| Date | Homework Due | |
|---|---|---|
| Fri 29 August | Introductions | |
| Mon 1 September | Paradoxes | Reading: Maor pp. 2-5, Handout on Paradoxes. Just for fun: The play Words, Words, Words by David Ives. It's only about 10 minutes long; you can find the script in the library in the collection All in the Timing. And related, this short mp3 by Bob Newhart. |
| Wed 3 September | Limits | Reading: Dunham pp. 84-99, 106-112. (Read these in the context of yesterday's Maor reading.) |
| Fri 5 September | Series | Reading: Maor pp. 17-20, 25-28 |
|
||
| Mon 8 September | Geometric Series | Reading: Maor pp. 29-33 |
| Wed 10 September | Alternating Series and the Harmonic Series | Reading: Maor pp. 34-39; Dunham pp. 184-206 |
| Fri 12 September | Practice with Series | Reading: Maor pp. 40-48, 236-237; Burger & Starbird Handout (Section 2.6) |
| Mon 15 September | Power Outage Holiday |
|
| Wed 17 September | Irrational Numbers | Problem Set #1; Reading: Burger & Starbird Handout (Section 2.7) |
| Fri 19 September | More on Irrational Numbers | Reading: Maor pp. 10-13 |
| Mon 22 September | Calculus | Problem Set #2 |
| Wed 24 September | Well-Orderings/ Ordinal Numbers | Reading: Ordinal Number Handout, pp. 1-8 |
| Fri 26 September | Ordinal Arithmetic | Problem Set #3; Reading: Ordinal Number Handout, pp. 9-12. |
| Mon 29 September | Counting | Reading: Maor pp. 54-60, Dunham pp. 245-258 |
| Wed 1 October | Infinite Counting | Problem Set #4 Reading: The Jorge Luis Borges story The Book of Sand. For those who want a little more of a challenge, The Book of Sand is also presented as a puzzle where the pages are out of order and you have to find clues in the story itself to discover what order the pages go in. (There are only 8 pages, so it's not as daunting as it sounds.) If you want to try the puzzle, don't read the in-order version (the first link) before you do! |
| Fri 3 October | Countable Sets | Problem Set #5 |
| Mon 6 October | More on Countable Sets | Paper #1: Limits |
| Wed 8 October | Uncountable Sets | Reading: Dunham pp. 259-266 |
| Mon 13 October | Counting in Space | Reading: Burger & Starbird Handout (Section 3.5) |
Wed 15 October |
Power Sets | Problem Set #6; Reading: Maor pp. 61-66 |
| Fri 17 October | Infinite Infinities | Reading: Dunham pp. 274-283 |
Mon 20 October |
Cardinal Numbers | Problem Set #7; Reading: Handout on Cardinal Numbers |
| Wed 22 October | Abstraction and Deductive Reasoning | Reading: Morris Kline Handout (Chapters I and III) |
| Fri 24 October | Models of Non-Euclidean Geometry | Problem Set #8; Reading: Morris Kline Handout (Chapter XXVI) |
| Mon 27 October | The Poincare Disc | Reading: Maor pp. 118-134 |
| Wed 29 October | Midterm Exam | Covers material through 20 October (plus Problem Set #8) |
| Fri 31 October | The Art of M.C. Escher | Reading: Maor pp. 139-148, 164-178 |
| Mon 3 November | 1, 2, 3, ... | Reading: Handout (Axioms for Arithmetic), plus another story by Jorge Luis Borges: Funes the Memorious. |
| Wed 5 November | Mathematical Induction | Reading: Handout (Induction Examples) |
| Fri 7 November | Induction Practice | Reading: Dunham pp. 68-75, 81-83; Maor pp. 235-236 |
| Mon 10 November | Infinity and the Prime Numbers | Reading: Handout (Infinitude of Primes) |
| Wed 12 November | Formal Set Theory and The Continuum Hypothesis | Reading: Handout (The Continuum Hypothesis); Problem Set #9a |
| Fri 14 November | Incompleteness | Readings in this order: (1) First Incompleteness Theorem handout, Sections 1-3; (2) Second Incompleteness Theorem handout; (3) This very short piece by George Boolos |
| Mon 17 November | A Proof of Incompleteness | Reading: First Incompleteness Theorem handout, Section 4. |
| Wed 19 November | The Halting Problem | Reading: Halting Problem handout |
| Fri 21 November | Complex Numbers/Flying with Fractals | Problem Set #9b |
| Mon 1 December | Iteration/Devil's Staircase | |
| Wed 3 December | The Koch Snowflake | Reading: Maor pp. 68-82 |
| Fri 5 December | The Mandelbrot Set | Problem Set #10 |
| Mon 8 December | Mandelbrot Experiments | Extra Credit: Watch video on reserve in the Multimedia Room |
| Wed 10 December | Mandelbrot Experiments Continued | Paper #2: TBA |
| Fri 12 December | Completing Infinity | Problem Set #11 |