# Teaching Points

This page for teaching points and examples. Teaching point is my terminology for a concise statement of important information presented to your class.

Example of teaching points for vectors:  TeachPointEx  (tex file)      TeachPointEx   (PDF)

Integration has lots of applications (1): IntApp1 (tex file)  IntApp1  (PDF)

Combinatorics teaches us to count without counting: CombDie  (tex file)  CombDie  (PDF)

You can find functions all around you in the world. Func1  (tex file)  Func1  (PDF)

A function goes from one set to another set. SetToSet (tex file) SetToSet  (PDF)

You can’t cross multiply to prove an identity. PrIdent  (.tex)  PrIdent  (PDF)

Numbers are polynomials.  NumbPoly (.tex)  NumbPoly (PDF)

... is ambiguous: Lagrange (.tex)  Lagrange  (PDF)

If $latex m$ and $latex n$ are integers then $latex a^{\frac{m}{n}}=\left(\sqrt[n]{a}\right)^m=\sqrt[n]{a^m}$ provided $latex \sqrt[n]{a}$ exists.  ExpQuiz2 (.tex) ExpQuiz2 (PDF)

Proof is necessary, even when things seem obvious. (The rational numbers have measure 0)

Law of Sines (ambiguous case): LawOFsinesAmb (PDF)  LawOFsinesAmb (tex) To run the tex file you need the diagrams. They're posted on the Graphics page.

Graphs and digraphs help us see the relationship between things.

Graphs:  The Prediction

Digraphs: Rock, Paper, Scissors, Lizard, Spock