Rigel Kent

Suppose we have a function \(y = f(x)\) and its value at \(x = a\), \(f(a)\) is a nice value and can be easily calculated. Apparently, a slight perturbation on \(x\) from \(x = a\) to \(x = a + \epsilon\) will be accompanied by a slight change in the value of \(y\), where \(a \gg \epsilon\). Computation of the new value of \(y\), that is, \(f(a + \epsilon)\) is one of the standard operating procedure taught in the fourth-form calculus. For instance, in 2017, the following question appeared as the second question in the second paper of the SPM additional mathematics exam. It is given that the equation of a curve is \(y = \frac{5}{x^2}\). Find the value of \(\frac{{\rm d}y}{{\rm d}x}\) when \(y = 3\). Hence estimate the value of \(\frac{5}{2.98^2}.\) The standard textbook trick uses only the first two terms in the following series: $$f(a + \epsilon) = \sum_{k=0}^\infty \frac{f^{(k)}(a) \epsilon^k}{k!}$$ that is, $$f(a + \epsilon) \approx f(a) + f'(a) \epsilon$$ a...

The SIR (susceptible/infected/removed) model in epidemiology is first considered nearly 100 years ago by two Scottish doctors, William Kermark (1898-1970) and Anderson McKendrick (1876-1943) (see W. O. Kermack and A. G. McKendrick (1927) Contribution to the mathematical theory of epidemics , Proc. Roy. Soc. Lond A 115, 700-721). In 1927, they opened their paper with the following line: One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population... When a group of infectious species, \(I\), is introduced into a community of susceptible species, \(S\) (which is not previously exposed to the RNA materials), the virus spreads from the infectious species to the susceptible species, thus diminishing the susceptible species and growing the size of the infectious species. $$I + S \longrightarrow I' + S'...

Cyril Northcote Parkinson (b. 1909, d. 1993) 是馬來亞大學的第一任萊佛士歷史教授。 他是第二任萊佛士歷史教授K. G. Tregonning (b. 1923, d. 2015) 的博士論文導師，而Tregonning後來是邱繼金 Khoo Kay Kim (b. 1937, d. 2019) 的學士論文導師。所以算起來，Parkinson是邱老師的師公。 By skipping over Tan Sri Khoo’s PhD supervisor, Eddin Khoo Bu Eng 邱武英 has helpfully demonstrated his unique scholarly method: if you don’t know something, simply pretend it never existed. A bold strategy, historically used by small children and certain governments. For anyone actually interested in Tan Sri Khoo’s academic journey — which, unlike Eddin’s version, involves real dates, real theses, and real supervisors — here it is: K. K. Khoo (1960) The municipal government of Singapore, 1887 - 1940, B. A. Thesis, Department of History, University of Malaya. Tan Sri was 23, which is around the age when most of us were still trying to figure out how library catalogues worked. K. K. Khoo (1967) The western Malay states, 1861 - 1873: The political effe...