12, T) #25 induction, part 2
(Oct 14, R) #26 proof V: contrapositive
(Oct 19, T) #30 injectivity
(Oct 21, R) #30 surjectivity
(Oct 28, R) #30 bijectivity
(Nov 2, T) #27 divisions
(Nov 4, R) #27 divisions, part 2
(Nov 9, T) #28 Euclidean algorithm
(Nov 11, R) #28 Euclidean algorithm, part 2
(Nov 16, T) #29 modular arithmetic
(Nov 18, R) #29 modular arithmetic, part 2
(Nov 23, T) more examples
(Nov 30, T) #31 equivalence relations
(Dec 2, R) #31 equivalence relations, part 2
(Dec 7, T) review
(Dec 9, R) review