18.310 - Fall 2002

 

Lecturer: Professor Daniel Kleitman  Teaching Assistant: Carly Klivans

Introduction

Syllabus 2002 (tentative)

Assignment 1

Questions for Exam 1 (Take-home exam will consist of 5 of these questions.)

Exam 1 (due Wednesday Ocober16, 2002)

Exam 2 (due Monday November 25, 2002)

 

1.   Non-Adaptive Weighing

2.   Sorting

3.   Finding the Median

4.   Non-Adaptive Sorting: Batcher's Algorithm

5.   Coding for Efficiency

6.   Finding Efficient Compressions; Huffman and Hu-Tucker Algorithms

7.   The Theory of Probability

8.   Coding for Error Correction: the Shannon Bound

9.   Matrix Hamming Codes

10. Polynomial Codes and some lore about Polynomials

11. BCH  Codes: Constructing them and finding the Syndrome of a Message

12. Correcting Errors in BCH Codes

13. Properties and Generalizations of our BCH Codes

14. Some Graph Theory

15. Planarity and Coloring

16. Counting Trees

17. Symmetries

18. Counting Patterns

19. Coding For Secrecy

19. Coding For Secrecy.pdf

20. Secret Coding 2

20. Secret Coding 2.pdf

21. Factoring Numbers

21. Factoring Numbers.pdf

22. Factoring II - Elliptic Curves

22. Factoring II - Elliptic Curves.pdf

23. The Finite Fourier Transform

23. The Finite Fourier Transform.pdf

24. FFT and Multiplication of Numbers

24. FFT and Multiplication of Numbers.pdf

 Assignment 8

25.  Matrix Operations and Strassens Algorithm

25.  Matrix Operations and Strassens Algorithm

 Term paper

 Sample Topics for Term Paper

26 and 27 Linear Programming

26 and 27 Linear Programming.pdf

 Review Topics for Second Exam

 Review Topics for Second Exam.pdf

 Parentheses.pdf

28. Duality in Linear Programming

 Last Assignment