Fall 2017

Math 1250 Seminar in Mathematics:
Mathematical Thinking in the Real World

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Homework and In-class Assignments

Assigned work is listed here with most recent work listed first:
  • For May 5 (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 7.6
    • Mindscapes: 1-18, 22-24, 26-31
    • Due Monday May 1 (assigned April 28): reading response and number 4
  • Section 7.5
    • Mindscapes: 1-5, 6, 7, 12-15, 21, 22, 24, 30-32, 38, 39
    • Due Friday April 28 (assigned April 26): reading response and number 3
    • Due Monday May 1 (assigned April 28): find a favorite Conway's Game of Life starting pattern online and also create your own starting pattern. Turn in these patterns and write about why you chose them.
  • Section 7.4
    • Mindscapes: 1-5, 6, 8, 1, 12-15, 20-23, 26-30, 36, 38, 40
    • No reading response
    • Due Friday April 28 (assigned April 26): one of 41, 43, 44
  • Section 7.3
    • Mindscapes: 1-7, 1-12, 14, 17, 18, 20, 21
    • Due Monday April 24 (assigned April 21): reading response and number 2
  • Section 7.2
    • Mindscapes: 1-5, 6, 9, 10, 13, 14, 15, 16, 21, 23, 24, 25, 27, 28, 32, 33, 37
    • No reading response
    • Due Monday April 24 (assigned April 21): one of 41, 43, 44
  • Section 7.1
    • Mindscapes: 1-6, 9
    • No reading response
  • Section 6.3
    • Mindscapes: 1, 4, 5, 6, 8, 10, 12, 13, 14, 15, 26, 29
    • Due Friday April 7 (assigned April 5): reading response and number 1
  • Section 6.2
    • Mindscapes: 7-9, 12, 14, 15, 19, 20, 24, 26, 27, 29, 30, 32, 33, 35-37, 39, 40
    • Due Wednesday April 5 (assigned April 3): reading response and number 2
  • Section 6.1
    • Mindscapes: 2-7, 9, 12, 14, 15, 19, 30
    • Due Monday April 3 (assigned March 31): reading response and number 1
  • Section 5.4
    • Mindscapes: 1-5, 6-12, 15, 16, 17, 19, 20, 21, 23
    • No reading response
    • Due Monday April 3 (assigned March 31): 24
  • Section 5.3
    • Mindscapes: 6, 10, 11, 13, 16, 19, 26-28, 35, 36, 38
    • Due Wednesday March 29 (assigned March 27): reading response and number 4
  • Section 5.2
    • Mindscapes: 1-5, 6-8, 14, 24, 26-28, 39
    • Link to Wind and Mr. Ug, a video story on a Möbius band
    • No reading response
    • Due Wednesday March 29 (assigned March 27): one of 41, 43, 44; and the answers to the questions in the following activity:
        (This activity is borrowed from the Math 1240 Wiki)
        Cut six strips of paper, each wide enough that you can cut them in half lengthways. Using these strips, make three identical figures in the shape of a cross by taping two of the strips of paper at right angles at the middle of each strip. Make sure you tape the strips to each other on both sides and at both edges (you'll need four pieces of tape).
      1. Take one of the crosses and tape together two opposite "arms" into an untwisted loop. Then tape the other two arms in another untwisted loop (if you taped the first loop on one side of the strip crossing, bend the other loop to the other side). The result will look like a twisted figure eight. Cut one loop down its middle (that is, cut along the length of the loop). What do you get after cutting one of the loops? Now cut the other loop down its middle. What do you get after cutting the second loop?
      2. Take the second cross. Again tape opposite ends into loops. This time make one a plain loop and one a Möbius band. What do you think you will end up with after cutting both loops? Cut the loops to find out. Report the result.
      3. Using the third cross, again tape opposite ends together to make two loops, this time twisting both loops into Möbius bands. What do you think you will end up with after cutting both loops? Cut the loops to find out. Report the result.
      4. In each case, make sure to report how many pieces you get and how many twists each piece has. Check carefully!
  • Section 5.1
    • Mindscapes: 1-5, 6, 7, 9, 10-12, 12, 24, 26-28, 31, 38, 39
    • Due on Wednesday March 22 (assigned March 20): reading response and number 4
  • Section 4.7
    • Mindscapes: 1-5, 6-8, 10, 11, 13, 16, 17, 19, 21, 22
    • No reading response
    • For Monday March 6 (assigned March 3), read at least the first 30 pages (the first 12 sections) of "Flatland: A Romance of Many Dimensions" by Edwin A. Abbott');
    • For Wednesday March 8 (assigned March 6), read "... And He Built a Crooked House --" by Robert A. Heinlein (make sure you click through all three web pages to read the whole story!).
    • Write a page or so on each of the readings on other dimensions:
      • describe life in Flatland (the inhabitants, their customs, episodes in their history), due Wednesday March 8 (assigned March 6); and
      • summarize 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, due Monday March 20 (assigned March 8).
    • For Friday March 24 (assigned March 8) (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
    • Mindscapes: 1-5, 9, 11, 14-17, 21
    • Due on Friday March 3 (assigned March 1): reading response and number 3
  • Section 4.4
    • Mindscapes: 6, 8, 9-12, 15, 16, 18, 21
    • Due on Wednesday March 1 (assigned February 27): reading response and number 5
    • Due on Friday March 3 (assigned March 1): a solution to # 8
  • Section 4.3
    • Mindscapes: 6, 7, 8, 13, 16, 20, 22
    • Due on Wednesday March 1 (assigned February 27): 23, 25 or 26
  • Section 4.2
    • Mindscapes: 7-11, 14-16, 19, 21, 22
    • Due on Friday February 24 (assigned February 22): reading response and Number 3
    • Due on Monday February 27 (assigned February 24): a solution to Mindscape 10, including triangulations, coloring of the vertices, counts of the colors, and conclusions about where to place video cameras.
  • Section 4.1
    • Mindscapes: 6-8, 10-13, 15, 16, 20-22
    • Due on Wednesday February 22 (assigned February 20): reading response and Number 2
    • Due on Friday February 24 (assigned February 22): a solution to one of 13, 15, 20, 21
    • Due on Friday February 24 (assigned February 22): a carefully explained proof of the Pythagorean theorem
  • Section 3.3
    • Mindscapes: 6, 7, 9, 10, 12-14, 16, 19, 20, 22
    • Due on Monday February 20 (assigned February 17): reading response and Number 4
    • Due on Wednesday February 22 (assigned February 20): read Section 3.4 up to the end of the four questions on Page 174. Write a 300 word reflection on infinity. What are the most interesting or surprising discoveries of Chapter 3?
  • Section 3.2
    • Mindscapes: 6, 8, 10, 13, 15, 20, 21, 24, 26, 27, 28, 31, 32, 34, 35
    • Due on Monday February 20 (assigned February 17): one of 41, 43 or 44
  • Section 3.1
    • Mindscapes: 1-20
    • No work due from this section. Make sure you can solve the "Hilbert Hotel" problems that you work(ed) on in class.
  • Section 2.6
    • Mindscapes: 1, 3, 4, 7, 6, 9, 11, 22, 26, 37, 40
    • Due on Monday September 25 (assigned September 20): Reading Response and Number 2
    • Due on Wednesday September 27 (assigned September 25): Turn in a proof that the square root of three is irrational
  • Section 2.5
    • Mindscapes: 7, 8, 11, 13, 15-17, 19, 22
    • Due on Monday September 25 (assigned September 20): one of 23, 25 or 26
  • Section 2.4
    • With reading: do Mindscapes 1-5
    • Mindscapes: 6, 10, 13, 17, 19, 20-22, 26, 29, 32, 33, 39, 40
    • Due on Friday September 15 (assigned September 13): Reading response and Number 1
  • Section 2.3
    • With reading: do one Mindscape from each of the following ranges: 1-5, 6-10, 11-15, 16-20, 21-25
    • Mindscapes: 1, 2, 3, 5, 7, 13, 14, 19, 20, 26-28, 31, 35, 36, 45
    • Due on Wednesday September 13 (assigned September 11): Write a complete and careful proof that there is an infinite number of primes.
    • Due on Friday September 15 (assigned September 13): A short paper of at least 300 words on one of the unanswered questions about prime numbers (the twin prime conjecture or the Goldbach conjecture). Discuss the question's history, describe what progress has been made on the question, and include any interested related information. Take note of the following requirements:
      • Include a list of references at the end of your paper.
      • If you include a quote from your sources, make sure that you give attribution to the source of the quote and make it clear exactly what is quoted.
      • Be careful not to plagiarize from any source - do not copy anything without attribution. Write the majority of the paper in your own words!
      • Your paper will be graded on content (amount of information), mathematical accuracy, use of correct grammar and spelling, and on overall quality.
    • Due on Wednesday September 16 (assigned September 4): second draft of the above paper.
  • Section 2.2
    • With reading: do calculations, play Fibonacci Nim
    • Mindscapes: 7, 8, 26, 6, 10, 12, 13, 16, 17, 18, 20, 45, 47, 49
    • Due on Monday September 11 (assigned September 8): One of 7, 8, 26 and one of 41, 43, 44
  • Section 2.1
    • With reading: do one Mindscape from each of the following ranges: 1-5, 6-10, 11-15, 16-20, then do 21, 22, 24, 25. Add the following to 21: (b) OTTFFSSEN... and (c) JFMAMJ...
    • Due on Wednesday September 6 (assigned September 1): Reading response and one of 1-5.
  • Section 1.4
    • Work on these stories: 1-3, 5-12. Number 15 is a semester challenge problem.
    • Due on Wednesday September 6 (assigned September 1): Write a solution for your favorite Mindscape from this section, and also explain why you chose this Mindscape.
  • Section 1.1
    • Work on the stories not discussed in class (omit Stories 7-9). You will takes turns presenting your solutions and ideas.
  • Due on Friday September 1 (assigned August 28): Please write (or, preferably, type) 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?

    Also: send an email to your family, telling them when your tests and final exam are in this class, advising them NOT to book travel that conflicts with these events.