Math 119 Ideas in geometry - Fall 2004

Class: MWF 15:00-15:50 in Altgeld Hall 159

Office hours: MWF 16:00-16:50 in Illini Hall 247A

Final exam date: Friday December 17, 13:30-16:30

Date of first Midterm: Wednesday September 22, 3:00-3:50

Date of second Midterm: Monday October 25, 3:00-3:50

Practice questions for the second midterm: (All of Chapter 2 will be covered. There might also be one or two questions on Chapter 6.) p. 44, questions 3,7,8,9, p. 58 question 2, p. 59 questions 11-15,19, p. 78 question 4, p. 79 questions 13, 16, p. 90 question 3, p. 91 questions 4,6,7,9,10, p. 92 any of the questions, p.109 questions 1,2,3,5,6,7, p. 120 questions 1,2,3, p. 476 questions 1,2, p.477 questions 7-10, p.492 questions 1-13.

Date of third Midterm: Wednesday December 1, 3:00-3:50

Practice questions for the third midterm: (All of Chapter 3 and Chapter 4 up to 4.3.) p. 143 q. 1, p. 144 q. 8, p. 145 q. 2, p. 159 q. 9, 10, p. 160 q. 20, 16, 17, p. 170 q. 1, 2, p. 171 q. 9, 7, p. 173 q. III 2, IV 2, p. 188, q. 4, 5, 6, p. 189 q. 8, 10, p. 203 q. 1, p 204 q. 4, 5, p. 215 q. 5, 7, p. 216 q. 9, p. 229 q. 2, p. 230 q. 5, 7, p. 246 q. 9, 10, p. 247 q. 4, p. 248 q. III 2.

Syllabus: pdf.

The textbook is The Heart of Mathematics by Edward B. Burger and Michael Starbird.

Homework (due in class on the day indicated):

1. Due Friday September 3: Pick one of the stories from Chapter 1 of the textbook and cleanly write down the solution to the problem in your own words.
2. Due Friday September 10: p. 365 in the book, questions 5, 7, 8, 14, 15, 19, 20. Challenge: p. 369, question 5.
3. Due Friday September 17: p. 351 ff. in the book, questions 3, 5, 6, 7, 9, 17, 18. p. 354 questions 5 and 10. Challenge: III.1.
4. Due Friday September 24: Creative writing: pick any subject from Chapter 5 and write a story in which it plays a role.
5. Due Friday October 8: p. 420, question 6, p. 453, questions 1 and 7, p.477, question 5, p. 497, question 19; challenge: p.480, question 3.
6. Due Friday October 15: You need graph paper and a ruler. Draw a rectangle, which is 13 squares across and 21 squares down. Inside it, draw a vertical line from top to bottom which is 5 squares from the left and eight squares from the right and a horizontal line from left to right which is 8 squares from the top and 13 squares from the bottom. Now draw the diagonal from the upper left corner to the lower right corner. The two big triangles that you get have the same area. You also have two pairs af smaller triangles with the same areas - one pair in the upper left rectangle, the other one in the lower right rectangle. So the upper right rectangle and the lower left rectangle must also have the same area. But count the squares! Here are the two questions I want you to answer: (a) What is wrong with the picture? Hint: The numbers 5, 8, 13, 21 are consecutive Fibonacci numbers. Try to draw the same picture with another consecutive sequece of Fibonacci numbers, like 8, 13, 21, 34. How about small Fibonacci numbers? (b) Which property of the Fibonacci numbers that we discussed in class makes this trick work?
7. Due Friday October 22: p.56 question 1, p.78 question 3, p. 79 questions 12 and 15, p. 90 questions 1 and 2, p.91 questions 5 and 8.
8. Due Friday November 5: p159 question 8, questions 11-13, plus: assume that now (countably) infinitely many busses (bus 1, bus 2, ...) each with (countably) infinitely many passengers (bus 1: pass. (1,1), pass. (1,2), pass. (1,3), ...) (bus 2: pass. (2,1), pass. (2,2), pass. (2,3), ...) ... arrive at the hotel. Can the night manager fit everybody into a single room? How / why not? p.160 questions 15 and 19, p.143 questions 3,4,5; p.144 question 7; p. 145 question 5.
9. Due Friday November 12: p. 170 question 3, p. 171 q. 8, p. 172 q. 4, p. 187 q. 1,2, p. 188 q. 3, p. 189 q. 9, p. 206 q. III 1.
10. Due Monday November 22: p. 215 q. 3, 4, p. 216 q. 10, p.229 q. 4, \ p. 230 q. 6, 8, p. 245 q. 4, 7.

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