Teddy Rocks Maths Essay Competition: Calculus and Probability

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.

Euler’s Identity

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

Formal Power Series and Generating Functions: Constructing the Link Between Algebra and Combinatorics

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. 

Loveable Limits

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. 

Fourier Transform and Music

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. 

The Josephus Problem

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.

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