[Today’s class: Big quiz, patterns in Pascal’s Triangle (lots of ‘em!)]
Mathematics 115
Homework Assignment #5
Due Tuesday, January 15, 2002
A mathematician, like a painter or a poet, is a maker of patterns. If his [or her]
patterns are more permanent than theirs, it is because they are made with ideas. . . . The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test; there is no permanent place in the world for ugly mathematics. - G. H. Hardy
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Prof. Beery's office hours this week: Monday 1/14 10:30 a.m.-12:30 p.m., 4-5 p.m.
Tuesday 1/15 10:30 a.m.-12:30 p.m., 4-5 p.m.
Wednesday 1/16 11 a.m.-12:30 p.m., 4-5 p.m.
Thursday 1/17 11 a.m.-12:30 p.m., 4-5 p.m.
Friday 1/18 2:30 - 4:30 p.m.
and by appointment (Hentschke 203D, x3118)
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DO: Write your mathematics autobiography. (See reverse.)
Tuesday's quiz (10 points) covers Pascal’s Triangle.
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Just for fun:
A traveler is captured by a group of cannibals, whose plan is to barbecue her for supper.
The cannibals give the traveler one way out. There are two types of cannibals, those who always tell the truth and those who always lie. The traveler will be allowed to ask one cannibal exactly one question in order to determine if that cannibal is a truth-telling cannibal or a lying cannibal. If the traveler guesses correctly, she will be freed; if she guesses incorrectly, she will be eaten. What should the traveler ask the cannibal? (There are several correct questions.)
For even more fun:
A hiker is lost in the wild, and comes to a fork in the trail she is following. She knows that
one branch of the fork leads to a town where she can find food and shelter and that the other fork leads deeper into the wild. She wants to take the fork leading to the town. Two townspeople are waiting at the fork in the road; each announces that he is a "guide" and offers to tell the traveller which trail leads to town. The traveller knows that these "guides" know which trail leads to town; she also knows that one of the guides always lies and the other always tells the truth, but she doesn't know which one is which. What single question should the traveller ask either one of the guides in order to find out which road leads to town?
Mathematics Autobiography
Tell the story of your involvement with mathematics---in school, at home, at play, and at work---from your earliest pre-school memories to the present. Be sure to discuss your current attitude toward mathematics and how you think it evolved.
If your handwriting is good, your autobiography may be handwritten; otherwise, please type it! Approximately 3 pages of double-spaced typing or reasonably-sized writing should suffice. You may write informally, but please do pay attention to grammar and spelling.
If you are having trouble getting started (or even if you are not), you might begin by completing some or all of the following thoughts.
My mother's attitude toward mathematics was/is . . .
My father's attitude toward mathematics was/is . . .
Games I played as a child which probably helped/help me understand mathematics then/later/now include . . .
What I remember about doing mathematics in elementary school is . . .
My elementary school teachers' attitudes toward mathematics were . . .
What I remember about doing mathematics in middle / junior high / high school is . .
My middle / junior high / high school mathematics teachers . . .
My mathematics studies in college were/are/will be . . .
The first job I had in which I used mathematics was . . .
My most positive experience with mathematics was . . .
My most negative experience with mathematics was . . .
When I do mathematics, I feel . . .
My attitude toward mathematics is . . .
I think this is because . . .
Adapted from Overcoming Math Anxiety, by Sheila Tobias