### Forty-Fifth Annual

State of Jefferson Mathematics Congress

September 30 — October 2, 2016

Whiskeytown Lake, CA

PROGRAM

** A User-Friendly Derivation of E = mc²**
by Rick Luttmann,
Sonoma State University.

Einstein's famous formula quantifies the equivalence of mass and energy. But when Einstein
proposed it in his 1906 paper, he wasn't thinking of mass-energy conversion, a phenomenon not then
known or even suspected. He was merely trying to update the classical physics formula for Kinetic
Energy to allow for the new and counter-intuitive conclusion which his
remarkable Theory of Relativity predicted: that mass, time, and distance are not absolute and
objective but depend on the speed *v* (relative to the speed *c* of light) between the observer and
the observed via the factor
√1−(*v/c*)².
We look at the derivation of both the old and the new Kinetic Energy formulae and
sketch briefly where the
√1−(*v/c*)²
factor comes from. [Lecture Notes]

** Paradoxical Elections and Voting Theory**
by Randall Paul,
Oregon Institute of Technology.

There are many different ways to determine the winner of an election when there are three or more candidates. Plurality and run-off elections are the most common, but various methods using preferential ballots (where candidates are ranked) also occur. It is generally assumed that in all but the most closely contested races all of these methods will elect the same "most popular" candidate. Voting theory tells us that this assumption is false — the clear winner by one method can easily lose badly by another method. We look at how these "voting paradoxes" occur, as well as how mathematics can help us judge the relative merits of different methods.

**Discussion Under the Oaks — Flipped Classes, Open Source Textbooks, and Creating
Significant Learning Experiences** led by
Larry Shrewsbury,
Southern Oregon University.

SOU was one of 44 universities chosen to participate in the "Reimagining the First Year of College" program — the idea of which is to review, adopt and share practices, programs and implementation strategies aimed at improving student success. One part was to redesign our "Introduction to Statistical Methods" course (MTH 243) to improve the student success rate. To me, "success rate" means that significantly more of our students who finish our MTH 243 will retain that knowledge and successfully apply it in future coursework. This past year has been a wild (and wonderful) ride; this is what I've learned, and what I'm going to be trying out this next year.

PARTICIPANTS | |
---|---|

NAME | AFFILIATION |

Kelso Quan | Chico State |

Shannon Hussey | Chico State |

Steve Samons | Chico State |

Thomas Mattman | Chico State |

Kyle Falbo | College of the Redwoods |

Caleb Hill | Humboldt State |

Jeff Haag | Humboldt State |

Ken Yanosko | Humboldt State |

Walden Freedman | Humboldt State |

George Lowe | Mayland |

Dibyajyoti Deb | Oregon Tech |

Kathryn Rooney | Oregon Tech |

Kenneth Davis | Oregon Tech |

Randall Paul | Oregon Tech |

Andres Anlas Salman | Sacramento State |

Corey Shanbrom | Sacramento State |

Matt Krauel | Sacramento State |

Greg Detweiler | Southern Oregon |

Joe Collins | Southern Oregon |

Kemble Yates | Southern Oregon |

Larry Shrewsbury | Southern Oregon |

Bethany Johnson | Sonoma State |

Elaine Newman | Sonoma State |

Jillian Kimzy | Sonoma State |

Maddalena Heisler | Sonoma State |

Martha Byrne | Sonoma State |

Nick Franceschine | Sonoma State |

Rick Luttmann | Sonoma State |

Robert Lattimer | Sonoma State |

Shannon Zorn | Sonoma State |

Terris Becker | Sonoma State |

Travis Hayes | Sonoma State |

Dmitry Shemetov | UC Davis |

Jordan Snyder | UC Davis |