Fall 2006
Math 125 Seminar in Mathematics:
Mathematical Thinking in the Real World
Infinity, the Fourth Dimension, Primes and Chaos
Homework and In-class Assignments
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Assigned work is listed here with most recent work listed first:
- For Friday December 8 (you will give brief presentations that day): Creative project on Fractals and/or Chaos is due. This can be any creative work. You must also turn in a 300-word essay explaining your work, how it relates to fractals and/or chaos, and why you chose to create your particular project.
- Section 6.6
- I: 1-5; II: 6, 7, 10, 11, 12, 14; III: 17, 18, 20; IV: 21
- no work due for this section
- Section 6.5
- I: 1-5; II: 6-8, 22-24, 25; III: 26-31
- no work due for this section
- Section 6.4
- I: 1-5; II: 6, 8, 10, 12-15, 20-23, 25; III: 26-30; IV: 36, 38, 40 V: 41, 43 or 44 (due Wednesday December 6)
- Section 6.3
- I: 1-5; II: 6, (9), 10, 11, 13, 15, 16, 21, 23, 24, 25; III: 27, 28, 32; IV: 37-39 V: 41, 43 or 44 (due Monday December 4)
- Section 6.2
- I: 1-5; II: 6, 7, 9, 12-15, 20-22, 24; III: 26, 30-32; IV: 36, 38, 39
- Due Friday November 17: Find online a favorite starting pattern for the Game of Life and also create your own interesting starting pattern. Write a paragraph explaining why you chose these patterns
- Section 6.1
- I: 1-6, 9
- no work due for this section
- Section 5.5
- I: 1-5; II: 6-12, 15; III: 16, 17, 19, 20; IV: 21, 23; V: 24 (due Monday November 13)
- Section 5.4
- I: 1-5; II: 6, 10, 11, 13, 19; III: 26-28, 35; IV: 36, 38
- no work due for this section
- Section 5.3
- I: 1-5; II: 7-9, 12, 14, 15, 19, 20, 24; III: 26, 27, 29, 30, 32, 33, 35; IV: 36, 37, 39, 40
- turn in a solution to 40 (due Wednesday November 8)
- Section 5.2
- I: 1-5; II: 6-8, 14, 24; III: 26-28; IV: 39; V: one of 41, 43, 44 (due Monday November 6)
- Section 5.1
- I: 1-5; II: 6, 7, 9, 10-12, 12, 24; III: 26-28, 31; IV: 38, 39
- no work due for this section
- Section 4.7
- I: 1-5; II: 6-8, 10, 11, 13; III: 16, 17, 19; IV: 21, 22
- For Friday October 20, read at least the first 30 pages (the first 9 sections) of "Flatland: A Romance of Many Dimensions" by Edwin A. Abbott');
- For Wednesday October 25, read "... And He Built a Crooked House --" by Robert A. Heinlein
- Due Friday October 27:Write a page or so on each of the two readings on other dimensions:
- describe life in Flatland (the inhabitants, their customs, episodes in their history); and
- outline the plot of the short story "-- And He Built a Crooked House ---" by Robert A. Heinlein; make connections with our study of the fourth dimension.
- For Wednesday November 1 (you will give brief presentations that day): Creative project on the fourth dimension is due. This can be any creative work.
You must also turn in a 300-word essay explaining your work, how it relates to the fourth dimension, and why you chose to create your particular project.
- Section 4.5
- I: 1-5; II: 9, 11, 14 (use CD-ROM), 15; III: 16, 17; IV: 21
- no work due for this section
- Section 4.4
- Mindscapes: do all of I, then II: 6, 8, 9, 10, 11, 12, 15; III: 16, 18; IV: 21
- Turn in a solution to 8 (due Friday October 13)
- Section 4.3
- Mindscapes: do all of I, then II: 6, 7, 8, 13; III: 16, 20; IV: 22; V: one of 23, 25 or 26 (due Wednesday October 11)
- Section 4.2
- Mindscapes: do all of I, then II: 7, 8, 9, 10, 11, 14, 15; III: 16, 19; IV: 21, 22
- Turn in a solution to 10; also color the vertices and show the positions of cameras needed to view the entire gallery (due Monday October 9)
- Section 4.1
- Mindscapes: do all of I, then II: 6, 7, 8, 10, 11, 12, 13, 15; III: 16, 20; IV: 21, 22
- Turn in a group solution to one of 13, 15, 20, 21 (due Friday October 6)
- Section 3.3
- Mindscapes: do all of I, then II: 6, 7, 9, 12, 13, 14; III: 16, 20; IV: 22
- Read the questions about infinity on page 174. Write a 300 word reflection on infinity - what are the most interesting or surprising discoveries of this chapter? (Due Friday October 6)
- Section 3.2
- Mindscapes: do all of I, then II: 6, 8, 10, 13, 15, (16-17), 20, 21, 24; III: 26, 27, 28, 31, 32; IV: 36, 39; V: one of 41, 43 or 44 (due Monday October 2)
- Section 3.1
- Mindscapes: think about all of I - IV
- Section 2.6
- Mindscapes: do all of I, then II: 6, 8, 9, 12, 16; III: 26, 29; IV: 36, 40
- Turn in a proof that the square root of three is irrational, due Wednesday September 27
- Section 2.5
- Mindscapes: do all of I, then II: 6-15; III: 16-18; IV: 22; V: 23, 25 or 26 (due Monday September 25)
- Section 2.4
- Mindscapes: do all of I, then II: 6, 10, 13, 17, 19, 20, 21, 23, 24; III: 26, 29, 31, 32, 34, 35; IV: 38, 39, 40
- Section 2.3
- Mindscapes: do all of I, then one of II: 6-10, one of II: 11-15, one of II: 16-20, and one of II:21-25
- In class, do: Mindscapes III: 26, 27, 28, (30, 31), (35, 36), IV: 39
- Turn in a proof that there are an infinite number of primes on Friday September 15
- Write a paper of 300 words or more on one of the open problems on primes. Discuss its history and any related interesting information. Be sure to list all sources. First draft due Wednesday September 20; final draft due Monday September 25.
- Section 2.2
- Mindscapes: do all of I, then II: 6, 7, 8, 15, 16, 18-23; III: 26, 29, 31-33; V: one of 41, 43 or 44
- Turn in 8 and one of 41, 43 or 44 on Wednesday September 13
- Section 2.1
- Mindscapes: do all of I, choose one from II:6 - 10, one from II:11 - 15, one from III, IV.21, IV.22. Add the following sequences to problem IV.21: (b) OTTFFSSEN... and (c) JFMAMJ...
- Section 1.4
- Due Wednesday September 6: Write a solution to your favorite puzzle in section 1.4. Explain why you chose this puzzle.
- Section 1.1
- Work on the stories not discussed in class (omit Story 7). You will takes turns presenting your solutions and ideas.
- Due on Friday September 1: Please write a paragraph or two about yourself. What is your major? What is your mathematical background? Why are you taking this class? What are you hoping to get out of this class? How do you intend to ensure a successful experience in this class? Visit the web site for this class - tell me something about it that you like, and something that could be improved. Write anything else you wish.
Where is New Zealand?
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