Undergraduate Colloquium Fall 2016
September 2, 2016
- October 3, 2016
- October 10, 2016
October 18, 2016
"Cooperative Learning"
Judith Montgomery, University of California Santa Cruz
Cooperative Learning is a teaching strategy in which participants work together to solve a problem. When implemented well, cooperative learning encourages achievement, student discussion, active learning, student confidence, and motivation. The skills students develop while collaborating with others are different from the skills students develop while working independently.
- October 24, 2016
November 2, 2016
"The ABC's of the ABC-Conjecture"
Sean Gasiorek, University of California Santa Cruz
The ABC-Conjecture is an important unsolved problem in number theory. Originally stated by Oesterl\'{e} and Masser in 1985, the conjecture deals with relatively prime integers $A+B=C$ (hence the name) and relates the prime factors of the sum $C$ to the prime factors of $A$ and $B$. We will state the $ABC$-Conjecture, provide some examples, and explore some of the numerous corollaries, should it be proven to be true. In August 2012, Mochizuki provided an alleged proof of the $ABC$-Conjecture, but the world's best number theorists are still combing through the details to determine whether his proof is valid. This talk will be self-contained and no prior experience with number theory will be assumed.
- November 9, 2016
"The Kepler problem and the Principle of Least Action"
Connor Jackman, University of California Santa Cruz
In this talk, I'll introduce the Kepler problem and we'll solve the differential equation. Then we can look at the principle of least action and discuss this principle in a few examples. We can also discuss some problems such as embedding surfaces corresponding to Kepler problems (after a question of Rick Moeckel) and minimizing orbits with positive energy. For background some calculus should be necessary to understand the ideas.
- November 16, 2016
- November 23, 2016
- November 30, 2016
"The ABC’s of the ABC Conjecture (Part 2)"
Sean Gasiorek, University of California Santa Cruz
We will begin with a quick review of the ABC Conjecture and all relevant definitions. We will then delve into a handful of the numerous corollaries of the ABC Conjecture, and provide an argument as to why mathematicians might think the conjecture is true. While this talk is a sequel, it is not necessary to have at- tended the first talk on November 2nd. This talk will be entirely self-contained and no previous experience with number theory will be assumed.
- December 7, 2016
