Zipf's Law (UMAP)

From this module students will learn how to: 1) use partial fractions to explain summation; 2) calculate relative errors to measure quality of match-up between two sets of data; 3) carry out a word-count study on any lengthy text in any language; 4) convert item-count study data into rank-frequency data; 5) use log-log paper to graphically test whether rank-frequency data obeys Zipf's Law; and 6) give an example of pure, apparently impractical research that has practical implications for a sophisticated system like a human language.

Table of Contents:

1. PARTIAL SUMS CAN HELP US ADD UP A SERIES

2. SUMMING THE SERIES ZIPF USED

3. WORD COUNTS IN JOYCE'S ULYSSES

4. HOW GOOD IS THIS SERIES MODEL

5. THE EXTENSIVE RESEARCH INTO WORD-COUNTS AND RELATED LANGUAGE PATTERNS

6. ZIPF'S LAW (THE RANK-FREQUENCY LAW)

7. A LOG-LOG GRAPH REVEALS OBEDIENCE TO ZIPF'S LAW

8. EXERCISES: ZIPF'S LAW AND THE SERIES MODEL ARE RELATED

9. MANDELBROT'S EXPLANATION OF THE LANGUAGE PATTERNS

10. SOURCES

11. ANSWERS TO EXERCISES