m3hw2.tex Week 2 15-18.10.2013
THE GREEKS: THALES TO EUCLID
Sources:
B, Ch. 4-11;
Thomas HEATH, A history of Greek mathematics, Vol. I, From Thales to
Euclid; Vol. II, From aristarchus to Diophantus, OUP, 1921/1960;
D. H. FOWLER, The mathematics of Platos
m3hw0.tex Week 1. 8 11.10.2013
PRE-HISTORY TO GREEK HISTORY
Timeline
Ice Age, ended (in Britain) c. 13,000 years ago
Stone Age (lithos = stone, Greek):
early (paleolithic);
Lower Paleolithic, c. 2.6 million 300 thousand years ago;
Middle Paleolithic, 300k
m3hw3.tex Week 3 22-25.10.2013
THE GREEKS: ARCHIMEDES TO PAPPUS
Dramatis Personae
Eudemus (of Rhodes), . c. 320 BC: history of mathematics (now lost: see
W4)
Archimedes (of Syracuse, c. 287-212 BC)
Apollonius (of Perga, Asia Minor, .262 c.190 BC)
Aristarc
m3hw4.tex Week 4. 29.10-1.11.2013
THE GREEKS (POSTSCRIPT); THE ROMANS; THE ARABS;
INDIA and CHINA
Farewell to Pappus, and to Alexandria
The Golden Age of Greek geometry had ended with Apollonius some 500
years before Pappus. Of Pappus, Heath writes (p. 35
m3hw5.tex Week 5. 5.11.2013
FROM THE ARABS TO GALILEO
Edward GIBBON, Decline and fall of the Roman Empire, 1776
Boyer Ch. 14; Dreyer Ch. X, Mediaeval cosmology
Al-Kwarizmis Algebra (concluded). Its strengths include logical exposition
and proof (shared by
m3hw6.tex Week 6. 12.11.2013
17th C.: DESCARTES to NEWTON and LEIBNIZ
Background
We are now well into the 17th C., and what we take for granted books,
universities, the scientic method etc. is starting to emerge.
Christianity had split a century before, i
m3hw7.tex Week 7. 19.11.2013
18th C.
The Bernoulli family
The Bernoullis produced more distinguished mathematicians than any
other family in history. Of Netherlands origin, tfe family ed to Basel in
Switzerland in 1583 to escape preligious persecution in
m3hw8.tex Week 8. 26.11.2013
19th C.
Pierre-Simon de Laplace (1749-1827), Professor at the Ecole Normale and
the Ecole Polytchnique.
e
Laplace has been called the French Newton. He was a great mathematician, whose name appears in the Laplace transform, La
m3hw9.tex Week 9. 3.12.2013
From the 19th C. to the 20th C.
Analysis
While great strides have been taken in the Analysis so far, modern standard of rigour had not yet been achieved. These emerged gradually during
the 19th C.
Bernhard Bolzano (1781-1848),
m3hw10.tex Week 10. 10.12.2013
20th C.: Early
We move now to the 20th C. Week 10 will focus on the rst half, Week 11
(not taught for info) on the second half. The core of the undergraduate
curriculum is based on the 19th C. The mathematics of the 20th C.
m3h11.tex Week 11 (not taught for info and completeness)
20th C.: Late
The mid-20th C. was within living memory1 . This makes its history more
interesting in some ways, as more immediately relevant to us, and how we
got here. On the other hand, this is a
m3hsoln1.tex
M3H SOLUTIONS 1. 25.10.2013
Q1 (Theorem of Thales). Let the triangle be ABC , with AB a diameter
of a circle, with centre O and radius r say. Join CO. Triangle AOC
is isosceles (AO = CO = r), so with the angle CAO, = ACO
also. So AOC = 2 (to
m3hsoln2.tex
M3H SOLUTIONS 2. 25.10.2013
Q1 (Angle at centre twice angle at circumference). Let the chord be AB ,C
be the point on the circumference, O the centre of the circle. Required
AOB = 2ACB . Let := OAC , := OBC . Triangles AOC ,
BOC are isosceles