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This course unit is aimed at students studying, or about to study mathematics, sciences, computer science or philosophy at A-level or International Baccalaureate Diploma and other pre-university courses. It provides opportunities for pre-University students to practice and hone vital problem solving, communication, and mathematical modelling skills. In addition, it especially relevant for IB Diploma students who seek to gain inspiration and ideas for their Mathematics SL/HL Explorations and Mathematics Extended Essays.

The course is based on a selection of movie scenes in which a mathematical technique, theorem, conjecture or application is featured. In highlighting the key ideas, consequences or generalizations that arise from the underpinning mathematical content from scenes in SIX different movies, the course introduces students to the deeper mathematical background or concepts behind the mathematics. In so doing, this course exposes the student to the mathematical branches of algorithms, graph theory, probability, logic, number theory, infinity, analysis and proof construction.

This distance learning course is structured around a specific hierarchy of concepts through which the student is guided. Individual learning steps are accordingly broken down into bite-sized chunks that are linked to particular mathematical themes, which are in-turn grouped into sections. The material is designed to stretch all students. For example, optional ‘higher-level’ activities are included for the especially gifted or motivated student.

The broad aims of this deceptively titled course are to utilize specific mathematics movie scenes as a stimulus for students to undertake further mathematical investigation, formulate their own hypotheses, experiment with developing problem-solving strategies and to attempt their own proofs of conjectures.

This course unit is broken down into three sections:

SECTION 1: Algorithms and Mathematical Modelling

SECTION 2: Challenging Intuition or Methodical Construction ?

SECTION 3: Infinity and the Beauty of Prime Numbers

which should be followed in sequence.

Section 1 opens with reference to a tense scene from the movie **Die Hard **in which John McClane (Bruce Willis) with assistance from Zeus Carver (Samuel L. Jackson) are given 5 minutes to solve a logic problem before a bomb detonates. Our investigation of the original problem then leads us into the more general realm of mathematical modelling and the use of algorithms. The second film clip is from the British Film **X+Y,** which is based on the struggles of a child mathematics prodigy Nathan (Asa Butterfield) who is diagnosed with autism. The classroom scene chosen perfectly exemplifies how in mathematics, an original problem can be redefined in order to reveal an underpinning essential structure or pattern.

The first math movieclip we analyse in Section 2, is the seminal scene in **Good Will Hunting**, in which a young school caretaker (played by Matt Damon) anonymously scribes on a blackboard in a corridor at MIT, a solution to a graph theory problem posed by a Fields Medal winning Professor. We will focus on the second part of the original problem, and by recourse to some basic graph theory concepts, work our way through a methodical construction and logical classification in order to produce all the required solutions. The next movie clip chosen in this section is taken from the film **21** and takes place in a lecture theatre, in which the lecturer (played by Kevin Spacey) poses the infamous Monty Hall Problem to the class. The film’s protagonist Ben Campbell (a student played by Jim Sturgess), much to the applause of his peers, correctly responds to the challenge. This famous probability puzzle has notoriously challenged even professors of statistics because its solution seems paradoxical to our intuition. We will carefully apply the fundamental definition of probability to reproduce and generalize the argument used by Ben in the film.

The third section uses scenes from the TV series **Person of Interest **and the film **The Man Who Knew Infinity**, to explore how the nature of infinity is revealed in numbers. We begin with a consideration of the claims made by the character Mr Finch (played by Michael Emerson) about the number π, in Person of Interest (episode: *2 Pi R*,2013):

“Let me show you. Pi, the ratio of the circumference of a circle to its diameter, and this is just the beginning; it keeps on going, forever, without ever repeating. Which means that contained within this string of decimals, is every single other number. Your birthdate, combination to your locker, your social security number, it's all in there, somewhere. And if you convert these decimals into letters, you would have every word that ever existed in every possible combination; the first syllable you spoke as a baby, the name of your latest crush, your entire life story from beginning to end, everything we ever say or do; all of the world's infinite possibilities rest within this one simple circle. Now what you do with that information; what it's good for, well that would be up to you.”

Impressively acted as this scene is by Michael Emerson; is he correct ? What if any, is the mathematical basis for his dramatic claim?

The movie **The Man Who Knew Infinity**, is a historical mathematical biopic about the short life and brilliant achievements of the Indian mathematics genius Srinivasa Ramanujan (1887-1920), played by Dev Patel. A core theme that becomes increasingly developed in the movie, is the essential nature of what constitutes a mathematical ‘proof ’. We will explore a selection of Ramanujan’s results including reference to some of his formulas which are believed to be true, but as yet unproven.

Statement to a friend, quoted in *Ramanujan, the Man and the Mathematician* (1967) by Shiyali Ramamrita Ranganathan, p. 88

*It will be important for you to understand the subtle, but precise, use of notation that will be introduced in this distance learning course. So take your time. The supporting exercises and Progress Checks will give you plenty of opportunities to check your understanding and are designed to guide you through a carefully selected set of examples,pre-requisite theory and application of concepts. *

We wish you every success. Enjoy your course!

Ian Tame

Senior Tutor