How to think about algorithms

Iterative algorithms: measures of progress and loop invariants

Examples using more-of-the-input loop invariants

Abstract data types

Narrowing the search space: binary search

Iterative sorting algorithms

Euclid's GCD algorithm

The loop invariant for lower bounds

Abstractions, techniques, and theory

Some simple examples of recursive algorithms

Recursion on trees

Recursive images

Parsing with context-free grammars

Definition of optimization problems

Graph search algorithms

Network flows and linear programming

Greedy algorithms

Recursive backtracking

Dynamic programming algorithms

Examples of dynamic programs

Reductions and NP-completeness

Randomized algorithms

Existential and universal quantifiers

Time complexity

Logarithms and exponentials

Asymptotic growth

Adding-made-easy approximations

Recurrence relations

A formal proof of correctness.