# Lecture 1: Three Divide and Conquer Algorithms

### Background Material

- Chapters 1-6 of Cormen, Lieserson, and Rivest
- Recurrence Relations
- Geometric series
- Summation Notation and Manipulation
- Growth Rates and Asymptotic Analysis

### Reading

- Cooley, J. M. and J. W. Tukey, "An algorithm for the machine
calculation of complex Fourier series", Math. Comp., 19, 297-301, 1965.
- A. Karatsuba and Y. Ofman, "Multiplication of multidigit numbers on
automata," Dokl. Akad. Nauk SSSR 145, 293-294, 1962.
- V. Strassen, "Gaussian elimination is not optimal",
Numerische Mathematik, 13, 354-356, 1969.

### Topics

- Overview of the course.
- Objectives
- Topics
- Grading policy and expectations

- Three Problems/Three Algorithms
- Matrix Multiplication and Strassen's algorithm
- Discrete Fourier transform (DFT) and the fast Fourier transform (FFT)
- Integer multiplication and Karatsuba's algorithm

### Lecture Notes

- lec1p0.pdf (Part zero - overview - of lecture notes)
- lec1p1.pdf (Part one - Strassen - of lecture notes)
- lec1p2.pdf (Part two - FFT - of lecture notes)
- lec1p3.pdf (Part three - Karatsuba - of lecture notes)

### Resources

### Assignments

- None, however, students should read the article from
Lecture 2

Created: Sept. 27, 2006 by jjohnson@cs.drexel.edu