- Math includes topics like algebra, fractals, big and small numbers, board games, puzzles, strange shapes, chaos, discoveries, and inventions. - Fractals can be seen in nature and generated using algorithms like the Sierpinski gasket. Small numbers describe scales like the width of a hair. - Geometry studies shapes and spaces and includes topics like Euclidean, algebraic, differential, and fractal geometry. Chaotic systems like pendulums can generate fractal patterns. - Other areas of math discussed include group theory, topology, brain-inspired computing, and using math to model neuronal circuits and potential cures for diseases.

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Stephen LynchStephen Lynch
STEM AmbassadorSTEM Ambassador
What is Maths?What is Maths?
e
i

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SummarySummary
• AlgebraAlgebra
• FractalsFractals
• Big NumbersBig Numbers
• Small NumbersSmall Numbers
• Board GamesBoard Games
• PuzzlesPuzzles
• Strange ShapesStrange Shapes
• ChaosChaos
• DiscoveriesDiscoveries
• InventionsInventions
• Brain Inspired ComputingBrain Inspired Computing

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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
100
10
100
10
10
Googol
Googol Plex
Infinity

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Small NumbersSmall Numbers
Switching time for a transistor circuit.seconds10 9−
metres101.7 15−
× The size of the atomic nucleus of a lead atom.
metres0075.0 Average width of a single human hair.
Nanoscale microscopes focus at this scale.metres1050 9−
×
Switching time for a Josephson junction circuit.seconds10 11−

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A Zoom in and out of the UniverseA Zoom in and out of the Universe
http://www.youtube.com/watch?v=0fKBhvDjuy0

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The Mandelbrot Set Zoom 2x10The Mandelbrot Set Zoom 2x10
275275

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GeometryGeometry
A 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
i
e

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Group TheoryGroup Theory
* e a b c
e e b c
a a b c e
b c a
c c
* e a b c
e e a b c
a e
b b c a
c 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 aQuestion 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 confided
That a Mobiüs band is one-sided
And you’ll get quite a laugh
If you cut one in half
For 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 Memristor
Memristor – 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 SupercomputerTowards the Zettascale Supercomputer
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 and
our 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

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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 Puzzles
Problem 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 Course
At MMU 2012At MMU 2012

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ConclusionConclusion
Maths is:Maths is:
FUNFUN
BEAUTIFULBEAUTIFUL
INTERESTINGINTERESTING
LOVEDLOVED
and has manyand has many
APPLICATIONSAPPLICATIONS
Thank You!Thank You!