Jasmine Tang

Prologue

Hi everyone, this is a retroactive post about an expository paper I did for Twoples.

Twoples is a free online mentoring program for undergrads in math. Twoples especially aims to provide such mentorship to students from underrepresented groups or non-traditional backgrounds, as well as to students at non-research oriented colleges and universities.

I was accepted while being a sophomore at Santiago Canyon College in Orange, CA. With my mentor being Anna Brosowsky, I set on exploring the topics of probabilistic method and wrote an expository paper on it.

Before reading the paper, please enjoy the following previews of it:

Introduction:

Consider the probabilistic method pioneered by the late Paul Erdős. This expository paper then gives a gentler introduction to the topic of Games and attempts to explain the use of the probabilistic method in this field to the reader. Throughout the paper, Jasmine embeds herself and her friend Lucy into common games and describes the winning strategy of each individual through diverse usages of the method.

Page 5 out of 16:

At some point, we also need to consider Jasmine in the equation. After all, humans are complex creatures with intelligence capable of adapting to new situations and manipulating them using knowledge. It would do Jasmine no justice, just allowing her to answer only “Yes” or “No” to Lucy’s mundane queries. Let her make use of the information around her! And give her a chance to actually compete in this game too!

Page 12 out of 16:

“Wait a minute!” - a group of Lucifers (fans of Lucy) exclaims. “I want Lucy to win!” - they angrily argue. “A person so beautiful, kind, and smart deserves to have her own winning play in this game. We are tired of Jasmine always winning ever since you promoted her to an even playing field.” And thus, the author of this expository paper rolls her eyes, lets out a subtle “hmmphh” and is forced to introduce a lemma and a theorem that reveals Lucy’s winning play.