Math 170 Schedule
Monday |
Tuesday |
Wednesday |
Thursday |
Week 1: Numbers, digits, and identification.
|
May 21
Lecture:
- Introduction to course/texts.
- What are numbers? How do we think about them?
- History of number systems.
Reading:
| May 22
Lecture:
- Identification numbers.
- Check digits and example.
Reading:
- FAPP
Ed. 6, Ch. 9 Ed. 7, Ch. 16
| May 23
Lecture:
- Numbers for computers.
- Different bases, binary.
- Encoding messages, the beginnings of cryptography.
Reading:
- FAPP
Ed. 6, Ch. 9 Ed. 6, Ch. 10.1 Ed. 7,
Ch. 16 Ed. 7, Ch. 17.1
| May 24
Lecture:
Activity
- Searching for numbers outside.
Reading:
- FAPP
Ed. 6, Ch. 10.2 Ed. 7, Ch. 17.2
|
Week 2: Graph theory, streets, and networks.
|
May 28
Memorial Day
(no class)
| May 29
Lecture:
- What is a graph? Where do they come from?
- Circuits and Eulerian circuits.
- Eulerization.
Reading:
- FAPP
Ed. 6, Ch. 1
Ed. 7, Ch. 1
- In class hand-out.
Homework 1 due.
| May 30
Lecture:
- Hamiltonian circuits.
- More traveling problems.
Reading:
- FAPP
Ed. 6, Ch. 2.1 - 2.3
Ed. 7, Ch. 2.1 - 2.3
Quiz.
| June 1
Lecture:
- Coloring graphs, Ramsey theory.
Activity
-
Circuits on Penn's campus. Canceled.
Reading:
|
Week 3: Symmetries and patterns.
|
June 4
Lecture:
- Symmetries of shapes in the plane.
- Compositions of symmetries.
Reading:
- FAPP
Ed. 6, Ch. 19.4 - 19.8
Ed. 7, Ch. 19.4 - 19.8
| June 5
Lecture:
- Abstract groups and groups of symmetries.
- Symmetries of regular n-gons: the dihedral groups.
Reading:
- Ed. 6, Ch. 19.4 - 19.8
- Ed. 7, Ch. 19.4 - 19.8
Homework 2 due.
| June 6
Lecture:
- Tilings: Penrose and Muslim patterns.
- Symmetries of tillings.
Reading:
- Ed. 6, Ch. 19.10 - 19.11, 20.1 - 20.9
- Ed. 7, Ch. 19.10 - 19.11, 20.1 - 20.9
-
Article in Science magazine about non-periodic
Islamic tilings.
- Wikipedia article on Penrose tiling.
| June 7
Lecture:
- More tilings.
- Fibonacci numbers.
- The golden ratio in nature and art.
Activity:
- Tilings and Fibonacci numbers on Penn's campus.
Reading:
- Ed. 6, Ch. 19.1 - 19.2
- Ed. 7, Ch. 19.1 - 19.2
- Wikipedia article
on the 17 wallpaper patterns.
- Interactive website
about phyllotaxis.
|
Week 4: Logic.
|
June 11
Lecture:
- Boolean logic: AND, OR, NOT, and IMPLICATION.
- Truth tables.
Reading:
- FAPP
Ed. 6, Ch. 11.5
Ed. 7, Ch. 17.4
- In class handout.
| June 12
Lecture:
- Computer logic.
- Paradoxes(?) of negation.
Reading:
- Handout.
- Wikipedia article on
truth tables.
Homework 3 due.
| June 13
Lecture:
- First order propositional calculus: how to write logical sentences.
Reading:
Quiz.
| June 14
Lecture:
- Lewis Carroll's logic games.
Activity:
- Lewis Carroll's syllogisms.
Reading:
|
Week 5: More logic.
|
June 18
Lecture:
- Inclusive or exclusive OR. Equivalence.
- Quantifiers: existential and universal.
- Logical meaning of common connectives.
Reading:
| June 19
Lecture:
- Translating everyday life.
Reading:
| June 20
Lecture:
- Advanced logic(s).
- Beginning cake cutting.
Activity:
- Short set of logic problems.
Reading:
HW 2 extra credit due.
| June 21
Class canceled.
Choose your
adventure course final selection due at noon (via email).
|
Week 6: Voting systems.
...
|
June 25
Lecture:
- Fair division: how to divide estates and cut cakes?
Reading:
- FAPP
Ed. 6, Ch. 14
Ed. 7, Ch. 13
| June 26
Lecture:
- Voting systems.
- Arrow's paradox.
Reading:
- FAPP
Ed. 6, Ch. 12
Ed. 7, Ch. 9
| June 27
Lecture:
- The 2000 presidential election.
Reading:
- FAPP
Ed. 6, Ch. 17
Ed. 7, Ch. 12
| June 28
Lecture:
Quiz.
Final paper due.
|