# Course Outline:

1. Notation and Abbreviations

2. Sets and Set Notation
1. Elements and set construction
2. Containment and equality
3. Operations on sets
4. Proofs involving containment and equality
5. Power set of a set
6. Cartesian product of two sets

3. "If-then" and "If-and-only-if" Statements
1. Basic approach
2. Converse and contrapositive
4. P iff Q

4. "For all" and "There exists" Statements
1. Basic approach
2. Illustrations
3. Negations

5. Functions
1. Definition
2. Notation and terminology
3. One-to-one and onto functions
4. Compositions and inverses
5. Images and preimages

6. Induction
1. Definition
2. How to use it
3. Formal justification
4. Recursion

7. Equivalence Relations
1. Definitions
2. Equivalence classes and quotient sets
3. Partitions

8. Infinite Sets
1. Definitions
2. Size of N and Z and Q
3. Size of R
4. Continuum Hypothesis

See the course calendar for the timing of exams and problem sets. The final exam will be scheduled by the registrar; see the official exam schedule when it is available.

 Math 199 (Fall 2019) web pages Created: 09 Sep 2019 Last modified: 09 Sep 2019 00:00:00 Comments to: `dpvc@union.edu`