Math 201: Objectives for First Midterm Exam
Definitions
- Divisibility, as in "a divides b"
- Congruence
- Field
- Ordered Field
Theorems and Methods of Proof
- Logic
- Truth Tables
- Logical equivalences (De Morgan's Laws, Conditional Statements, etc.)
- Quantifiers, negation of statements with quantifiers
- Counterexamples
- Sets
- Roster notation, set-builder notation
- Equality of sets; Subsets
- Operations on sets: union, intersection, complement
- Disjoint sets
- Element-chasing
- Set algebra
- Cartesian product
- Algebra
- Division Algorithm
- Congruence and arithmetic operations
- Fields, Ordered Fields
- Cancellation laws for addition and multiplication in a field
- Sign rules for multiplication in ordered fields
- In ordered fields, 1 is positive; nonzero squares are positive
- Density of ordered fields
- Absolute value, triangle inequality
