Assignments for MAT115H

• Visit the website, and the timeline of Lewis Carroll's life; check out some of the links I've already discovered.
• Propose one addition (or change!) to the timeline. Include text, and an image and link, if possible.
• Read the Introduction (through p. 19) -- if we've got a little time today, we'll get started on one or two.

• Read the first Fit (pp. 21-37): Carroll's early years.
• Find (or conjure up) one application of a mobius band (see Scene 7: Fortunatus's Purse).
• Devise your own two final stanzas the Scene 5: The Beaver's Lesson. Keeping the first line of the second to last stanza:
  "Taking Three as the subject to reason about --
  finish the poem in the style of Lewis Carroll, concocting your own mathematical identity, so that you preserve the final line:
  Exactly and perfectly true."
  You fill in the six lines between!

• Finish your Beaver's Tail, and email it to me.
• Pick your favorite poem, and explain why you like it.
• Perform a check of the calculations proposed by your colleagues in their Tail poems for the Beaver's Lesson -- do they have an identity, which results in the number three?
• Finish your mobius exercise.

• For Tuesday, 9/8: submit
  1. your calculations (sheet of paper) and checks for each poem
  2. A short (half page) description of why you chose your favorite. This should be typed and well-written. These will distributed to the authors of each.
  3. A short (half page) description of your own, including the calculation.
• Thursday, 9/10: submit your answers to the following from the reading "The Band That Wouldn't Stop Playing": Problems 8, 9, 10, 18, 19, 20. These may be done by hand (you needn't type anything up). You may want to include some pieces of bands, if you wish. Put them in an envelope, however!;)

"Let me see: four times five is twelve, and four times six is thirteen, and four times seven is -- oh dear! I shall never get to twenty at that rate!"

Also begin reading "Fit the Second".

• Type a one-page response to Carroll's "Hints for how to do mathematics", pp. 49-51. Are these good hints? Have you ever followed any of them? Do you have others to add? This is due Thursday, 9/17.
• Have a look at the algebra problems of Fit the Second (p. 50), and attempt some solutions. Or at least understand the problems!;) This is for Thursday. Just bring your work to class.
• Write a Carroll-like piece, working in the binary card trick of "The Great Fraudini" (a la Fortunatus's Purse). Due Tuesday, 9/22. Please email in advance of class, if possible.

• Prepare the binary problems assigned (distributed in class) to hand in (due 9/29). Show your work!
• Learn each of the three tricks on page 65. Attempt them first on your own. Then, as noted in the text, they are explained on p. 215 in the notes. You will be expected to know how to do these! They will be discussed on Thursday.
• Attempt to decode the message on p. 77 (created with the matrix cipher), without referring to the notes. Once again, you will be expected to know how to do this, so do not proceed until you have mastered this mathematical difficulty!;)

• Begin Fit the Fourth (finish it by Thursday next)
• Read "Crazy Clocks and Checking out Bars" for next time (distributed in class). Please write up the following for Thursday, 10/1 (revised due date: Tuesday, 10/6): #2, 4, 6, 7, 9, 12 (check my colleague, who suspects that they're all wrong), 20, 24, 32 (the ISBN for The Heart of Mathematics is 1-931914-41-9). The method of #32 doesn't work for our text ("Lewis Carroll in Numberland"), because our text uses a 13-digit code. Visit http://en.wikipedia.org/wiki/International_Standard_Book_Number to find out how to check it.

• For 10/15: read (what you can get through easily of) Fit the Fifth -- "Send Me the Next Book...." Read for enjoyment.
• Problems due 10/27:
  • p. 160-162: solve/explain the "Geometrical Puzzles"
  • p. 166: the coloring maps problem. Try to construct a map that requires more than 4 colors. You can do it, but you'll have to "cheat" somehow. Find a way to cheat!;)
  • p. 169: solve the isosceles triangle problem
  • p. 28: complete the proof that Charles began. Since we don't have his next page, you're on your own! But I'm sure that Charles managed to complete it. Notice that he makes an error (that he corrects) in his write-up....

• Write up (and resolve) the following syllogisms of Lewis Carroll:
  1. Easy:
     1. All Dragons are uncanny;
     2. All Scotchmen are canny.
  2. Harder!
     1. All my sons are slim.
     2. No child of mine is healthy who takes no exercise.
     3. All gluttons, who are children of mine, are fat.
     4. No daughter of mine takes any exercise.
• Write up (and resolve) a syllogism of your own requiring three different blocks (trilateral diagram) in the Logic Game

• Please read the "Conclusion: Math and Aftermath" for next time (our last class discussion of new material!).
• Test the trios of your handout (#1-26); for any that are not valid, demonstrate using the bi/tri-lateral diagrams of Carroll (due next Tuesday, 12/8).