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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:
  • More cryptography.
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:
  • Handout.
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:
  • Handout.
June 19

Lecture:
  • Translating everyday life.
Reading:
  • Handout.
June 20

Lecture:
  • Advanced logic(s).
  • Beginning cake cutting.
Activity:
  • Short set of logic problems.
Reading:
  • Handout.
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:
  • Mathematics of sudoku.
Quiz.

Final paper due.


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