Relationships between algebra, differential equations and logic in England 18001860.
Panteki, Maria (1991) Relationships between algebra, differential equations and logic in England 18001860. PhD thesis, Middlesex University.

PDF
Download (15MB) 
Abstract
This thesis surveys the links between mathematics and algebraic logic in England in the first half of the 19th century.
In particular, we show the impact that De Morgan's work on the calculus of functions in 1836 had on the shaping of his logic of relations in 1860. Similarly we study Boole’s background in Doperational methods and its impact on his calculus of logic in 1847.
The starting point of the thesis is Lagrange’s algebraic calculus and Laplace’s analytical methods prominent in late 18th century French mathematics. Revival in mathematical research in early 19th century England was mainly effected through the diffusion of Lagrange’s calculus of operations as further developed by Arbogast, Servois and others in the 1800’s and of Laplace’s theory of attractions.
.Lagrange’s algebraic calculus and Laplace’s methods in analysis – particularly on functional equations – were considerably developed by Herschel and Babbage during the period 18121820. Further research on the foundations of the calculus of operations and functions was provided by Murphy, De Morgan and Gregory in the late 1830’s.
.Symbolic methods in analysis were further extended by Boole in 1844. Boole was followed by several analysts distinguished in their obsession in further vindicating these methods through applications on two differential equations which originally appeared in Laplace’s planetary physics.
We record the main issues of De Morgan’s logic and their mathematical background. Special reference is given to his logic of relations and its connection with his foundational study of the calculus of functions. On similar lines we study Boole’s algebraic cast of logic drawing consequently a comparison between his two major works on logic. Moreover we emphasise his epistemological views and his evaluation of symbolical methods within logic and analysis.
Item Type:  Thesis (PhD) 

Additional Information:  A thesis submitted in partial fulfilment of the requirements of the Council for national Academic Awards for the degree of Doctor of Philosophy. 
Research Areas:  A. > School of Science and Technology > Computer and Communications Engineering B. > Theses 
Item ID:  6482 
Depositing User:  Repository team 
Date Deposited:  08 Sep 2010 11:12 
Last Modified:  03 Mar 2016 14:24 
URI:  http://eprints.mdx.ac.uk/id/eprint/6482 
Actions (login required)
Edit Item 
Full text downloads (NB count will be zero if no full text documents are attached to the record)
Downloads per month over the past year