history of mathematics - National STEM Centre

History of mathematics
the mathematics of East and West. In many history books you may find the
subsequent contribution of the Arab mathematicians has been understated, and
indeed it will be difficult to give a comprehensive evaluation while many Arabic
texts remain untranslated. Perhaps one of the major new contributions made by the
Arab mathematicians was to use the ideas of Greek geometry to help with the
solution of algebraic problems.
Due to its eastern origins, the algebra of the middle ages tended to be algorithmic,
compared with the axiomatic foundation of geometry laid by the Greeks. The
European algebraists of the 16th century had available to them the Arab and Greek
texts, translated via Spanish into Latin. The next great step can be thought of as
making the whole field of classical geometry available to the algebraists. In the
fourth unit, you will learn how, like the Arab mathematicians, Descartes was
interested in the use of algebra to solve geometric construction problems and how
he took the extra step of using coordinates to study this relationship.
From Greek times and before, mathematicians had been finding ways to calculate
areas bounded by curves and constructing tangents. Solutions had involved clever
constructions or algorithms applied to particular curves, but there was no general
method. After the development of the analytical geometry of Descartes and his
contemporaries, it took only some 40 years more work by a variety of
mathematicians, including Newton and Leibniz, to develop what we now know as
calculus, a tool by which problems of finding area and tangents can be unified and
solved in a general way. In the fifth unit you will see a snapshot of how this came
about.
Finally, in the sixth unit, you will be able to follow some of the developments in
making mathematics rigorous in the context of the struggle of mathematicians to
make sense of negative and complex numbers.
This book is designed to take about 80 hours of your learning time. About half of
this time will be outside the classroom.
The units include many mathematicians' names. You need to learn only a few
which are detailed in the 'What you should know' lists at the end of each chapter.
Reference list
The crest of the peacock: non-European roots of mathematics, G G Joseph, Penguin,
ISBN 0141 125299
A concise history of mathematics, D J Struik, Dover, ISBN 0 486 60255 9
A history of mathematics, V J Katz, Harper Collins, ISBN 0673 38039 4
A history of mathematics (Second edition), by Carl B Boyer and Uta C Merzbac,
Wiley, New York 1989, ISBN 0471 50357 6
The history of mathematics: a reader, edited by J Fauvel and J Gray, Open
University Press, ISBN 0 33 42791 2