Mid-term review outline
- Mathematical data types
- Sets
- definitions and representations of set and subset
- set operations
- A = B iff (A is a subset of B, and B is a subset of A)
- finite set, cardinality, and inlusion-exclusion principles
- power set
- partition
- Relations
- definition and representations of relation
- compositions
- types of relations:
- reflective
- symmetric
- antisymmetric
- transitive
- equivalence relations
- equivalence relation and partition
- Functions
- Definition and representations
- one-to-one, onto, and invertible function
- composition
- frequently used functions:
- permutation
- floor and ceiling
- INT and ABS
- remainder: k (mod m)
- exponential
- logarithm
- recursively defined functions
- Propositional logic
and Proof techniques
- Propositional logic
- Proposition
- Compound propositions and truth tables:
negation, conjunction, disjunction,
and exclusive disjunction
- Implication, bicondition and truth tables
- Logical equivalence
- Propositional functions
- Universal and existential quantifications
- Proof techniques
- Direct proof
- Proof by contraposition
- Proof by contradiction
- Constructive proof
- Proof by counterexample
- Proof by mathematical induction
- Homework problem sets and quizzes
- Homework problem sets #1 - #4
- Quizzes #1-#3