Lecture Description
An introduction to proof techniques, covering proof by contradiction and induction, with an emphasis on the inductive techniques used in proof by induction.
Course Index
- Introduction and Proofs
- Mathematical Induction
- Strong Induction
- Number Theory I
- Number Theory II
- Graph Theory and Coloring
- Matching Problems
- Graph Theory II: Minimum Spanning Trees
- Communication Networks
- Graph Theory III
- Relations, Partial Orders, and Scheduling
- Sums
- Sums and Asymptotics
- Divide and Conquer Recurrences
- Linear Recurrences
- Counting Rules I
- Counting Rules II
- Probability Introduction
- Conditional Probability
- Independence: Independent and Dependent Events
- Random Variables
- Expectation I
- Expectation II
- Large Deviations
- Random Walks
Course Description
This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.