The conscious use of certain concepts is important for learning mathematics in a way that encourages creative application and theoretical advance, says mathematics Professor Emeritus F. William Lawvere of the University at Buffalo (UB), part of the State University of New York.
Lawvere will deliver one in a series of York U50 lectures in the Laboratory of Mathematical Parallel Systems (LAMPS) Colloquium Series on Mathematics & Interdisciplinary Science – “The Role of Explicit Concept in Mathematical Sciences” – Friday, May 8 from 2:30 to 3:30pm in the York Senate Chamber, N940 Ross Building, Keele campus.
Right: F. William Lawvere
It is concepts such as homomorphism and functional and extensive variation that Lawvere considers important for learning.
Lawvere has given categorical definitions of unity and identity of opposites, extensive versus intensive variable quantities, spatial versus quantitative categories and more, showing that such philosophical distinctions can lead to concrete mathematical results and conjectures.
He is the co-author of Conceptual Mathematics: A First Introduction to Categories (Cambridge University Press, 1997) and Sets for Mathematics (Cambridge University Press, 2002), which strive to use category theory to bring modern mathematical concepts to the broad population which must use mathematics-based technology, and to help students cross the gap between undergraduate mathematics and the mathematics needed for theoretical science.
At the 1970 International Congress of Mathematicians in Nice, France, Lawvere introduced an algebraic version of Topos Theory which unified geometry and set theory. This theory had been developed in collaboration with mathematician Myles Tierney and has since been applied to several fields of mathematics. Two of these fields had previously been introduced by Lawvere.
Lawvere completed his PhD at Columbia University in 1963. He held positions at Reed College, the University of Chicago and the City University of New York. From 1969 to 1971, he was Killam Professor at Dalhousie University in Halifax and from 1977 to 1982 was the Martin Professor at UB.
Each LAMPS lecture features a leading expert in the field of mathematics and related multidisciplinary areas. The lectures are open to everyone and registration is free. The event is sponsored by the Faculty of Science & Engineering and the Department of Mathematics & Statistics.