This is an archived course. A more recent version may be available at ocw.mit.edu.

Lecture Notes

Very many people have contributed to these notes in some way or other over the years, including Curtis Greene, Mark Haiman, Joe Killian, Debbie Berkovitz, Mike Hawrilycz, Lenore Cowen, Richard Ehrenborg, Jennifer Huang, Jim Propp, Wayne Goddard, David Gupta, Miklos Bona, Satomi Okazaki, and Esther Jesurum, and several former and current graduate students.

Unless otherwise noted, the notes in the Previous Terms column are from the Fall 2004 version of the course. The lecture notes from 2004 were prepared by four students — Jonathan Lii, Steven Kannan, Jacob Green, and Scott Ostler — with input and guidance from Professor Kleitman.

SES # TOPICS LECTURE NOTES PREVIOUS TERMS
L1 Non-adaptive weighing (PDF)

(PDF)

2006 notes (PDF)
L2 Sorting (PDF) (PDF)
L3 Finding the median

(PDF)

Supplement (PDF)

 (PDF)
L4 Non-adaptive sorting: Batcher's algorithm (PDF) (PDF)
L5 Shannon source coding: coding for efficiency (PDF) (PDF)
L6 Huffman and Hu-Tucker algorithms; finding efficient compression

6.1 (PDF)

6.2 (PDF)

Hu-Tucker (PDF)

Lempel-Ziv (PDF)

 (PDF)
L7 Theory of probability

(PDF)

Supplement (PDF)

 (PDF)
L8 Coding for error correction: the Shannon bound (PDF) (PDF)
L9 Matrix hamming codes (PDF) (PDF)
L10 Polynomial codes

(PDF)

Supplement (PDF)

 (PDF)
L11 BCH codes: constructing them and finding the syndrome of a message

(PDF)

Supplement (PDF)

 (PDF)
L12 Correcting errors in BCH codes (PDF) (PDF)
L13 Properties and generalizations of our BCH codes (PDF) (PDF)
L14 Coding for secrecy

(PDF)

Euclidean algorithm (PDF)

 (PDF)
L15 Secret coding 2 (PDF) (PDF)
L16 Factoring numbers (PDF) (PDF)
L17 Quadratic sieve and elliptic curves (PDF) (PDF)
L18 Some graph theory

(PDF)

Kuratowski's theorem (PDF)

Kuratowski's planarity (PDF)

 (PDF)
L19 Planarity and coloring; matching problems

19.1 (PDF)

19.2 (PDF)

 (PDF)
L20 Counting trees

(PDF)

Supplement (PDF)

 (PDF)
L21 Symmetries (PDF) (PDF)
L22 Counting patterns; generating functions

22.1 (PDF)

22.2 (PDF)

 (PDF)
L23 The finite Fourier transform (PDF) (PDF)
L24 FFT and multiplication of numbers

(PDF)

FFT (PDF)

Supplement (PDF)

 (PDF)
L25 Sequential choice (PDF)  
L26-27 Linear programming (PDF)

(PDF)

(PDF)
L28 Duality in linear programming

(PDF)

Duality (PDF)

Supplement (PDF)

 (PDF)
L29 Matching

(PDF)

Parenthesis (PDF)

  
L30 Strassen's fast multiplication of matrices, algorithm and spreadsheet matrix multiplications (PDF) (PDF)