The third group of essays from the Teddy Rocks Maths Competition feature topics from Calculus and Probability. The competition was organised with St Edmund Hall at the University of Oxford and offers a cash prize plus publication on the university website. It will be running again in early 2021 so be sure to follow Tom (Instagram, Twitter, Facebook, YouTube) to make sure you don’t miss the announcement!

All essays can be read in full (as submitted) by clicking on the title below. If you enjoy any of them please let the author know by leaving a comment!

#### Calculus

The beauty of Euler’s Number and Euler’s identity

*Ben discusses several different interpretations of Euler’s number and Euler’s identity.*

*Grace talks about Euler’s identity in the context of power series. *

*Honggyun invites you to play with power series and perhaps even invent your own. *

Differentiation and Integration

*Imogen explains why calculus is her favourite mathematical topic.*

Can Integration be made Algorithmic?

*Jake talks us through the various methods used by computers to calculate integrals. *

*Karolina discusses limits in the context of some famous paradoxes. *

Is e^iπ+1=0 really that amazing?

*Nikki explains how the beauty of Euler’s identity lies in the mathematics behind it. *

*Yash conducts an in-depth study to discover the secret to a catchy song. *

#### Probability

Different Interpretations of Probability

*Daniel introduces us to the frequentist versus Bayesian argument. *

Combinatorics: the Josephus Problem

*Jaimy explores a historical counting problem. *

What has Texting got to do with Thermodynamics?

*James provides a whirlwind tour of Information Theory. *

*Krishna investigates a famous counting problem. *

Saving the World with Statistics and Psychology

*Rachel saves the world from aliens by devising a winning strategy for rock, paper, scissors.*