Notes on Julian's First Oration

Notes on first semester calculus

Proof. First, check that f is one-to-one, so that f−1 exists. Given two points in the domain of f , x = t, we want to show f(x) = f(t). From x = t, there are two cases: x < t or x > t. If x < t, then f(x) < f(t) because f is increasing, and similarly if t < x, then f(t) < f(x). In either case, f(x) = f(t). Second, suppose, toward a contradiction, that f−1(x) is not increasing. This means the fo...

Notes on First Order Logic Notes for PHIL370

Definition 1.1 (Terms) Let V be a set of variable, C a set of constant symbols and F a set of function symbols. Each function symbol is associated with an arity (a positive integer specifying the number of arguments). Write f (n) if the arity of f is n. A term τ is constructed as follows: • Any variable x ∈ V is a term. • Any constant c ∈ C is a term. • If f (n) ∈ F is a function symbol (i.e., ...

Harveian Oration

William Harvey and the Harveian Trust William Harvey was born in Folkestone on April 1, 1578. He was educated at the King’s School, Canterbury, Gonville, and Caius College, Cambridge, and the University of Padua, graduating as doctor of arts and medicine in 1602. He became a Fellow of the Royal College of Physicians in 1607 and was appointed to the Lumleian lectureship in 1615. In the cycles of...

Notes on Music Segmentation (a first draft...)

Abraham Colles oration: 200 years on

It is 200 years since Abraham Colles published his famous article where he described the common dorsal deformity of the distal radius fracture with an associated dislocation of the distal radio-ulnar joint. He provided a detailed description of the fracture, 80 years before the developed of radiographs. The fracture still bares his name, despite the fact that this article was never cited during...