11Stephen LynchStephen Lynch

STEM AmbassadorSTEM Ambassador

What is What is Maths?Maths?

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SummarySummary

• Algebra Algebra • FractalsFractals• Big NumbersBig Numbers• Small NumbersSmall Numbers• Board GamesBoard Games• PuzzlesPuzzles• Strange ShapesStrange Shapes• ChaosChaos• DiscoveriesDiscoveries• Inventions Inventions • Brain Inspired Brain Inspired ComputingComputing

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Fractals in the ClassroomFractals in the Classroom

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Sierpinski GasketsSierpinski Gaskets

Stage 1

Stage 2

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Fractals in NatureFractals in Nature

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Big NumbersBig Numbers

∞

1000000000

1000000

0001000000000

One million

One billion

One trillion

100101001010

Googol

Googol Plex

Infinity

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Small NumbersSmall Numbers

Switching time for a transistor circuit.seconds 10 9

metres 101.7 15 The size of the atomic nucleus of a lead atom.

metres 0075.0 Average width of a single human hair.

Nanoscale microscopes focus at this scale.metres 1050 9

Switching time for a Josephson junction circuit.seconds 10 11

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A Zoom in and out of the A Zoom in and out of the UniverseUniverse

http://www.youtube.com/watch?v=0fKBhvDjuy0

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The Mandelbrot Set Zoom 2x10 The Mandelbrot Set Zoom 2x10 275275

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GeometryGeometryA branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

Euclidean geometry

Algebraic geometry

Differential geometry

Fractal geometry

Spherical geometry

Hyperbolic geometry

Eucid’s Elements of Geometry (300 BC) is the second best-selling book of all time!

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The Chaotic PendulumThe Chaotic Pendulum

CHAOS: Unpredictable seemingly random behaviour.CHAOS: Unpredictable seemingly random behaviour.Fractal patterns emerge from chaotic behaviour!Fractal patterns emerge from chaotic behaviour!

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The Chaotic PendulumThe Chaotic Pendulum

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Board Games QuizBoard Games Quiz

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Card Games QuizCard Games Quiz

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PuzzlesPuzzles

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SudokuSudoku

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Group TheoryGroup Theory

* e a b ce e b ca a b c eb c ac c

* e a b ce e a b ca eb b c ac c a

What is a*b*c for each table?

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Group TheoryGroup Theory

In abstract algebra group theory studies the algebraic structure of groups.

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Strange Shapes (Topology)Strange Shapes (Topology)

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The Mobiüs BandThe Mobiüs Band

Question 1: What happens if you cut a Question 1: What happens if you cut a Mobiüs band in half?

Question 2: What happens if you cut it into thirds?

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The Mobiüs BandThe Mobiüs Band

A mathematician confidedThat a Mobiüs band is one-sidedAnd you’ll get quite a laughIf you cut one in halfFor it stays in one piece when divided!

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The Klein BottleThe Klein Bottle

If you could join two Mobiüs bands together you would get a Klein bottle, a four-dimensional object!

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The MemristorThe MemristorMemristor – the missing circuit element

In 1971, Leon Chua mathematically proved the existence of the memristor.

In 2008, HP Labs built first memristor – industry said to be worth $250 billion!

Fundamental circuit variable relationships.

Professor Leon Ong Chua.

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The NeuristorThe Neuristor

A memristor circuit that acts like a neuron.

Connecting CMOS neurons with memristors.

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Brain Inspired ComputingBrain Inspired Computing

IBM researchers have simulated a virtual brain comparable in complexity to that of a human. The power used in gathering thousands of sensory inputs and interpreting and storing the data is estimated to run to about 25W. According to IBMs own estimates, a computer of comparable complexity using current CMOS technology would require in the order of 100MW of power.

The average brain has about 80 billion neurons and trillions of synaptic connections.

The average brain has about 80% excitatory and 20% inhibitory connections.

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Towards the Zettascale Towards the Zettascale SupercomputerSupercomputer

Lynch S. & Borresen J., Binary half adder using oscillators, International Publication Number, WO 2012/001372 A1, 1-57 (2012). Lynch S. & Borresen J., Binary half adder and other logic circuits, UK Patent Number, GB 2481717 A, 1-57 (2012).Borresen J. & Lynch S., Oscillatory threshold logic, PLOS ONE, 7(11) 1-25 (2012).

A zettascale Josephson junction based supercomputer would perform a thousand, million, million, million Floating Point Operations (FLOPs) per second!

Half-adder input and output.

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Set Reset (SR) flip-flop (Memory)

SR flip-flop schematic. Input and output of a Fitzhugh-Nagumo ODEs SR flip-flop.The memory switches on ballistic propagation. Simulation run in MATLAB®.

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SupercomputersSupercomputers

June 2011: Japan’s K supercomputer A peak performance of 8.16 Petaflops and consumes nearly 10 MW.

12/11/12 – USA’s Titan supercomputer achieved 17.59 petaflops beating IBM’s BlueGene/Q.

Using superconducting Josephson junctions andour invention, we believe it is possible to build a zettascale supercomputer. One zettasecond is equivalent to 32 trillion years!!!!

June 17, 2013 (China): Tianhe-2 - meaning Milky Way-2 - operates at 33.86 petaflop/sec.

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An Assay for Neuronal DegradationAn Assay for Neuronal Degradation

Growing neurons on chips and looking for cures to Alzheimer’s, Parkinson’s disease and epilepsy, for example.

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Professor Mark Slevin (Professor in Cell Pathology – Alzheimer’s)

Dr Chris Murgatroyd (Molecular Biologist – STEM cells)

Dr Kirstie Andrews (Bio-engineering)

Measuring electrical activity of cultured electrogenic cells (e.g. neurons, heart, retina, muscle):

1. Patch clamp technique (intrusive).

2. Extracellular recording (non-intrusive).

3. Optical measuring using voltage sensitive or fluorescent dyes.

Neuronal Circuits: MMU GroupNeuronal Circuits: MMU Group

31313131

MicroElectrode Array (or MEA) for In-Vitro Applications

Multi Channel Systems MCS GmbH, Reutlingen Germany.

UK sourcing company: Scientifica Limited (www.scientifica.uk.com)

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Lego Cubestormer IILego Cubestormer II

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Mathematical PuzzlesMathematical PuzzlesProblem 1: Suppose that you have two jugs. One holds exactly 9 litres and the other exactly 4 litres. How do you get exactly 6 litres given a plentiful supply of water? What is the minimum number of steps involved?

9 litres 4 litres Water tank

Problem 2: Obtain exactly 10 litres of fluid without throwing any fluid away.

19 litres 13 litres 7 litres

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Maths Voted Best Overall CourseMaths Voted Best Overall CourseAt MMU 2012At MMU 2012

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ConclusionConclusion

Maths is: Maths is: FUNFUN

BEAUTIFULBEAUTIFULINTERESTINGINTERESTING

LOVEDLOVEDand has manyand has manyAPPLICATIONSAPPLICATIONS

Thank You!Thank You!