Math 131

Spring 2000

This is due Friday, January 21 at the beginning of class. It is worth 10 points. Papers turned in before class on Monday lose 3 points; papers will not be accepted after Monday. Write neatly or use a wordprocessor. There are not "right" or "wrong" answers on this, so your grade will depend on the depth of your ideas and how well you express them. You may discuss your work with me but not with others in the class.

The syllabus for this course refers to ambiguity on more than one occasion. Mathematics and computer science do not generally tolerate ambiguity well. Briefly discuss how the definition of a mathematical function or a statement in a computer language (choose one) rules out ambiguity.

One of the challenges in applying mathematics to the real world is that ambiguity plays a large role in our lives. To see how this works, consider the following statements:

The women drank two cups of coffee because they were cold.

The women drank two cups of coffee because they were warm.

For each sentence, explain what "they" refers to and how you know which is which. If the cups of coffee came from one vendor, discuss how many cups the vendor sold to the women.

Pick two of the following newspaper headlines (source: Goodbye Descartes by Keith Devlin). Explain what you think the headline meant to say and also what it says if you read it differently. Reword the headline so that it unambiguously says what was intended.

FARMER BILL DIES IN HOUSE

BRITISH LEFT WAFFLES ON FALKLANDS

TEACHER STRIKES IDLE KIDS

REAGAN WINS ON BUDGET, MORE LIES AHEAD

MINERS REFUSE TO WORK AFTER DEATH

JUVENILE COURTS TO TRY SHOOTING DEFENDANT

SISTERS REUNITED AFTER 18 YEARS IN CHECKOUT LINE

Briefly discuss why you think mathematicians and computer scientists are so picky about definitions and the precise use of symbols.