Spring 2004
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 6.6
- I: 1, 2, 5, 6, 7, 9; II: 2 (see page 501), 3, 5; III: 1
- no work due for this section
- For Monday April 26 (you will give brief presentations that day): Creative project on Fractals and/or Chaos fourth 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 6.5
- I: 1-13, 17-19; II: 1-6
- no work due for this section
- Section 6.4
- I: 1, 3, 5, 7-10, 15-18, 20; II: 1-5; III: 1, 3, 5
- due Friday April 23: IV: one of 1, 3 or 4
- Section 6.3
- I: 1, 4, 5, 6, 8, 10, 11, 16, 18, 19; II: 2, 3, 7; III: 2, 3, 4
- due Monday April 19: IV: one of 1, 3 or 4
- Section 6.2
- I: 1, 2, 4, 7 - 10, 15, 16, 17, 19; II: 1, 5, 6, 7; III: 1, 3, 4
- Project due Monday April 12: Find a favorite starting pattern for the Game of Life, and also create a starting pattern that appeals to you. Write a paragraph or two about your patterns.
- Section 6.1
- I: 1, 2, 3, 4, 5, 6, 9
- no work due for this section
- Section 5.5
- I: 1, 2, 3, 4, 5, 6, 7, 10; II: 1, 2, 4, 5; III: 1, 3
- due Monday April 5: IV: 1
- Section 5.4
- I: 1, 5, 6, 8, 14; II: 1, 2, 3, 10; III: 1
- no work due for this section
- Section 5.3
- 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
- I: 1, 2, 3, 9, 19; II: 1, 2, 3; III: 4
- due Wednesday March 24: one of IV: 1, 3 or 4
- Section 5.1
- I: 1, 2, 4, 5, 6, 7, 9, 19; II: 1, 2, 3, 6; III: 3, 4
- no work due for this section
- Section 4.7
- I: 1 - 3, 5, 6, 8; II: 1, 2, 4; III: 1, 2
- For Wednesday March 17, read at least the first 30 pages (the first 9 sections) of "Flatland: A Romance of Many Dimensions" by Edwin A. Abbott
- For Friday March 19, read "... And He Built a Crooked House --" by Robert A. Heinlein
- Due Monday March 22, 2003: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 Monday March 29 (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: 4, 6, 9 (use CD-ROM), 10; II: 1, 2; III: 1
- no work due for this section
- Section 4.4
- I: 1, 3, 4, 5, 6, 7, 10; II: 1, 3; III: 1
- due Monday March 1: I: 3
- Section 4.3
- I: 1, 2, 3, 8; II: 1, 5; III: 2
- due Friday February 27: one of IV: 1, 3 or 4
- Section 4.2
- I: 2, 3, 4, 5, 6, 8, 9; II: 1, 4; III: 1, 2
- Hand in I: 5, in addition to triangulating each figure, color the vertices as explained in this section and show the positions of cameras to efficiently view each entire gallery.
- Section 4.1
- I: 1, 2, 3, 5, 7, 9, 8, 10; II: 1, 5; III: 1, 2
- no work due for this section
- Section 3.3
- I: 1, 2, 4, 7, 8, 9; II: 1, 5; III: 2
- due Friday February 27: Read the questions about infinity on pages 174-175 (Section 3.4), then write a 300-word reflection on infinity - what are the most interesting or surprising discoveries of this chapter?
- Section 3.2
- I: 1, 3, 5, 8, 10, (11-12), 15, 16, 19; II: 1, 2, 3, 6, 7; III: 1, 4
- due Friday February 13: one of IV: 1, 3 or 4
- Section 3.1
- Think about all the Mindscapes in sections I - III, come to class ready to discuss
- no work due for this section
- Section 2.6
- I: 1, 3, 4, 7, 11, 14; II: 1, 4; III: 1, 2
- no work due for this section
- Section 2.5
- I: 1-10; II: 1, 2, 3; III: 2
- due Monday February 9: one of IV: 1, 3 or 4
- Section 2.4
- I: 1, 4, 8, 12, 14, 15, 16, 18, 19; II: 1, 4, 6, 7, 9, 10; III: 3, 4, 5
- no work due for this section
- Section 2.3
- One from each of the following: I: 1 - 5; I: 6 - 10; I: 11 - 15; I: 16 - 20
- II: 1, 2, 3, 5, 6, 10; III: 1
- Write a proof of the Infinitude of Primes, due Friday January 30
- Write a paper (300 words minimum) on an open problem about primes numbers. Discuss the history of the problem and any related information. You may choose one of the problems mentioned in the book, or one you find in your research. Please list all sources. The first draft of this paper is due on Monday February 2 (you are required to turn in this draft). It will be returned by Wednesday so that you can turn in the final version on Monday February 9.
- Section 2.2
- I: 1, 2, 3, 10, 11, 13 - 18; II: 1, 4, 6 - 8
- due Monday January 26: one of IV: 1, 3 or 4; also I: 3
- Section 2.1
- Mindscapes: choose one from I.1 - I.5, one from I.6 - I.10, one from II, III.1, III.2. Add the following sequences to problem III.1: (b) OTTFFSSEN... and (c) JFMAMJ...
- 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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