This year History of Mathematics (HoM) is
offered as a 5-credit module (MATH281) to BA2 students and a 7.5-credit module
(MATH304) to BA3 students. MATH281 (with 33 contact hours) is a subset of
MATH304 (with 47 contact hours). Detailed announcements are given in Moodle
and on departmental notice boards (outside D204
& outside D115).
purpose of this course is to:
students with a framework for appreciating the historical development of
the end of the course students should be able to:
in very general terms the timeline of the development of mathematics
significant historical periods when key changes in mathematical thought
occurred and new areas emerged
some important contributions of prominent mathematicians
how topics arising in school mathematics developed historically
important examples of cultural factors influencing the development of
the technical details of specific mathematical problems pertinent to 2-5,
points 2-5, above, in a broader historical context
methods (with approximate hours allocated to each, MATH281/MATH304):
(23/31, including possible lab sessions)
homework (with possible use of GeoGebra
& Maple worksheets)
questions motivating the course:
was the problem of the solution of polynomial equations solved?
have geometry and algebra interacted over time?
lead up to the discovery of the calculus?
we always have the mathematical notation we use today?
if anything, is particularly important about ‘Irish’ mathematics?
cultures contributed importantly to mathematics?
did it all start?
makes a mathematical result ‘important’?
do application and abstraction interact in the development of mathematics?
are the ‘big’ names in the discipline?
have rigour and intuition interacted in mathematical history?
has the notion of certainty evolved in mathematics?
Key resources (others will appear on the
course's Moodle site):
- Mac Tutor
History of Mathematics
- Derbyshire, J: Unknown
Quantity: A real and imaginary history of algebra with Errata,
Joseph Henry Press, Washington DC 2006
- Hodgkin, L:
A History of Mathematics: From Mesopotamia to Modernity, OUP
book (FMCS, Tehran); MAA review
Proof? A Historian's Perspective [missing
pages 148,149, 155,156, 162 & 163] in Gila Hanna &
Michael de Villiers (eds) Proof and Proving in Mathematics Education
- MAA's Convergence
translation (1831) of al-Khwarizmi's al-jabr w'al muqabala
translation (1963; Dover 1993) of Cardano's Ars
- Other resources
- Math history books in
Past exam papers: 2008,
||Mesopotamia (incl. Babylon) & Egypt ...
tablet (c. 1700 BCE)
papyrus (c. 1550 BCE)
||Greece & China ...
||India & Japan...
||Irish 'Golden Age' 600-850
II (b. 1194) was Holy Roman Emperor from 1220 until 1250.
famous for his sequence (published in his Liber Abaci of 1202),
tackled the solution of a cubic equation posed by Johannes of Palermo, in
his Flos of 1225.
were involved in intrigue surrounding the general solution of a cubic
polynomial, published in Cardano's Ars Magna of 1545.
||England: Charles I &
II with Oliver Cromwell in between
Europe: the glories of the Hapsburgs and of
Louis XIV; securing
against the Ottoman empire ...
were rivals in what must be the greatest battle for priority in the
history of mathematics: who invented the calculus? Jacob
Bernoulli belonged to the Leibnizian tradition, as did L'Hopital
who tried to 'buy' all the latter's work. L'Hopital wrote the first
textbook on the calculus without giving due credit to Johann B - more
||Prussia's Frederick the Great ...
American & French revolutions
|Following Johann's work, Euler
made huge advances in the establishment of analysis with outstanding
original contributions to the calculus as well as pioneering work on
notation and textbooks.
||Just about everything in France ...
The British Empire dominates the world ...
Ireland's famine ...
Both Germany &
Italy unite ...
|It wasn't until this century that the concept of limit was
well established with the work of Cauchy,
and others. The completeness of the real line (Dedekind,
1872) provided a rigorous understanding of how limits extend the rational
numbers to the real numbers.
emerged from determinants
algebras, via matrices,
vector spaces, fields
and much more. The dramatis personae include: Cauchy,
||Two World Wars & many others ...
Global use of millions of gadgets depending on mathematics!
Most of us were born!
|The theory of integration was developed into the 20th
century with the work of Lebesgue