6.006 Introduction to Algorithms (Fall 2011, MIT OCW). Taught by Professor Erik Demaine and Professor Srinivas Devadas, this course provides an introduction to mathematical modeling of computational problems. It covers the common algorithms, algorithmic paradigms, and data structures used to solve these problems. The course emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems.
(from ocw.mit.edu)
This lecture starts with how to define useful subproblems for strings or sequences, and then looks at parenthesization, edit distance, and the knapsack problem. The lecture ends with a brief discussion of pseudopolynomial time.