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Principles of Applied Mathematics >> Content Detail



Lecture Notes



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 #TOPICSLECTURE NOTESPREVIOUS TERMS
L1Non-adaptive weighing(PDF)

(PDF)

2006 notes (PDF)

L2Sorting(PDF)(PDF)
L3Finding the median

(PDF)

Supplement (PDF)

(PDF)
L4Non-adaptive sorting: Batcher's algorithm(PDF)(PDF)
L5Shannon source coding: coding for efficiency(PDF)(PDF)
L6Huffman and Hu-Tucker algorithms; finding efficient compression

6.1 (PDF)

6.2 (PDF)

Hu-Tucker (PDF)

Lempel-Ziv (PDF)

(PDF)
L7Theory of probability

(PDF)

Supplement (PDF)

(PDF)
L8Coding for error correction: the Shannon bound(PDF)(PDF)
L9Matrix hamming codes(PDF)(PDF)
L10Polynomial codes

(PDF)

Supplement (PDF)

(PDF)
L11BCH codes: constructing them and finding the syndrome of a message

(PDF)

Supplement (PDF)

(PDF)
L12Correcting errors in BCH codes(PDF)(PDF)
L13Properties and generalizations of our BCH codes(PDF)(PDF)
L14Coding for secrecy

(PDF)

Euclidean algorithm (PDF)

(PDF)
L15Secret coding 2(PDF)(PDF)
L16Factoring numbers(PDF)(PDF)
L17Quadratic sieve and elliptic curves(PDF)(PDF)
L18Some graph theory

(PDF)

Kuratowski's theorem (PDF)

Kuratowski's planarity (PDF)

(PDF)
L19Planarity and coloring; matching problems

19.1 (PDF)

19.2 (PDF)

(PDF)
L20Counting trees

(PDF)

Supplement (PDF)

(PDF)
L21Symmetries(PDF)(PDF)
L22Counting patterns; generating functions

22.1 (PDF)

22.2 (PDF)

(PDF)
L23The finite Fourier transform(PDF)(PDF)
L24FFT and multiplication of numbers

(PDF)

FFT (PDF)

Supplement (PDF)

(PDF)
L25Sequential choice(PDF)
L26-27Linear programming(PDF)

(PDF)

(PDF)

L28Duality in linear programming

(PDF)

Duality (PDF)

Supplement (PDF)

(PDF)
L29Matching

(PDF)

Parenthesis (PDF)

L30Strassen's fast multiplication of matrices, algorithm and spreadsheet matrix multiplications(PDF)(PDF)

 








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