Week 1 (due Monday, January 14):
Entry 1: Write down one definition of "mathematics" from a dictionary or encyclopedia (including those on the web).
Entry 2: Read and comment on the Pólya article. Bonus: Solve triangle problem.
Entry 3: Read and comment on pp. xi-xiv in the textbook.
Entry 4: Read and comment on the "W is for..." article.
Entry 5: Find some interesting properties (both mathematical and non-mathematical) of your favorite two-digit number. (The best way to do this is to search your number on Wikipedia.)
Week 2 (due Tuesday, January 22):
Entry 6: Write down two or three ideas for your mini-presentation topic.
Entry 7: Use Wikipedia to research perfect numbers. Bonus: Find an odd perfect number.
Entry 8: Comment on Fibonacci numbers and the golden ratio. Is it merely a coincidence that Fibonacci numbers show up often in nature? Do you believe that famous artwork contains the golden ratio?
Entry 9: Read and comment on "The Vast Unknown" (pp. 75-76 in the text).
Week 3 (due Monday, January 28):
Entry 10: Comment on "The Proof."
Entry 11: Check two UPCs and two ISBNs.
Week 4 (due Monday, February 4):
Entry 12: Read and comment on pp. 105-106. More generally, comment on the RSA encryption system. Do you feel secure? Should we be working to find a weakness in the current system?
Entry 13: Read and comment on "Accepting Reality," pp. 114-115. Are things different today?
Week 5 (due Monday, February 11):
Entry 14: Comment on Zeno's paradox. How would you resolve it?
Entry 15: Read and comment on pp. 162-163. Why are new ideas often rejected at first?
Entry 16: Write down three titles that interest you in the QA section of the library.
Week 6 (due Monday, February 18):
Entry 17: Research the Continuum Hypothesis. Bonus: Find a set of numbers that is larger than the counting numbers, but smaller than the real numbers.
Entry 18: Read and comment on "A Fascination with Geometrical Ideas," pp. 211-212.
Entry 19: Read and comment on "The Mystical Allure of Platonic Solids," pp. 273-274.
Week 7 (due Monday, February 25):
Entry 20: Read and comment on "The Shape of Our Universe," pp. 297-299.
Entry 21: Read and comment on the "Beginnings of Topology" article.
Week 8 (due Monday, March 3):
Entry 22: Research Eulerian and Hamiltonian paths (or circuits). Comment on your findings.
Entry 23: Which (if any) of the three suggested topics for the research paper are you leaning towards? Give a short outline of your plan for the paper.
Weeks 9 and 10 (due Thursday, March 13):
Entry 24: Play the planar graph game at planarity.net. Try to complete levels 1-4 (or more!). Record your reactions to the game.
Entry 25: Research compass and straightedge constructions.
Entry 26: Read and comment on "The Birth of Probability," p. 527.
Entry 27: Read and comment on "Farewell," pp. 716-8.