October 6

• Continuing with the algebra of remainders. $15^{23}\mod 7=?$
• Create your own problem!
• Recall how to solve linear equations,
• and use it to find sums of geometric progressions. 
• ...like $1+2+4+8+\ldots=-1$!
• How to write down arithmetic expressions:
  $$(2+3)*5-7$$
• ...using trees!
• or Polish notation
  $$-*+2,3,5,7$$
• Trees are useful in syntactic ambiguities:
  The professor said on Monday he would give an exam...
  One morning, I caught an elephant in my pajamas...
  The professor attacked the student with the umbrella...
• Back to sets: complements. What is $\overline{A\cup B}$?
• Game: bulls and cows