| Date |
Topics |
Assignments
|
|
| Wednesday | 1/10 |
First-day logistics. Learn to fold a triangle
module. Hand in your first-day origami object. |
Read sections 1 and 2, do problems 2.1, 2.3, 2.5, 2.6.
Start folding triangles! (30-40 per pair of students by next Friday) |
| Friday | 1/12 |
How to make formal definitions in mathematics, including
the definitions of odd/even, prime, and divisibility. |
Read section 3. Keep folding those triangles. Have
the book and paper to show on Wednesday! |
|
| Monday | 1/15 |
(Martin Luther King, Jr. Day; no class) |
(keep doing previous assignment) |
| Wednesday | 1/17 |
Work on problems 3.1, 3.2, 3.3, 3.4, 3.8. |
Have triangles ready for Friday. Think about what
the definition of a regular polygon should be. |
| Friday | 1/19 |
Triangle assembly day! Try to make as many "stable
solids" as possible out of your triangles. |
Find any remaining stable solids with triangle faces,
and make an argument for why you think you have found all of
them. |
|
| Monday | 1/22 |
The "roommate" argument for why there are only three
stable solids with triangle faces. Learn to fold square module, and try to
assemble a stable solid with square faces that isn't a cube. |
Type up the "roommate" argument. Anyone who finds a
non-cube stable solid with square faces will get a sphere. |
| Wednesday | 1/24 |
Use edge modules to construct a stable solid with pentagon
faces and valence 3. |
Finish any of the remaining 30 edge modules (per group)
so that we can complete assembly of the model on Friday. |
| Friday | 1/26 |
Finish assembly of the 3-valent stable solid with pentagon
faces. Discuss why there are no stable solids with faces that have six or
more edges. |
Writing assignment: One page typed "roommate argument"
about why there are only five stable solids, due Monday. See handout. |
|
| Monday | 1/29 |
Write a direct proof that the square of any odd number
is odd. Also discuss the negations of "or" and "and" statements. |
Read section 4 and be ready to discuss on Wednesday. |
| Wednesday | 1/31 |
Work on problems 4.1-4.5, proving that odd + odd = even,
odd + even = odd, (odd)(odd) = odd, and (odd)(even) = even. Start thinking
about the truth/liar puzzle. |
Do parts (a) and (b) of the truth/liar puzzle handout. |
| Friday | 2/2 |
Learn how to do a "proof by contradiction". Write
three separate proofs for the solution to the truth/liar puzzle. |
Read Section 19. |
|
| Monday | 2/5 |
Discover that the Euler characteristic of any
sphere-like object is 2, and prove it. |
Think about the proof we did today until you are
confident that you could explain it out loud for next class. |
| Wednesday | 2/7 |
(snow day) |
(snow day) |
| Friday | 2/9 |
MOVIE DAY (yes, there will be an attendance quiz):
The Platonic Solids |
Enjoy life. |
|
| Monday | 2/12 |
Explain the proof that V-E+F=2 out loud. Start working on the proof
that the Euler characteristic formula implies that there are only five Platonic solids. |
Start studying for Monday's exam. |
| Wednesday | 2/14 |
(snow day) |
(snow day) |
| Friday | 2/16 |
Finish the proof that the Euler characteristic implies that there are only five Platonic solids. |
Keep studying for the exam. The exam will include questions about the
three major proofs we have covered in class (the Euclid/roommate argument that there are 5
Platonic solids, the proof that V-E+F=2 for a sphere-like object, and the proof that the
Euler characteristic implies that there are only 5 Platonic solids), as well as questions
about the methods of direct proof (with even/odd examples) and proof by contradiction (with
truth/liar puzzle examples) and logic. |
|
| Monday | 2/19 |
TEST 1 |
Get your origami paper together and ready for next class! |
| Wednesday | 2/21 |
Learn about fractals.
Start constructing a Level 1 Menger sponge. |
Make a 1-page document describing an example of a fractal,
including its name, a picture, and a description of how it is made. You can
take the information directly from any (cited) website. Also make more
cubes for your Menger sponge. |
| Friday | 2/23 |
Hand back tests and midterm grades. Discuss fractals. Keep
working on your Level 1 Menger sponge. |
Finish the Level 1 Menger sponge and bring it to class on Monday. |
|
| Monday | 2/26 |
Determine how much paper it takes to construct various levels of
the Menger sponge. Start discussion of how the Mandelbrot set is constructed. |
Work on problem 3 on the Mandelbrot handout. |
| Wednesday | 2/28 |
Finish Mandelbrot handout. Start watching movie The Colours
of Infinity about the Mandelbrot set. |
Rest. Think about fractals. |
| Friday | 3/2 |
Finish watching movie The Colours of Infinity. |
Have a great spring break! |
|
| Monday | 3/5 |
(Spring Break) |
(Spring Break) |
| Wednesday | 3/7 |
(Spring Break) |
(Spring Break) |
| Friday | 3/9 |
(Spring Break) |
(Spring Break) |
|
| Monday | 3/12 |
Learn about Eulerian and Hamiltonian circuits.
Plan a 3-coloring for the dodecahedron by using a Hamiltonian
circuit on a planar graph. |
Find a Hamiltonian circuit on the planar graph of the
dodecahedron, and try to figure out a way to use it to obtain a proper
3-coloring. |
| Wednesday | 3/14 |
Make PHiZZ units to construct another model of a dodecahedron. |
Make the color map that your group will use to
construct their dodecahedron. |
| Friday | 3/16 |
Work in groups constructing properly 3-colored dodecahedrons. |
Read the New Yorker article about origami. For next time,
be ready with a very clear color map that shows the Hamiltonian circuit you
used, and have at least two rings of your group's dodecahedron completed. |
|
| Monday | 3/19 |
Finish construction and have your dodecahedron and color map
checked for compatibility by another group. |
Finish object if not done already. |
| Wednesday | 3/21 |
Discuss truncated polyhedra, and in particular the Buckyball
that can be obtained by truncating an icosahedron. Start planning for
construction of this Buckyball/soccer ball. |
Construct a planar graph for your Buckyball, and make a stack
of PHiZZ units for assembly in the next class. |
| Friday | 3/23 |
Determine how the V, E, F numbers for the Buckyball can
be obtained by thinking about the V, E, F numbers for the dodecahedron and the
icosahedron and the truncation process. Finish Buckyball worksheet. |
Find a Hamiltonian circuit on the planar graph of your
Buckyball. |
|
| Monday | 3/26 |
QUIZ: On planar graphs, Hamiltonian circuits, and proper
3-colorings. Continue with Buckyball and circuit constructions. |
Keep working towards completing the Buckyball assignment:
A planar graph with a Hamiltonian circuit and a proper 3-coloring, a (possibly
different) color map that you will use to construct the Buckyball, and the
PHiZZ Buckyball itself. |
| Wednesday | 3/28 |
Assembly day. Work in groups to finish Buckyball assignment. |
Continue working on Buckyball assignment. |
| Friday | 3/30 |
(no class) |
Continue working on Buckyball assignment. The origami model
and color map(s) are due by the end of Monday's class period. |
|
| Monday | 4/2 |
Final assembly of PHiZZ Buckyball/soccer ball and corresponding
color map(s). Work on knot coloring worksheet if done early. |
If you finished on time, then enjoy the sun. If you didn't,
then hunker down and have everything ready by the start of Wednesday's class. |
| Wednesday | 4/4 |
Use the Euler characteristic to prove the surprising fact that
every Buckyball - no matter how large - must have exactly 12 pentagon faces. |
Make sure you understand the proof we did today; it is one of the
three major proofs you are responsible for in this class. |
| Friday | 4/6 |
MOVIE DAY: Math Life documentary. |
Have a nice weekend and final breathing room before
final projects are announced on Monday. |
|
| Monday | 4/9 |
Overview of the available final projects (Menger sponge,
semi-regular polyhedra, Buckyballs, Sonobe units). Select projects and groups. |
Start work on your final project. Collect any materials that
you will need for Wednesday's group work day. |
| Wednesday | 4/11 |
Work in groups on final projects. |
Meet outside of class to meet with your final project group. |
| Friday | 4/13 |
Work in groups on final projects. |
More outside-of-class group meetings. |
|
| Monday | 4/16 |
Work in groups on final projects. |
Even more group meetings, whatever it takes. |
| Wednesday | 4/18 |
PRESENTATION DAY |
Remaining groups work on presentations. |
| Friday | 4/20 |
Group work meeting time for those students who have not
yet presented their final projects. |
Remaining groups work on presentations. |
|
| Monday | 4/23 |
PRESENTATION DAY |
Remaining groups work on presentations. Rest of groups
start studying for the final exam. |
| Wednesday | 4/25 |
PRESENTATION DAY |
|
| Friday | 4/27 |
(no class) |
Study for the final exam! |
|
| Monday | 4/30 |
FINAL EXAM FOR SECTION 01 (the 10:10-11:00 class).
EXAM 10:30 AM -- 12:30 PM IN ROOP 127. |
|
| Wednesday | 5/2 |
FINAL EXAM FOR SECTION 02 (the 11:15-12:05 class).
EXAM 10:30 AM -- 12:30 PM IN ROOP 129. |
|