Fall 2001
MT-A125 Seminar in Mathematics: Infinity, the Fourth Dimension, Primes and Chaos: Mathematical Thinking in the Real World
Homework Assignments
Assigned homework is listed here with most recent homework listed first:- Section 6.5
- Mindscapes I: 1 -13, 17 - 19; II: 1 - 6
- Use Bob Devaney's "Target Practice" and "Cycle Practice" applets (linked here).
- Due on Wednesday December 5: A creative project that reflects on the topic of Fractals and Chaos. You can choose to produce a fractal or chaos image, or an artistic impression of a fractal/chaos image. You are also free to express your impressions in any other creative way. Your project should be accompanied by a description which includes a discussion of the mathematics involved in your work.
- Section 6.4
- Mindscapes I: 1, 3, 5, 7 - 10, 15 - 18, 20; II: 1 - 5; III: 1, 3, 5
- To hand in on Monday December 3: IV: 1, 3, or 4.
- Section 6.3
- Mindscapes I: 1, (4), 5, 6, 8, 10, 11, 16, 18, 19, 20; II: 2, 3, 7; III: 2, 3, 4
- To hand in on Friday November 30: IV: 1, 3, or 4.
- Section 6.2
- Mindscapes I: 1, 2, 4, 7 - 10, 15 - 17, 19; II: 1, 5, 6, 7; III: 1, 3, 4
- Due Wednesday November 28: Find a favorite starting pattern for the Game of Life on-line, and also create one yourself. Turn in both starting patterns, and a paragraph about your patterns.
- Section 6.1
- Mindscapes I: 1, 2, 3, 4, 5, 6, 9
- Section 5.4
- Mindscapes I: 1, 5, 6, 8, 14; II: 1, 2, 3, 10; III: 1.
- Section 5.3
- Mindscapes I: 1, 2, 3, 7, 9, 10, 14, 15, 19; II: 1, 2, 4, 5, 7, 8, 9; III: 1, 2, 4, 5.
- Section 5.2
- Mindscapes I: 1, 2, 3, 9, 19; II: 1, 2, 3; III: 4.
- Hand in IV: 1, 3 or 4 on Wednesday November 8.
- Section 5.1
- Mindscapes I: 1, 2, 4, 5, 6, 7, 9, 19; II: 1, 2, 3, 6; III: 3, 4.
- Section 4.7
- Mindscapes I: 1, 2, 3, 5, 6, 8; II: 1, 2, 4; III: 1, 2.
- Read at least Part I of "Flatland: A Romance of Many Dimensions" by Edwin A. Abbott. Write a one-page reflection on the reading. Due Monday October 29.
- Read "... And He Built a Crooked House --" by Robert A. Heinlein. Write a one-page reflection on the reading. Due Wednesday October 31.
- Due Wednesday November 6: Creative project on the fourth dimension. This can be any kind of creative work on the topic of the fourth dimension. Also turn in a one-page explanation or reflection on your work.
- Section 4.5
- Mindscapes I: 4, 6, 9, 10; II: 1, 2; III: 1.
- Section 4.4
- Mindscapes I: 1, 3, 4, 5, 6, 7, 10; II: 1, 3; III: 1.
- Hand in I: 3 on Wednesday October 24.
- Section 4.3
- Mindscapes I: 1, 2, 3, 8; II: 1, 5; III: 2.
- Hand in IV: 1, 3 or 4 on Friday October 19.
- Section 4.2
- Mindscapes I: 2, 3, 4, 5, 6, 8, 9; II: 1, 4; III: 1, 2.
- Hand in Mindscape I: 5 - in addition, color the vertices as explained in the text, and show the position of cameras needed to view each entire gallery. Due on Monday October 15.
- Section 4.1
- Mindscapes I: 1, 2,3 , 5, 7, 9, 8, 10; II: 1, 5; III: 1, 2.
- Section 3.3
- Mindscapes I: 1, 2, 4, 7, 8, 9; II: 1, 5; III: 2.
- Paper: Read the questions about infinity on pages 174-175 of the text. Write a 300 word reflection on infinity - what are the most interesting or surprising discoveries in this chapter? Due on Friday October 12.
- Section 3.2
- Mindscapes I: 1, 3, 5, 8, 10, 15, 16, 19; II: 1, 2, 3, 6, 7; III: 1, 4.
- Hand in IV: 1, 3 or 4 on Monday October 8.
- Section 3.1
- Mindscapes I: 1 - 10; II: 1- 5; III: 1 - 2.
- Section 2.6
- Mindscapes I: 1, 3, 4, 7, 11, 14; II: 1, 4; III: 1, 2.
- Section 2.5
- I: 1 - 10; II: 1, 2, 3; III: 2; IV: 1, 3 or 4
- Hand in IV: 1, 3 or 4 on Monday September 24.
- Section 2.4
- I: 1, 4, 6, 8, 12, 14, 15, 16, 18, 19; II: 1, 4, 6, 7, 9, 10; III: 3, 4, 5
- Section 2.3
- I: one from each of 1 - 5, 6 - 10, 11 - 15, 16 - 20; II: 1, 2, 3, 5&6, 10& III.1; III: 4
- Paper: 300 words or more on one of the open problems; discuss its history and any related information. Be sure to list all sources (internet searches encouraged). Due on Friday September 14.
- Section 2.2
- I: 1, 2, 3, 10, 11, 13 - 18; II: 1, 4, 6 - 8; IV: 1, 3 or 4
- Hand in IV: 1, 3 or 4 on Monday September 10.
- Section 2.1
- Work on at least two of the Mindscapes in section I, one in section II, and 1 in section III. Hint for III.1: continue the sequences JFMAMJ... and ottffs...
- Section 1.4
- Pick out five of the stories, one from each of 1-3, 4-6, 7-9, 10-12 and 13-15, for Friday's class.
- Due Wednesday September 5: Write about story number 5 on page 26 - try to give a careful and complete argument about how to solve the problem.
- Section 1.1
- Work on the stories not discussed in class (omit Story 7). You will takes turns presenting your solutions and ideas.
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