All assignments will emphasize writing rigorous proofs. Make sure you justify every single step and statement you make. Provide proper references from the textbook (such as Proposition X or Definition Y).
Chapter 1, pages 44-45: problems 4, 6
Chapter 2, pages 91-92: problems 1, 2, 6, 8, 9
Chapter 3, Exercises on congruence (pages 150-152): problems: 24, 26, 27, 29, 32
Write an essay about the taxicab plane described in
Major Exercise 6
(Chapter 3, page 156). Here is a list of what you may want to include in
your essay: (i) state and explain the new
geometry, (ii) provide some historical background, (iii) address most
(preferably all) points of the exercise 6, (iv) discuss practical,
real-world applications of such a geometry. And of course, you are
certainly encouraged to be creative and add to this list.
Important notes
Academic dishonesty (including plagiarisms) is very well described on the university policies webpage:
General comments
after marking the mini-projects:
Overall we were quite impressed by the level
of research and thought put into these
papers. Very frequently, the results made enjoyable and instructional reading. For the most
part, the mini-projects successfully conveyed an introductory summary and some original
results of Taxicab Geometry. The average was 7.5 out of 10. We made extensive comments to
provide as much feedback as possible. The\ main\ comment\ that\ applies\ to\
most\ of\ you\ relates\ to\ proper\ citation.\ See\ the\ \"Important\ notes\"\ for\ the\
final\ project\ listed\ below.\ There\ is\ an\ item\ that\ discusses\ citation.\ Read\ the\
information\
provided\ by\ the\ library\ link\ and\ learn\ how\ to\ reference\ properly.\
Chapter 4, pg. 194-200: Exercises 9, 12, 14, 28, 32 and Major Exercise 1.
Homework #5 - Due Tuesday, March 8, in class