Monday  Wednesday  Friday  
August 

26 Logical connectives: " ¬ ", " ∧ ", " ∨ ". 
28 De Morgan’s laws; the distributive laws; conditional sentences: " ⇒ ". 
31 Logical connectives: " ⇐ ", " ⇔ "; conditional proof. 

September 

2 Modus ponens; proof by contradiction. 
4 Proof by contraposition; quantifiers: " ∀ ", " ∃ "; common sets of numbers. 
7 LABOR DAY 
9 Examples and counterexamples; free and bound variables; generalized De Morgan`s laws. 
11 Generalized distributive laws. 

14 Order of quantifiers; uniqueness; even numbers and odd numbers. 
16 Rational numbers; irrational numbers. 
18 Divisibility; prime numbers. 

21 Congruences of integers; induction. 
23 Review 
25 More induction. 

28 MIDTERM 1 
30 Pascal's triangle. 


October 


2 Sums of powers revisited. 
5 Sums of geometric progressions. 
7 Complete induction. 
9 More complete induction. 

12 More complete induction. 
14 More complete induction; review of proofs. 
16 Autumn Break 

19 Sets: definition, description and examples. 
21 Sets: empty set, union, intersection. 
23 Sets: relative complement, Venn Diagrams. 

26 Sets: disjointness, intervals 
28 Unions and intersections of sets of sets 
30 The power set of a set; cartesian product. 

November 
2 Functions: definition and examples 
4 Review 
6 Functions: composition and range 
9 MIDTERM 2 
11 Veterans Day 
13 Restriction and extension of functions; surjective and injective functions. 

16 Functions: bijections and examples. 
18 Functions: properties of bijections. 
20 Equinumerosity 

23 The fundamental property of finite sets. 
25 Thanksgiving Break 
27 Columbus Day 

30 The fundamental property of infinite sets; Infinite sets equinumerous to ℕ 



December 

2 Examples of bijections between intervals (and real line) 
4 Cantor's Theorems 
7 Some useful exercises 
9 Review 

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