Gresham College: Over four centuries of adult education€¦ · Gresham College: Over four centuries of adult education Raymond Flood ALM-23, Maynooth Wednesday 6th July 2016 . Sir

Gresham College: Over four

centuries of adult education

Raymond Flood

ALM-23, Maynooth

Wednesday 6th July 2016

Sir Thomas Gresham (1519-79)

Sir Thomas Gresham, 1544

(aged 26)

Sir Thomas Gresham, 1565-70

(aged 46-50)

Career

• Employed on Business abroad; trading in gunpowder for Henry VIII

• Royal agent for Edward VI, then Mary I

• Raising loans and negotiating interest for the Crown; saved Crown from bankruptcy by application of ‘Gresham’s Law’

• Continued under Elizabeth I (1558). Knighted in 1559

• Built Royal Exchange 1565

• Died in 1579 and left his estate for benefit of the City of London

The Will: the Corporation

I Will and Dispose that one Moiety.. shall be unto the Mayor and Commonalty and Citizens of London … and the other to the Mercers … and from thence, so long as they and their Successors shall by any means or title have hold or enjoy the same , they and their successors, shall give and distribute, to and for the sustenation, maintenance and Finding Four persons, from Tyme to Tyme to be chosen, nominated and appointed …. And their successors to read the Lectures of Divinity, Astronomy, Musick and Geometry…

The Will: the Corporation

I Will and Dispose that one Moiety.. shall be unto the Mayor and Commonalty and Citizens of London … and the other to the Mercers … and from thence, so long as they and their Successors shall by any means or title have hold or enjoy the same , they and their successors, shall give and distribute, to and for the sustenation, maintenance and Finding Four persons, from Tyme to Tyme to be chosen, nominated and appointed …. And their successors to read the Lectures of Divinity, Astronomy, Musick and Geometry…

The Mercers were responsible for the appointment of the other

three original professorships in Law, Physic (Medicine) and

Rhetoric.

Dr. Valerie Shrimplin, Academic Registrar of Gresham College

… an important fact for the history of science in England is that the Chairs for Astronomy and Geometry at Gresham were the first Chairs in those subjects at any English university. In choosing these subjects, Thomas Gresham appeared to have clearly understood and recognised their importance as separate disciplines in scholarship, many years earlier than either Oxford or Cambridge, where they continued to be studied only as part of a broader classical curriculum. Gresham recognised the importance of applying in practice the knowledge gained from theoretical study. In astronomy for example, the emphasis was on its use for mariners in navigation and geography generally.

10 Andrew Tooke 1704

11 Thomas Tomlinson 1729

12 George Newland 1731

13 William Roman 1749

14 Wilfred Clarke 1759

15 S Kittleby 1765

16 Samuel Birch 1808

17 Robert Pitt Edkins 1848

18 Benjamin Morgan Cowie 1854

19 Karl Pearson 1890

20 William Henry Wagstaff 1894

1939–45 Lectures in abeyance

21 Louis Melville Milne-Thomson 1946

22 Thomas A A Broadbent 1956

23 Sir Bryan Thwaites 1969

24 Clive W. Kilmister 1972

25 Sir Christopher Zeeman 1988

26 Ian Stewart 1994

27 Sir Roger Penrose FRS 1998

28 Harold Thimbleby 2001

29 Robin Wilson 2004

30 John D. Barrow 2008

31 Raymond Flood 2012

1 Henry Briggs 1596

2 Peter Turner 1620

3 John Greaves 1631

4 Ralph Button 1643

5 Daniel Whistler 1648

6 Laurence Rooke 1657

7 Isaac Barrow 1662

8 Arthur Dacres 1664

9 Robert Hooke 1665

Gresham Professors of Geometry

Henry Briggs Logarithms

log10 1 = 0 and log10 10 = 1.

Then to multiply two

numbers one simply added

their logarithms.

log10 ab = log10 a + log10 b

Karl Pearson

1857 - 1936

Charles Darwin

1809 - 1882

10 Andrew Tooke 1704

11 Thomas Tomlinson 1729

12 George Newland 1731

13 William Roman 1749

14 Wilfred Clarke 1759

15 S Kittleby 1765

16 Samuel Birch 1808

17 Robert Pitt Edkins 1848

18 Benjamin Morgan Cowie 1854

19 Karl Pearson 1890

20 William Henry Wagstaff 1894

1939–45 Lectures in abeyance

21 Louis Melville Milne-Thomson 1946

22 Thomas A A Broadbent 1956

23 Sir Bryan Thwaites 1969

24 Clive W. Kilmister 1972

25 Sir Christopher Zeeman 1988

26 Ian Stewart 1994

27 Sir Roger Penrose FRS 1998

28 Harold Thimbleby 2001

29 Robin Wilson 2004

30 John D. Barrow 2008

31 Raymond Flood 2012

1 Henry Briggs 15967

2 Peter Turner 1620

3 John Greaves 1631

4 Ralph Button 1643

5 Daniel Whistler 1648

6 Laurence Rooke 1657

7 Isaac Barrow 1662

8 Arthur Dacres 1664

9 Robert Hooke 1665

Gresham Professors of Geometry

Sir Christopher Zeeman

Sir Roger Penrose

Ian Stewart

Harold Thimbleby

Robin Wilson

John Barrow

Current Gresham Professors

www.gresham.ac.uk

• Background of the audience

• Expectations of

– The audience

– Me!

• Accessibility

– Assume little technical familiarity

– Assume little notational familiarity

– Use History

– Take a visual approach where possible

Accessibility

• Selection of lecture topic

• Visual aids

• Computer simulations

• Modelling the world

• Proof or framework

Shaping Modern Mathematics

Applying Modern Mathematics

Great Mathematicians, Great Mathematics

Great Mathematicians, Great Mathematics

Accessibility


• Visual aids




Isaac Newton’s memorial in Westminster Abbey

From Newton’s A Treatise of the System of the

World

Gottfried Leibniz

1646 - 1716

First appearance of the Integral sign, ∫

on October 29th 1675

d (or dy/dx) notation for differentiation:

∫ notation for integration:

Leibniz notation

Memorials

Accessibility


• Visual aids




Symmetric random walk

1/2

1/2

At each step you move one

unit up with probability ½ or

move one unit down with

probability ½.

An example is given by tossing

a coin where if you get heads

move up and if you get tails

move down and where heads

and tails have equal probability

Coin Tossing

Law of long leads or arcsine law

• In one case out of five the path stays for about

97.6% of the time on the same side of the axis.

Law of long leads or arcsine law

• In one case out of five the path stays for about

97.6% of the time on the same side of the axis.

• In one case out of ten the path stays for about

99.4% on the same side of the axis.

• A coin is tossed once per second for a year.

– In one in twenty cases the more fortunate player is in

the lead for 364 days 10 hours.

– In one in a hundred cases the more fortunate player is in

the lead for all but 30 minutes.

Accessibility


• Visual aids




The tide predictor

www.ams.org/featurecolumn/archive/tidesIII2.html

Weekly record of the tide in

the River Clyde, at the

entrance to the Queen’s

Dock, Glasgow

William Thomson (1824–1907),

soon after graduating at

Cambridge in 1845. He became

Lord Kelvin in 1892.

Accessibility


• Visual aids




Leonhard Euler, 1707–1783Read Euler, read Euler, he is the master of us all!

Portrait by Jakob Emanuel Handmann, 1756

Polyhedra

Comes from the Greek roots, poly meaning manyand hedra meaning seat.

Convex polyhedron has the property that the line joining any 2 points in the object is contained in the polyhedron, or it can rest on any of its faces.

A polyhedron has many

seats – faces - on which it

can be set down

Polyhedra

Convex Non convex

Icosidodecahedron Hexagonal torus

Euler’s formula for convex polyhedra,

V – E + F = 2

V = number of vertices

E = number of edges

F = number of faces

Tetrahedron

V – E + F = 2

Vertices, V = 4

Edges, E = 6

Faces, F = 4

V – E + F = 4 – 6 + 4 = 2

Cube or Hexahedron

V – E + F = 2

Vertices, V = 8

Edges, E = 12

Faces, F = 6

V – E + F = 8 – 12 + 6 = 2

Octahedron

V – E + F = 2

Vertices, V = 6

Edges, E = 12

Faces, F = 8

V – E + F = 6 – 12 + 8 = 2

Dodecahedron

V – E + F = 2

Vertices, V = 20

Edges, E = 30

Faces, F = 12

V – E + F = 20 – 30 + 12 = 2

Icosahedron

V – E + F = 2

Vertices, V = 12

Edges, E = 30

Faces, F = 20

V – E + F = 20 – 30 + 12 = 2

V – E + F

• If we remove an edge and a face at the same

time then number of vertices – number of edges + number of faces

stays the same. Because you are taking away one

less edge but adding on one less face

• Similarly we remove an edge and a vertex at the

same time then number of vertices – number of edges + number of faces

stays the same. Because you are taking away one

less edge but adding on one less vertex.

1: Deform the convex polyhedron into a

sphere

V – E + F left unchanged

2: Remove an edge so as to merge two

faces. Leaves V – E + F unchanged

Remove this edge, so merging the two adjacent faces into one

3: End up with only 1 face and the edges

and vertices forming a graph with no

loops – a treeRemove this edge, so merging the two adjacent faces into one

4: remove a terminating vertex and edge

from the tree.

Leaves V – E + F unchanged


Remove this terminating edge and vertex from the tree

5: As F = 1, E = 0 and V = 1

V – E + F = 2


Remove this terminating edge and vertex from the tree

Picture Source: 17 Equations that Changed the World, Ian Stewart, Profile Books, 2012

In a regular polyhedron all the faces are the same

and the arrangement of faces at each vertex is the

same.

Tetrahedron – four faces

each an equilateral triangle

Cube – six faces, each a

square

Octahedron – eight faces


Dodecahedron – twelve faces

each a regular pentagon

Icosahedron – twenty faces


Thank You!

Documents

Gresham College: Over four centuries of adult education€¦ · Gresham College: Over four centuries of adult education Raymond Flood ALM-23, Maynooth Wednesday 6th July 2016 . Sir