Math history
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Credits
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).

The purpose of this course is to:

Provide students with a framework for appreciating the historical development of mathematics.

At the end of the course students should be able to:

  1. Outline in very general terms the timeline of the development of mathematics
  2. Describe significant historical periods when key changes in mathematical thought occurred and new areas emerged
  3. Summarise some important contributions of prominent mathematicians
  4. Explain how topics arising in school mathematics developed historically
  5. Discuss important examples of cultural factors influencing the development of mathematics
  6. Discuss the technical details of specific mathematical problems pertinent to 2-5, above
  7. Situate points 2-5, above, in a broader historical context

Teaching methods (with approximate hours allocated to each, MATH281/MATH304):

Lectures (23/31, including possible lab sessions)

Seminars (5/8)  

Tutorials (5/8)

Assessment instruments:

Journal 

Hand-in homework (with possible use of GeoGebra & Maple worksheets)

Essay

Final examination (70%)

Typical questions motivating the course:

  1. How was the problem of the solution of polynomial equations solved?
  2. How have geometry and algebra interacted over time?
  3. What lead up to the discovery of the calculus?
  4. Did we always have the mathematical notation we use today?
  5. What, if anything, is particularly important about ‘Irish’ mathematics?
  6. Which cultures contributed importantly to mathematics?
  7. How did it all start?
  8. What makes a mathematical result ‘important’?
  9. How do application and abstraction interact in the development of mathematics?
  10. Who are the ‘big’ names in the discipline?
  11. How have rigour and intuition interacted in mathematical history?
  12. How has the notion of certainty evolved in mathematics?

Key resources (others will appear on the course's Moodle site):

  1. Fundamental
    1. Mac Tutor History of Mathematics
  2. Books/extracts
    1. Derbyshire, J: Unknown Quantity: A real and imaginary history of algebra with Errata, Joseph Henry Press, Washington DC 2006
    2. Hodgkin, L: A History of Mathematics: From Mesopotamia to Modernity, OUP 2005; introduction (U Laval, Québec); entire book (FMCS, Tehran); MAA review
    3. Grabiner, JV: Why 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 (19th ICMI Study, 2012)
  3. Web
    1. MAA's Convergence
    2. Rosen's translation (1831) of al-Khwarizmi's al-jabr w'al muqabala
    3. Witmer's translation (1963; Dover 1993) of Cardano's Ars Magna (1545)
  4. Other resources
    1. Math history books in library  
    2. GeoGebra Tube

Past exam papers: 2008, 2010, 2012

Tentative timeline:

Century

History

Mathematics

BC Mesopotamia (incl. Babylon) & Egypt ... Babylon: Cuneiform tablet (c. 1700 BCE) 
Egypt: Rhind papyrus (c. 1550 BCE)
BC-AD Greece & China ... Greece & China
AD India & Japan... India & Japan 
AD Irish 'Golden Age' 600-850 Geometry & Computus
     
13 Frederick II (b. 1194) was Holy Roman Emperor from 1220 until 1250. Fibonacci, 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.
14    
15    
16   Cardano and Tartaglia were involved in intrigue surrounding the general solution of a cubic polynomial, published in Cardano's Ars Magna of 1545.
17 England: Charles I & II with Oliver Cromwell in between ...
Europe: the glories of the Hapsburgs and of Louis XIV; securing Vienna against the Ottoman empire ... 
Newton and Leibniz were rivals in what must be the greatest battle for priority in the history of mathematics: who invented the calculus? Jacob and Johann 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 skullduggery!
18 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.
19 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, Weierstrass 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.

Abstract algebra emerged from determinants to Grassmann algebras, via matrices, quaternions, vector spaces, fields and much more. The dramatis personae include: Cauchy, Cayley, Galois, Hamilton, Klein, Sylvester, ...

20 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 and others.
     
 

Personal mathematics genealogy

 

page updated: 14 April 2014