The Math Extended Essay An opportunity to investigate a mathematical idea or application that you’ve found intriguing A mathematics EE means doing math as well as discussing it The applicability of math to solve both real and abstract problems The starting point should be the mathematics in the candidate’s IB Mathematics syllabus

CHOOSING A TOPIC: WHAT WORKS Math EEs should involve scholarly analysis of a mathematical formula, theory, or issue. The elegance of math in the proving of theorems The origin and subsequent development of a branch of math over time The link between different branches of math The way a branch of math has been born, or flourished, as a result of technology The beauty of math as in, for instance, geometry or fractal theory

CHOOSING A TOPIC: WHAT DOESN’T WORK Subjects not lending themselves to mathematical treatment and therefore having only trivial and negligible mathematical content. (e.g. mathematics and sports, mathematics and music, mathematics and architecture, mathematics and beauty). Subjects lending themselves (within the framework of an extended essay) to only minimal mathematical treatment, mostly enumeration and trivial arithmetical calculations (e.g. mathematics and blackjack, the Golden Proportion).

CHOOSING A TOPIC: WHAT DOESN’T WORK (continued) Statistical subjects that for the most part consist of an ill-conceived survey followed by an elementary (and often inappropriate) statistical treatment, again with no real mathematical content. Subjects too difficult for secondary school students (e.g. Fractals, Non Euclidean geometries, Game theory). Occasionally an exceptionally brilliant student may succeed with these subjects but it is quite rare.

CHOOSING A TOPIC: WHAT DOESN’T WORK (continued) Subjects in the history of mathematics, which could be quite adequate, are too often treated as a biography of mathematicians full of anecdotes and devoid of mathematical activity and understanding. It must be noted that this type of subject should be undertaken only by very competent candidates, to avoid sliding into pure biographies.

SAMPLE RESEARCH QUESTIONS: Here are some sample research questions from the EEG: What was the role of mathematics, and geometry in particular, in navigation when sailors relied on the stars? What is the legacy of Archimedes’ calculations of circular and parabolic areas in today’s methods of integration? How can mathematics be used to work out distance from the try line to position the conversion kick in rugby union?

Good concepts with poor execution: Candidates who scored poorly have a tendency to write an essay about mathematics, without actually doing any mathematics: Assert that there are infinitely many prime numbers rather than proving it Assert the golden ratio is 1.618, rather than derive the exact value by setting up and solving a quadratic equation