 Individual Projects |
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| P1. It is stated in the text that "Mathematics
is alive and constantly changing. As we complete the last decade of this
century, we stand on the threshold of major changes in the mathematics
curriculum in the United States." Write a report on some of these recent
changes. REFERENCES Lynn Steen, Everybody Counts: A Report to the Nation on the Future of Mathematics Education (Washington, D.C.: National Academy Press, 1989). See also, Curriculum and Evaluation Standards for School Mathematics from the National Council of Teachers of Mathematics (Reston, VA: NCTM, 1989).
P2. Begin a journal for this course. You should write in your journal
after each class and after you spend some time reading the book or doing
homework problems. Make notes about how much time you spent reading the
text and how much time you spent working on homework problems. As you
progress through this book, keep the following cartoon in mind.  P3. Write a paper or prepare an exhibit illustrating the Pythagorean theorem.
P4. Consider a square as shown in the fugure below. What is the
total length of the segments making up the stairs in each part of the
figure? Look for a pattern to answer the question, does the number of
stairs matter? 
P5. Find an irrational number with the requested property.
P6. This is an old problem but it is still fascinating. One day three men went to a hotel and were charged $300 for their room. The desk clerk then realized that he had overcharged them $50 and he sent the refund up with the bellboy. Now the bellboy, being an amateur mathematician, realized that it would be difficult to split the $50 three ways. Therefore, he kept a $20 "tip" and gave the men only $30. Each man had originally paid $100 and was returned $10. Thus it cost each man $90 for the room. This means that they spent $270 for the room plus the $20 "tip," for a total of $290. What happened to the other $10? P7. At a certain hamburger stand, the owner sold soft drinks out of two 16-gallon barrels. At the end of the first day, she wished to increase her profit, so she filled the soft-drink barrels with water, thus diluting the drink served. She repeated the procedure at the end of the second and third days. At the end of the fourth day, she had 10 gallons remaining in the barrels, but they contained only 1 pint of pure soft drink. How much pure soft drink was served in the four days? P8. Suppose it were possible to count all of the individual strands of hair on your head. Also suppose that it is possible to do that for any number of people. For example, if you have 4,890 hairs on your head, and I have 1,596 hairs, then the product of the number of hairs on both our heads is 7,804,440. How many hairs are there in the product for all persons in New York City at midnight on New Year's Eve, December 31, 2002? P9. Write a paper on the relationship between art and mathematics.
P10. What would happen if the entire world population moved to
California?
b. Now calculate the answer to part a, using the earth's population as given in Problem P10. P13. What is a bank debit card? Investigate and report on the advantages and disadvantages of using a bank debit card. Some aspects to consider: convenience, privacy, safety, record keeping, acceptance, and liability in case of loss or theft. Individually answer these questions, and then together, read, critique, and edit each other's work. Organize and submit a report.
P14. Look in a local newspaper and select a home to purchase. Write a report on necessary income, costs, and monthly payments for various options when buying this home. You might consider some of the questions described in the SITUATION for Section 7.6 of your textbook.
P15. A famous mathematician, Bertrand Russell, created a whole series of paradoxes by considering situations such as the following barber's rule: "Suppose in the small California town of Ferndale it is the practice of many of the men to be shaved by the barber. Now, the barber has a rule that has come to be known as the barber's rule: He shaves those men and only those men who do not shave themselves. The question is: Does the barber shave himself?" If he does shave himself, then according to the barber's rule, he does not shave himself. On the other hand, if he does not shave himself, then, according to the barber's rule, he shaves himself. We can only conclude that there can be no such barber's rule. But why not? Write a paper explaining what is meant by a paradox. Use the Historical Note below for some suggestions about mathematicians who have done work in this area. You might begin with this Internet site:
P16. a.Suppose that you are in class and your instructor makes
you the following legitimate offer. Take out a piece of paper and without
communicating with your classmates, write one of the following messages
under your name:
P18. Prepare a report or exhibit showing how statistics are used in educational testing.
P19. Prepare a report or exhibit showing how statistics are used in psychology. P20. Investigate the work of Adolph Quetelet, Franccois Galton, Karl Pearson, R. A. Fisher, and Florence Nightingale. Prepare a report or an exhibit of their work in statistics. | |
